ZeroshyGroupshyVelocity Modes of InsulatorshyMetalshyInsulator and
InsulatorshyInsulatorshyMetal Waveguides
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Department of General Physics Moscow Institute of Physics and Technology (State University)
Dolgoprudny Russiaeshymail feddumailru
AcknowledgementVladimir Tarakanov the athor of PIC code KARAT
OUTLINE
Lossless caseDispersion relations and dispersion curves of SPPs
in IMI and IIM waveguide structuresExistence conditions of waves with zero group velocity
Lossy caseEffect of losses on dispersion curvesNumerical calculations of energy velocityAn analysis of points of zero energy velocity
Excitation of zeroshygroupshyvelocity modesResults of numerical simulationApplications
History
Backward waves and waves with zero group velocity are typically associated with periodic structures Nevertheless a periodicity is not the only way to obtain such waves - particularly investigations of slow wave propagation in plasma-dielectric structures showed that plasma waveguides with a specially designed circular crosssection allow the existence of backward waves so are some kinds of planar plasmawaveguides
Trivelpiece A W Gould R W 1959 Space charge waves in cylindrical plasma columns J Appl Phys 30 1784 ndash 1793
Paik S F 1962 A backward wave in plasma waveguide Proc IRE 50 462 ndash 463Allis W P Buchsbaum S J Bers A 1963 Waves in Anisotropic Plasma
(Cambridge MA MIT Press)Oliner A A Tamir T 1962 Backward waves on isotropic plasma slabs
J Appl Phys 33 231 ndash 233Schumann W O 1960 Z angew Phys 12 4 145
Lossless caseLossless case
Metal is described by DrudeshyZener model
Dispersion Relation
where
For IMI waveguide structures with ε2=ε3 dispersion relation can be easily simplified and rearranged as two branches
thκ1 a=minusκ2 ε1
κ1ε2
antishysymmetric mode
symmetric mode
and a is a half thickness of the film
thκ1a=minusκ1 ε2
κ2 ε1
IMI IIM
AS shy antishysymmetric mode S shy symmetric mode
Dispersion Curves (Lossless Case)
AS
S
AS
S
ε2gtε3
The decay constant κ2 may be complex while κ1 and κ3 are real
Existence Conditions of Waves with Zero Group Velocity
Equation for Poynting vector in a complex form
SPPs group velocity is negative if and only if net energy flux is opposite to the phase velocity direction that could be written as
and the group velocity is zero if
It will be recall that the only nonshyradiative modes interest us thus the projection of net power flow on z axis is equal to zero
ck ω= where and
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma ]
Existence Conditions of Waves with Zero Group Velocity
IMI IIM
Re(Sx)x
Single metalshyinsulatorinterface
Existence Conditions of Waves with Zero Group Velocity
IMI IIMsmall kx
large kx
small kx
large kx
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
In order to satisfy the existence condition of waves with zero group velocity the power flow inside the metal must be equal (in absolute value) to the power flow in dielectric media Solving Maxwell equations we obtain that this requirement is equivalent to the following equality
This lengthy expression can be significantly simplified in case of antishysymmetric mode and ε2=ε3
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma chapter 7 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Dispersion curves of SPP in the insulatorshysilvershyinsulator structures for various permittivities Nonshyradiative modes are presented The value of ε2 is fixed and is equal to 25 film thickness d=15 nm Permittivity ε3 takes values from 1 till 12 (1 2 25 3 4 5 7 12) The upper curve corresponds to ε3=1
According to [Palik E D 1998 Handbook of Optical Constants of Solids I (San Diego CA Academic Press) ]and DrudeshyZener modelin a wavelength range 300ndash600 nm
silver
[ Johnson P B Christy R W 1972Phys Rev B 6 4370 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε3
Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are
considered ZrO2 SiO2 Al2O3 with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
OUTLINE
Lossless caseDispersion relations and dispersion curves of SPPs
in IMI and IIM waveguide structuresExistence conditions of waves with zero group velocity
Lossy caseEffect of losses on dispersion curvesNumerical calculations of energy velocityAn analysis of points of zero energy velocity
Excitation of zeroshygroupshyvelocity modesResults of numerical simulationApplications
History
Backward waves and waves with zero group velocity are typically associated with periodic structures Nevertheless a periodicity is not the only way to obtain such waves - particularly investigations of slow wave propagation in plasma-dielectric structures showed that plasma waveguides with a specially designed circular crosssection allow the existence of backward waves so are some kinds of planar plasmawaveguides
Trivelpiece A W Gould R W 1959 Space charge waves in cylindrical plasma columns J Appl Phys 30 1784 ndash 1793
Paik S F 1962 A backward wave in plasma waveguide Proc IRE 50 462 ndash 463Allis W P Buchsbaum S J Bers A 1963 Waves in Anisotropic Plasma
(Cambridge MA MIT Press)Oliner A A Tamir T 1962 Backward waves on isotropic plasma slabs
J Appl Phys 33 231 ndash 233Schumann W O 1960 Z angew Phys 12 4 145
Lossless caseLossless case
Metal is described by DrudeshyZener model
Dispersion Relation
where
For IMI waveguide structures with ε2=ε3 dispersion relation can be easily simplified and rearranged as two branches
thκ1 a=minusκ2 ε1
κ1ε2
antishysymmetric mode
symmetric mode
and a is a half thickness of the film
thκ1a=minusκ1 ε2
κ2 ε1
IMI IIM
AS shy antishysymmetric mode S shy symmetric mode
Dispersion Curves (Lossless Case)
AS
S
AS
S
ε2gtε3
The decay constant κ2 may be complex while κ1 and κ3 are real
Existence Conditions of Waves with Zero Group Velocity
Equation for Poynting vector in a complex form
SPPs group velocity is negative if and only if net energy flux is opposite to the phase velocity direction that could be written as
and the group velocity is zero if
It will be recall that the only nonshyradiative modes interest us thus the projection of net power flow on z axis is equal to zero
ck ω= where and
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma ]
Existence Conditions of Waves with Zero Group Velocity
IMI IIM
Re(Sx)x
Single metalshyinsulatorinterface
Existence Conditions of Waves with Zero Group Velocity
IMI IIMsmall kx
large kx
small kx
large kx
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
In order to satisfy the existence condition of waves with zero group velocity the power flow inside the metal must be equal (in absolute value) to the power flow in dielectric media Solving Maxwell equations we obtain that this requirement is equivalent to the following equality
This lengthy expression can be significantly simplified in case of antishysymmetric mode and ε2=ε3
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma chapter 7 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Dispersion curves of SPP in the insulatorshysilvershyinsulator structures for various permittivities Nonshyradiative modes are presented The value of ε2 is fixed and is equal to 25 film thickness d=15 nm Permittivity ε3 takes values from 1 till 12 (1 2 25 3 4 5 7 12) The upper curve corresponds to ε3=1
According to [Palik E D 1998 Handbook of Optical Constants of Solids I (San Diego CA Academic Press) ]and DrudeshyZener modelin a wavelength range 300ndash600 nm
silver
[ Johnson P B Christy R W 1972Phys Rev B 6 4370 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε3
Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are
considered ZrO2 SiO2 Al2O3 with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
History
Backward waves and waves with zero group velocity are typically associated with periodic structures Nevertheless a periodicity is not the only way to obtain such waves - particularly investigations of slow wave propagation in plasma-dielectric structures showed that plasma waveguides with a specially designed circular crosssection allow the existence of backward waves so are some kinds of planar plasmawaveguides
Trivelpiece A W Gould R W 1959 Space charge waves in cylindrical plasma columns J Appl Phys 30 1784 ndash 1793
Paik S F 1962 A backward wave in plasma waveguide Proc IRE 50 462 ndash 463Allis W P Buchsbaum S J Bers A 1963 Waves in Anisotropic Plasma
(Cambridge MA MIT Press)Oliner A A Tamir T 1962 Backward waves on isotropic plasma slabs
J Appl Phys 33 231 ndash 233Schumann W O 1960 Z angew Phys 12 4 145
Lossless caseLossless case
Metal is described by DrudeshyZener model
Dispersion Relation
where
For IMI waveguide structures with ε2=ε3 dispersion relation can be easily simplified and rearranged as two branches
thκ1 a=minusκ2 ε1
κ1ε2
antishysymmetric mode
symmetric mode
and a is a half thickness of the film
thκ1a=minusκ1 ε2
κ2 ε1
IMI IIM
AS shy antishysymmetric mode S shy symmetric mode
Dispersion Curves (Lossless Case)
AS
S
AS
S
ε2gtε3
The decay constant κ2 may be complex while κ1 and κ3 are real
Existence Conditions of Waves with Zero Group Velocity
Equation for Poynting vector in a complex form
SPPs group velocity is negative if and only if net energy flux is opposite to the phase velocity direction that could be written as
and the group velocity is zero if
It will be recall that the only nonshyradiative modes interest us thus the projection of net power flow on z axis is equal to zero
ck ω= where and
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma ]
Existence Conditions of Waves with Zero Group Velocity
IMI IIM
Re(Sx)x
Single metalshyinsulatorinterface
Existence Conditions of Waves with Zero Group Velocity
IMI IIMsmall kx
large kx
small kx
large kx
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
In order to satisfy the existence condition of waves with zero group velocity the power flow inside the metal must be equal (in absolute value) to the power flow in dielectric media Solving Maxwell equations we obtain that this requirement is equivalent to the following equality
This lengthy expression can be significantly simplified in case of antishysymmetric mode and ε2=ε3
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma chapter 7 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Dispersion curves of SPP in the insulatorshysilvershyinsulator structures for various permittivities Nonshyradiative modes are presented The value of ε2 is fixed and is equal to 25 film thickness d=15 nm Permittivity ε3 takes values from 1 till 12 (1 2 25 3 4 5 7 12) The upper curve corresponds to ε3=1
According to [Palik E D 1998 Handbook of Optical Constants of Solids I (San Diego CA Academic Press) ]and DrudeshyZener modelin a wavelength range 300ndash600 nm
silver
[ Johnson P B Christy R W 1972Phys Rev B 6 4370 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε3
Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are
considered ZrO2 SiO2 Al2O3 with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Lossless caseLossless case
Metal is described by DrudeshyZener model
Dispersion Relation
where
For IMI waveguide structures with ε2=ε3 dispersion relation can be easily simplified and rearranged as two branches
thκ1 a=minusκ2 ε1
κ1ε2
antishysymmetric mode
symmetric mode
and a is a half thickness of the film
thκ1a=minusκ1 ε2
κ2 ε1
IMI IIM
AS shy antishysymmetric mode S shy symmetric mode
Dispersion Curves (Lossless Case)
AS
S
AS
S
ε2gtε3
The decay constant κ2 may be complex while κ1 and κ3 are real
Existence Conditions of Waves with Zero Group Velocity
Equation for Poynting vector in a complex form
SPPs group velocity is negative if and only if net energy flux is opposite to the phase velocity direction that could be written as
and the group velocity is zero if
It will be recall that the only nonshyradiative modes interest us thus the projection of net power flow on z axis is equal to zero
ck ω= where and
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma ]
Existence Conditions of Waves with Zero Group Velocity
IMI IIM
Re(Sx)x
Single metalshyinsulatorinterface
Existence Conditions of Waves with Zero Group Velocity
IMI IIMsmall kx
large kx
small kx
large kx
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
In order to satisfy the existence condition of waves with zero group velocity the power flow inside the metal must be equal (in absolute value) to the power flow in dielectric media Solving Maxwell equations we obtain that this requirement is equivalent to the following equality
This lengthy expression can be significantly simplified in case of antishysymmetric mode and ε2=ε3
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma chapter 7 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Dispersion curves of SPP in the insulatorshysilvershyinsulator structures for various permittivities Nonshyradiative modes are presented The value of ε2 is fixed and is equal to 25 film thickness d=15 nm Permittivity ε3 takes values from 1 till 12 (1 2 25 3 4 5 7 12) The upper curve corresponds to ε3=1
According to [Palik E D 1998 Handbook of Optical Constants of Solids I (San Diego CA Academic Press) ]and DrudeshyZener modelin a wavelength range 300ndash600 nm
silver
[ Johnson P B Christy R W 1972Phys Rev B 6 4370 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε3
Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are
considered ZrO2 SiO2 Al2O3 with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Dispersion Relation
where
For IMI waveguide structures with ε2=ε3 dispersion relation can be easily simplified and rearranged as two branches
thκ1 a=minusκ2 ε1
κ1ε2
antishysymmetric mode
symmetric mode
and a is a half thickness of the film
thκ1a=minusκ1 ε2
κ2 ε1
IMI IIM
AS shy antishysymmetric mode S shy symmetric mode
Dispersion Curves (Lossless Case)
AS
S
AS
S
ε2gtε3
The decay constant κ2 may be complex while κ1 and κ3 are real
Existence Conditions of Waves with Zero Group Velocity
Equation for Poynting vector in a complex form
SPPs group velocity is negative if and only if net energy flux is opposite to the phase velocity direction that could be written as
and the group velocity is zero if
It will be recall that the only nonshyradiative modes interest us thus the projection of net power flow on z axis is equal to zero
ck ω= where and
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma ]
Existence Conditions of Waves with Zero Group Velocity
IMI IIM
Re(Sx)x
Single metalshyinsulatorinterface
Existence Conditions of Waves with Zero Group Velocity
IMI IIMsmall kx
large kx
small kx
large kx
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
In order to satisfy the existence condition of waves with zero group velocity the power flow inside the metal must be equal (in absolute value) to the power flow in dielectric media Solving Maxwell equations we obtain that this requirement is equivalent to the following equality
This lengthy expression can be significantly simplified in case of antishysymmetric mode and ε2=ε3
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma chapter 7 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Dispersion curves of SPP in the insulatorshysilvershyinsulator structures for various permittivities Nonshyradiative modes are presented The value of ε2 is fixed and is equal to 25 film thickness d=15 nm Permittivity ε3 takes values from 1 till 12 (1 2 25 3 4 5 7 12) The upper curve corresponds to ε3=1
According to [Palik E D 1998 Handbook of Optical Constants of Solids I (San Diego CA Academic Press) ]and DrudeshyZener modelin a wavelength range 300ndash600 nm
silver
[ Johnson P B Christy R W 1972Phys Rev B 6 4370 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε3
Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are
considered ZrO2 SiO2 Al2O3 with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
IMI IIM
AS shy antishysymmetric mode S shy symmetric mode
Dispersion Curves (Lossless Case)
AS
S
AS
S
ε2gtε3
The decay constant κ2 may be complex while κ1 and κ3 are real
Existence Conditions of Waves with Zero Group Velocity
Equation for Poynting vector in a complex form
SPPs group velocity is negative if and only if net energy flux is opposite to the phase velocity direction that could be written as
and the group velocity is zero if
It will be recall that the only nonshyradiative modes interest us thus the projection of net power flow on z axis is equal to zero
ck ω= where and
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma ]
Existence Conditions of Waves with Zero Group Velocity
IMI IIM
Re(Sx)x
Single metalshyinsulatorinterface
Existence Conditions of Waves with Zero Group Velocity
IMI IIMsmall kx
large kx
small kx
large kx
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
In order to satisfy the existence condition of waves with zero group velocity the power flow inside the metal must be equal (in absolute value) to the power flow in dielectric media Solving Maxwell equations we obtain that this requirement is equivalent to the following equality
This lengthy expression can be significantly simplified in case of antishysymmetric mode and ε2=ε3
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma chapter 7 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Dispersion curves of SPP in the insulatorshysilvershyinsulator structures for various permittivities Nonshyradiative modes are presented The value of ε2 is fixed and is equal to 25 film thickness d=15 nm Permittivity ε3 takes values from 1 till 12 (1 2 25 3 4 5 7 12) The upper curve corresponds to ε3=1
According to [Palik E D 1998 Handbook of Optical Constants of Solids I (San Diego CA Academic Press) ]and DrudeshyZener modelin a wavelength range 300ndash600 nm
silver
[ Johnson P B Christy R W 1972Phys Rev B 6 4370 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε3
Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are
considered ZrO2 SiO2 Al2O3 with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity
Equation for Poynting vector in a complex form
SPPs group velocity is negative if and only if net energy flux is opposite to the phase velocity direction that could be written as
and the group velocity is zero if
It will be recall that the only nonshyradiative modes interest us thus the projection of net power flow on z axis is equal to zero
ck ω= where and
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma ]
Existence Conditions of Waves with Zero Group Velocity
IMI IIM
Re(Sx)x
Single metalshyinsulatorinterface
Existence Conditions of Waves with Zero Group Velocity
IMI IIMsmall kx
large kx
small kx
large kx
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
In order to satisfy the existence condition of waves with zero group velocity the power flow inside the metal must be equal (in absolute value) to the power flow in dielectric media Solving Maxwell equations we obtain that this requirement is equivalent to the following equality
This lengthy expression can be significantly simplified in case of antishysymmetric mode and ε2=ε3
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma chapter 7 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Dispersion curves of SPP in the insulatorshysilvershyinsulator structures for various permittivities Nonshyradiative modes are presented The value of ε2 is fixed and is equal to 25 film thickness d=15 nm Permittivity ε3 takes values from 1 till 12 (1 2 25 3 4 5 7 12) The upper curve corresponds to ε3=1
According to [Palik E D 1998 Handbook of Optical Constants of Solids I (San Diego CA Academic Press) ]and DrudeshyZener modelin a wavelength range 300ndash600 nm
silver
[ Johnson P B Christy R W 1972Phys Rev B 6 4370 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε3
Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are
considered ZrO2 SiO2 Al2O3 with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity
IMI IIM
Re(Sx)x
Single metalshyinsulatorinterface
Existence Conditions of Waves with Zero Group Velocity
IMI IIMsmall kx
large kx
small kx
large kx
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
In order to satisfy the existence condition of waves with zero group velocity the power flow inside the metal must be equal (in absolute value) to the power flow in dielectric media Solving Maxwell equations we obtain that this requirement is equivalent to the following equality
This lengthy expression can be significantly simplified in case of antishysymmetric mode and ε2=ε3
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma chapter 7 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Dispersion curves of SPP in the insulatorshysilvershyinsulator structures for various permittivities Nonshyradiative modes are presented The value of ε2 is fixed and is equal to 25 film thickness d=15 nm Permittivity ε3 takes values from 1 till 12 (1 2 25 3 4 5 7 12) The upper curve corresponds to ε3=1
According to [Palik E D 1998 Handbook of Optical Constants of Solids I (San Diego CA Academic Press) ]and DrudeshyZener modelin a wavelength range 300ndash600 nm
silver
[ Johnson P B Christy R W 1972Phys Rev B 6 4370 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε3
Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are
considered ZrO2 SiO2 Al2O3 with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity
IMI IIMsmall kx
large kx
small kx
large kx
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
In order to satisfy the existence condition of waves with zero group velocity the power flow inside the metal must be equal (in absolute value) to the power flow in dielectric media Solving Maxwell equations we obtain that this requirement is equivalent to the following equality
This lengthy expression can be significantly simplified in case of antishysymmetric mode and ε2=ε3
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma chapter 7 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Dispersion curves of SPP in the insulatorshysilvershyinsulator structures for various permittivities Nonshyradiative modes are presented The value of ε2 is fixed and is equal to 25 film thickness d=15 nm Permittivity ε3 takes values from 1 till 12 (1 2 25 3 4 5 7 12) The upper curve corresponds to ε3=1
According to [Palik E D 1998 Handbook of Optical Constants of Solids I (San Diego CA Academic Press) ]and DrudeshyZener modelin a wavelength range 300ndash600 nm
silver
[ Johnson P B Christy R W 1972Phys Rev B 6 4370 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε3
Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are
considered ZrO2 SiO2 Al2O3 with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
In order to satisfy the existence condition of waves with zero group velocity the power flow inside the metal must be equal (in absolute value) to the power flow in dielectric media Solving Maxwell equations we obtain that this requirement is equivalent to the following equality
This lengthy expression can be significantly simplified in case of antishysymmetric mode and ε2=ε3
[ Allis W P Buchsbaum S J Bers A 1963Waves in anisotropic plasma chapter 7 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Dispersion curves of SPP in the insulatorshysilvershyinsulator structures for various permittivities Nonshyradiative modes are presented The value of ε2 is fixed and is equal to 25 film thickness d=15 nm Permittivity ε3 takes values from 1 till 12 (1 2 25 3 4 5 7 12) The upper curve corresponds to ε3=1
According to [Palik E D 1998 Handbook of Optical Constants of Solids I (San Diego CA Academic Press) ]and DrudeshyZener modelin a wavelength range 300ndash600 nm
silver
[ Johnson P B Christy R W 1972Phys Rev B 6 4370 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε3
Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are
considered ZrO2 SiO2 Al2O3 with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Dispersion curves of SPP in the insulatorshysilvershyinsulator structures for various permittivities Nonshyradiative modes are presented The value of ε2 is fixed and is equal to 25 film thickness d=15 nm Permittivity ε3 takes values from 1 till 12 (1 2 25 3 4 5 7 12) The upper curve corresponds to ε3=1
According to [Palik E D 1998 Handbook of Optical Constants of Solids I (San Diego CA Academic Press) ]and DrudeshyZener modelin a wavelength range 300ndash600 nm
silver
[ Johnson P B Christy R W 1972Phys Rev B 6 4370 ]
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε3
Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are
considered ZrO2 SiO2 Al2O3 with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε3
Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are
considered ZrO2 SiO2 Al2O3 with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
silver
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of permittivity ε3 Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are considered ZrO2 SiO2 Al2O3
with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε3
Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are
considered ZrO2 SiO2 Al2O3 with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε3
Permittivity ε3 takes values from 1 till 20
The value of ε2 is fixed (three materials are
considered ZrO2 SiO2 Al2O3 with permittivities 55 22 and 284 correspondibly) film thickness d=15 nm
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametricfunctions of film thickness d which takes values from 3 nm till 50 nmThe values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 3 nm till 50 nm The values of ε2 and ε3 are fixed
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity (IMI structures)
d=10 nm d=15 nm
Resonance circular frequency as function of permittivites ofsurrounding insulator media for fixed value of film thickness d
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nm
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points ofthe dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of permittivity ε2 Permittivity ε2 takes values from 1 till 15The value of ε3 is fixed (vacuum) Filmthickness is fixed too and three different values are considered
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various film thicknesses Permittivity ε2=55 (ZrO2)
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
silver
vacuum
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered dcoff is a cutoff thicknessie the maximum thickness thatallow the existence of zeroshygroupshyvelocity mode
=350 nmλ
=450 nmλ
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Existence Conditions of Waves with Zero Group Velocity (IIM structures)
Zeroshygroupshyvelocity points of the dispersion curves of SPPs as parametric functions of film thickness d which takes values from 2nm till 20nm The value of ε3 is fixed (vacuum) Four different materials as medium ldquo2rdquo are considered
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Lossy caseLossy case
Metal is described by DrudeshyZener model
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Silver
Γasymp7 10 13 sshy1
DrudeshyZener dielectric function with dumping factor
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Effect of Losses on Dispersion Curves
IMIIMIsilver
Al2O3
Dispersion curves of SPP in the Al2O3shysilvershyinsulator structures for various permittivities ε2 Film thickness d=10 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Effect of Losses on Dispersion Curves
IMIIMI
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Effect of Losses on Dispersion Curves
IMIIMIFilm thickness d=10 nmDashed lines showdependecies forlossless systemsOnly the region where |Re(kx)|gt( cω ) max( ε2 ε3) is consideredPoints A B C D correspond to crosspoints of dispersioncurves with light lines
A
B
C
D
Re( )
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Effect of Losses on Dispersion Curves
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Film thickness d=8 nmDashed lines showdispersion curves ina lossless systemOnly the region where |Im(kx)|lt|Re(kx)| is considered
silver
vacuum
Re( )
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Effect of Losses on Dispersion Curves
Re ( )
AB
C
AB
C
IIMIIM
Dispersion curves of SPP in the vacuumshyinsulatorshysilver Film thickness d=8 nm Negative values of Im(kx) correspond to backward waves
|Im(kx)|lt|Re(kx)|
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
=Γ Γ0+βω2
Modified DrudeshyZener model
Γ0=59 10 13 sshy1
=β 32 10 shy18 s[ Chen L Lynch D W 1987Phys Rev B 36 1425 ](red curve)
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Effect of Losses on Dispersion Curves
(cmshy1)
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various permittivities ε2 Modified DrudeshyZener model is used Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Effect of Losses on Dispersion Curves
Comparison of dispersion curves with different dumping factors Γ Silver dielectric functionobeys DrudeshyZener model Silver is covered byultrashythin insulator film of Al2O3Film thickness d=8 nm |Im(kx)|lt|Re(kx)|
IIMIIM
silver
vacuum
Al2O3
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Effect of Losses on Dispersion Curves
IIMIIM
silver
vacuum
Al2O3
Dispersion curves of SPP in the vacuumshyinsulatorshysilver structures for various dumping factors Γ Film thickness d=8 nm
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Excitation of Excitation of ZeroshyGroupshyVelocity ModesZeroshyGroupshyVelocity Modes
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Three-layer Kretschmann
geometry
εpr gt ε2 ε3
Excitation of ZeroshyGroupshyVelocity Modes
IMI
IIMThree-layer Kretschmann
geometry or Otto configuration
εpr gt ε2gt ε3
SimpleKretschmann
geometry
εpr gt ε2gt ε3
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Excitation of ZeroshyGroupshyVelocity Modes
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Results of NumericalResults of NumericalSimulationSimulation
ApplicationsApplications
andand
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Stored Light in NanoshyScale Plasmonic Cavity
d=10 nm
L=180 nm
s=50 nm IMIIMI=Γ 7 10 12 sshy1
εpr=74
=ω 566 10 15 sshy1
=Γ 7 10 13 sshy1
=ϴ 45⁰
and
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1E=E0sin(ωt)
V=V0sin(ωt)
point A
point B
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 12 sshy1
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Stored Light in NanoshyScale Plasmonic Cavity
IMIIMI=Γ 7 10 13 sshy1
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
FutureFuture
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention
Dmitry Fedyanin Aleksey Arsenin Vladimir Leiman and Anantoly Gladun
Moscow Institute of Physics and Technology (State University) Russiaeshymail feddumailru
httpphysicsmiptrusciencecenter
Thank you for your attention