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P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
FT-3: Magneto-optics and Magneto-plasmonics Part 2
P. Vavassori
-IKERBASQUE, Basque Fundation for Science and CIC nanoGUNE Consolider, San Sebastian, Spain.
550 600 650 700 750 800
-4
0
4
8
(mra
d)
Wavelength (nm)
-1x105
0
1x105
2x105
1/
(rad
-1)
684 687 690 693
Reflected electric field Et
Et
Ei
-
Et
H -HEi
Incident electric field Ei
MO-LPR phase
y
x
EiMO
H
LPR phase
Substrate
l’
FWHM
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Outline
NANOANTENNAs COMBINING MAGNETIC AND PLASMONIC FUNCTIONALITITES
➢ Localized surface plasmons & Magneto-optical Kerr effects (MOKE): Introduction
➢ Physical picture and modeling
➢ LSPR-based sensing: Towards molecular sensing
➢ Photonics technology: control of the non-reciprocal light propagation
MAGNETOPLASMONIC METAMATERIALS
➢ Surface lattice resonances in arrays of nanoantennae
➢ Arrays of elliptical nanoantennae
➢ Magnetoplasmonic gratings: arrays of antidots
CONCLUSIONS
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Localized surface plasmon resonances (LSPRs)
Small d for excitation of a
LSPR in the optical visible
range (air, glass….)
Subwavelength localization
of electromagnetic energy
G
0 0.5 1 1.5 2
0
0.2
0.4
0.6
0.8
1
Localized surface plasmon resonances (LSPRs or LSPs) collective oscillations of
conduction electrons in metallic nano structures.
G
axx
wavelength
frequency
p
ph
ase
F(t)
( )
( )tF
txxx
~=a( )tx~
p
d < l/2
+50
-50
0
0
12
10
8
6
4
2
d=150nm
h=32nm Au
Air
Glass
-100 0 +100 -100 0 +100[nm]
[nm]
λ=717nm λ=663nm|E|2 [V2·m2]
(a) (b)
Fig. 1 Example of strong lightconfinement related to excitation of plasma
resonance in a nano-disk of Au
Ellipsoid
=
zzzyzx
yzyyyx
xzxyxx
aaa
aaa
aaa
a~
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
p
Electric field lines due to an electric dipole oscillating vertically at the origin. Near the dipole,
the field lines are essentially those of a static dipole.
At a distance of the order of half wavelength or greater, the field lines are completely
detached from the dipole
q
a Imext
2a sca
Scattering and absorption remove energy from the incoming EM
Absorption
Scattering
Extinction
Wavelength
absscaext +=
sample
spectrometer
EM field irradiated by an oscillating dipole
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Extinction
Wavelength
LSPR
Localized surface plasmon resonances (LSPRs)
Size Embedding medium
Red-shift
Red-shift
Size Embedding medium
Red-shift
Red-shift
a Imext
2a sca
Scattering and absorption remove energy from the incoming EM
Absorption
Scattering
absscaext +=
a Imabs
+50
-50
0
0
12
10
8
6
4
2
d=150nm
h=32nm Au
Air
Glass
-100 0 +100 -100 0 +100[nm]
[nm]
λ=717nm λ=663nm|E|2 [V2·m2]
(a) (b)
Fig. 1 Example of strong lightconfinement related to excitation of plasma
resonance in a nano-disk of Au
sample
spectrometer
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
G
displacement
km
Displacement
in phase with E
Displacement
in anti-phase with EDisplacement 90°
out of phase with E
F
Phase
( )tx~
( )tx~
Phase (
px) Im
(a) (a
.u.)
LSPR
Frequencywavelength
frequency
[ ] a
Polarizability phasePhase
(px) 1.0
0.5
0.0
amplitude
G
[ ] a
LSPR as a damped harmonic oscillator
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Magnetoplasmonics
(SPPs MKSPP → K’SPP = KSPPKSPP)
Control of MO activity
Control of plasmon properties
G.Armelles , A. Cebollada , A. García-Martín , and M. Ujué González, Adv. Optical Mater. 2013, 1, 10–35
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Adv. Mater. 19, 4297 (2007)➢ Large areas
➢ Disordered distribution
➢ Insulating substrates
➢ Low concentration to avoid interactionsChalmers
Hole-Mask Colloidal Lithography
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
E-beam lithography on glass
Au
nanoGUNE – Aalto – Stockholm – Singapore
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Negative e-beam lithography on glass
nanoGUNE – Aalto – Stockholm – Singapore
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
650 nm490 nm350 nm
Ni nanoantennas
LSPR LSPR
LSPR
Disks 60x30 nm Disks 100x30 nm Disks 160x30 nm
Extin
ctio
n
Extin
ctio
n
Extin
ctio
n
Hole-Mask Colloidal Lithography (Ni disks on glass)Adv. Mater. 19, 4297 (2007)
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Is the effect due to a LSPR?
In press on SmallSmall 7, 2341 (2011)
Scanning Near-Field Optical (SNOM) microscopy: amplitude and phase!
Exticn
tio
n
In the NF, electric field is like the one
produced by a static electric dipole
Intense E fields of opposite sign
(p out of phase)
-p/2
+p/2
+p/2-p/2
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
A real LSPR?
In press on SmallSmall 7, 2341 (2011)
Scanning Near-Field Optical (SNOM) microscopy: amplitude and phase!
sample
spectrometer
60 nm
160 nm
100 nm
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
qK,F
K,F
P. Vavassori, APL 77, 1605 (2000)
Magnetic characterization
Magneto-Optical Kerr effect configurations
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Spectroscopic Polar MOKE
H
sample
x,y,z
Supercontinuum
Source
(400-2000 nm)
AO
Monochrom
(400-800 nm)
5mW
1nm
Lock-in ref (w, 2w)
I PEM (w)
pol
photodiode
pol
lens
lens
DC w 2w
q(H)(H)I0
P. Vavassori, APL 77 1605 (2000)
Modulation polarizationtechnique for recordingthe longitudinal and polarKerr effects, both q and .
H
sample
x,y,z
Supercontinuum
Source(420-2000 nm)
AO filter
(420-2000 nm)
5mW
1nm
ref (w,2w)PEM (w)
pol
photodiode
pol
lens
lens
Lock-in
(H) q(H)
t
H -H
l < l
l > l
lq
q,
H
y
x
EiEi
SO
M
ErqK K
EtqF F
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Polar MOKE spectra: polarization of reflectedlight linked to the LSPR position
➢ Maximum of qK and crossing
of K follow the LSPR position
Film – no crossings in the visible range
Ni film
450 600 750 900-2.0
0.0
2.0
4.0
Ni film
qk
k
Angle
(m
rad)
Wavelenght (nm)
650 nm
LSPR
Extin
ctio
n
450 500 550 600 650 700 750 800
-4,0x10-3
-2,0x10-3
0,0
2,0x10-3
4,0x10-3
Experimental
Disks 100 nm
Pol P
q
Pol S
q
An
gle
(ra
d)
Wavelength (nm)
450 500 550 600 650 700 750 800-3,0x10
-3
-2,0x10-3
-1,0x10-3
0,0
1,0x10-3
2,0x10-3
3,0x10-3
Experimental
Disks 60 nm
Pol S
q
Pol P
q
An
gle
(ra
d)
Wavelength (nm)
450 500 550 600 650 700 750 800-5,0x10
-3
-2,5x10-3
0,0
2,5x10-3
5,0x10-3
Experimental
Disks 160 nm
Pol P
q
Pol S
q
An
gle
(ra
d)
Wavelength (nm)
350 nm
LSPR
Extin
ctio
n
490 nm
LSPR
Extin
ctio
n
qK
K
P-MOKE Extinction
Refence Ni film
P. Vavassori, Appl. Phys. Lett. 77, 1605 (2000)
Phys. Rev. Lett. 111, 167401 (2013)
650 nm
2.0
1.0
0.0
-1.0
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
0 0.5 1 1.5 2
0
0.2
0.4
0.6
0.8
1
Damped harmonic oscillator
Phase contribution
Simple physical picture: two coupled damped harmonic oscillators!!!
➢ Damped H.O.: confinement
➢ S.O. coupling: material property
Phase (p)
Amplitude
Fundamental hypothesis here: linear and perturbative regime
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Induced electric dipoles
➢ MO enhancement depends only on ayy (shape can improve enhancement)
➢ Relative phase on both ayy and yx
1. Oscillator along x
3. Oscillator along y
2. S.O. Coupling
EPMO
M
pyS.O. = cyx Ex
i = yx Exi
px = cxx Exi = ( – m) Ex
i
Exi = E0 – Ex
d
EyS.O. = py
S.O./cyy = pyS.O./( –m)
py = ayy EyS.O. = Ex
i (ayy yx) / ( – m)
( )2
m
yyyx
x
y
p
p
a
−=
px = axx E0
Gives the polarization of the far-field radiated
in the z-direction by these two mutually
orthogonal oscillating electric dipoles
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Simple physical picture: two S.O. coupled damped harmonic oscillators: relative phase
➢ Damped H.O.: confinement
➢ S.O. coupling: material property
Kerr
Faraday
0< < p/2
p/2 < < p
qK = 0
K
K
= p/2
= p
= 0
( ) yy
m
yx
xy
x
ypp
p
p
a
+
−=
=−=
=
2
~~~
~Polarization of the radiated field
Wavelength
( )2m
yx
x
y
p
p
−=
ayy
Phys. Rev. Lett. 111, 167401 (2013)
z
E(z, t)
S.O.
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
N. Maccaferri et al., Opt. Express 21, 9875-89 (20113)
p = ( – m) Ei ; Ei = E0 + Ed
External field
Depolarizing field
Internal field
Oblate ellipsoidCilindrical disk
E0
Ed
p
++
+
---
Embedding medium
˜
Depolarizing field is the key
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Static depolarization: the sphere case
pE Lm
d
1−=
pNE~1
m
d
−=
3
1=L
More in general, for an ellipsoid:
Ei = E0 + Ed
0~Ep a=
( ) im Eεp −= ~
( )
( ) 02~
~3E
ε
εp
m
mm
+
−=
( )
( )
( )
( ) 00
3
02~
~4
2~
~3EE
ε
εE
ε
εP a
p
=
+
−=
+
−=
m
mm
m
mm aV
( )( )INI
IIεα ~~~~
~~~~
mm
mm
−+
−=
( ) ( ) ( )13 1
2 2 222 2
02
i j k
i i j k
a a aL q a q a q a dq
−− −
= + + +
Nii = Li
ak
ai
aj
a
Clausius-Mossotti
Internal and depolarizing fields: quasi static approx
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Wavelength dependent corrections to polarizability: modified long-wavelength approximation (MLWA)
N. Maccaferri et al., Opt. Express 21, 9875-89 (20113)
Oblate ellipsoidCilindrical disk
pp 64
32 VkiD
VkLN iiiiii −−=pNE
~1
m
d
−= zyxxdVr
rxD i
V
ii ,,;
2
22
=+
=
( )3 2
3
ˆ ˆ3 ˆ ˆ2 ( )
3 2d d
Pd i k k dV
r r
− = = + +
u P u P u P u
E E
k is the light wave vector modulus,
r the distance from the center of
the ellipsoid, and a unit vector in
the direction of r.
u
Static depolarization due
to a uniform E0 (shape of
the nanoparticle) → Li
Radiative reaction due to
the recoil force (Abraham–
Lorentz force) acting on an
oscillating dipole emitting
electromagnetic radiation
Dynamic depolarization
arising from de-phasing
of the radiation emitted
by different points in the
ellipsoid
DiLi
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
400 600 800 1000
-0.5
0.0
0.5
1.0
Wavelength (nm)
0.0
D = 160 nm
xy pp ~/~
..OS
yya yyaIm
[
py/
px]
(p
)
Im[a
yy ]
It is a phase business
350 400 450 500 550 600 650 700 750 800 850 900-8,0x10
-3
-6,0x10-3
-4,0x10-3
-2,0x10-3
0,0
2,0x10-3
4,0x10-3
6,0x10-3
8,0x10-3
Pol P
q
Pol S
q
NF Calculated
Disks 160 nm
An
gle
(ra
d)
Wavelength (nm)
( )
yyOSyy
m
yx
x
y
p
paa
+=+
−=
= ..2
( )2~
~
m
yyyx
x
y
p
p
a
−=
The polarization of the far-field
radiated in the z-direction by these
two mutually orthogonal oscillating
electric dipoles is given by the ratio
z
Kerr rotation and ellipticity spectra
for an isolated nanostructure
qK= Re[py/px] and K= Im[py/px].
qK
Eox
E(z,t)
K = 0
qK = 0
0=
x
y
p
p
2
p =
x
y
p
p
Phase difference between the two radiating dipoles px and py
Phys. Rev. Lett. 111, 167401 (2013)
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
-5.0
-2.5
0.0
2.5
K
70 nm
100 nm
160 nm
Angle
(m
rad)
450 600 750 900
-2.0
0.0
2.0
4.0
Wavelength (nm)
qK
70 nm
100 nm
160 nm
Angle
(m
rad)
It is a phase business
400 600 800 1000
-0.5
0.0
0.5
1.0
Wavelength (nm)
0.0
70 nm
100 nm
160 nm
100 nm 160 nm70 nm
Im[a
yy ]
[
py/
px]
(p)
( )
yyOSyy
m
yx
x
y
p
paa
+=+
−=
= ..2~
~
( )2~
~
m
yyyx
x
y
p
p
a
−=
qK = 0
2~
~p
=
x
y
p
p
qK
Eox
E(z,t)
K = 0
0~
~
=
x
y
p
p
Phys. Rev. Lett. 111, 167401 (2013)
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Model system
400 500 600 700 800 900 1000
Absorp
tion (
arb
. units)
Wavelength (nm)
m
Glass substrate, g
Ambient, o
d
Glass substrate, g
d EMA
Modeling the spectra
Our system
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
D. Stroud, Phys. Rev. B 12 (8), 3368 (1975)M. Abe, Phys. Rev. B 53 (11), 7065 (1996)M. Abe and T. Suwa, Phys. Rev. B 70, 235103 (2004)
M. Schubert, T. E. Tiwald and J. A. Woollam, Applied Optics 38 (1), 177 (1999)J. Zak, E. R. Mook, C. Liu and S. D. Bader, JMMM 89, 107 (1990)S. Visnovsky et al., Optics Express 9 (3), 121 (2001)
Step 2 (far-field)
qK
K
pp
sp
r
rRe
ss
ps
r
rRe
pp
sp
r
rIm
ss
ps
r
rIm
Fictitious MO film
Step 3 (far-field including substrate)
qK
K
pp
sp
r
rRe
ss
ps
r
rRe
pp
sp
r
rIm
ss
ps
r
rIm
Complete system
Transfer matrix method(multilayers)
Effective medium approximation (EMA)
Modeling the spectra: steps 2&3
N. Maccaferri et al., Opt. Express 21, 9875-89 (2013)
N. Maccaferri et al., Phys. Stat. Solidi (a) (2014)
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
450 500 550 600 650 700 750 800
-4,0x10-3
-2,0x10-3
0,0
2,0x10-3
4,0x10-3
Experimental
Disks 100 nm
Pol P
q
Pol S
q
An
gle
(ra
d)
Wavelength (nm)
450 500 550 600 650 700 750 800 850-3,0x10
-3
-2,0x10-3
-1,0x10-3
0,0
1,0x10-3
2,0x10-3
3,0x10-3
Calculated
Disks 100 nm
Pol S
q
Pol P
q
An
gle
(ra
d)
Wavelength (nm)
450 500 550 600 650 700 750 800-5,0x10
-3
-2,5x10-3
0,0
2,5x10-3
5,0x10-3
Experimental
Disks 160 nm
Pol P
q
Pol S
q
An
gle
(ra
d)
Wavelength (nm)
450 500 550 600 650 700 750 800-3,0x10
-3
-2,0x10-3
-1,0x10-3
0,0
1,0x10-3
2,0x10-3
3,0x10-3
Experimental
Disks 60 nm
Pol S
q
Pol P
q
An
gle
(ra
d)
Wavelength (nm)
450 500 550 600 650 700 750 800 850 900
-5,0x10-3
-2,5x10-3
0,0
2,5x10-3
5,0x10-3
Pol P
q
Pol S
q
Calculated
Disks 160 nm
An
gle
(ra
d)
Wavelength (nm)
450 500 550 600 650 700 750 800-4,0x10
-3
-3,0x10-3
-2,0x10-3
-1,0x10-3
0,0
1,0x10-3
2,0x10-3
3,0x10-3
4,0x10-3
Calculated
Pol S
q
Pol P
q
Disks 60 nm
An
gle
(ra
d)
Wavelength (nm)
Response of an ensemble of such oscillators randomly distributed on a glass substrate (EMA)
No adjustable parameters:
tabuled optical and MO constants;
sizes and nanoantennaedensity from SEM images
Substrate plays a role
N. Maccaferri et al., Phys. Status Solidi A 211, 1067-75 (2014)
N. Maccaferri et al., Opt. Express 21, 9875-89 (2013)
Agreement between
calculated and
experimental spectra is
almost perfect!
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
500 1000 1500 2000 2500-4,0x10
-3
-3,0x10-3
-2,0x10-3
-1,0x10-3
0,0
1,0x10-3
2,0x10-3
3,0x10-3
4,0x10-3
Ni film
Pol S
q
Pol P
q
An
gle
(ra
d)
Wavelength (nm)500 1000 1500 2000 2500
-1,0x10-2
-8,0x10-3
-6,0x10-3
-4,0x10-3
-2,0x10-3
0,0
2,0x10-3
4,0x10-3
6,0x10-3
8,0x10-3
1,0x10-2
NF Calculated (n=1.125)
Pol S
q
Pol P
q
Disks 100 nm
An
gle
(ra
d)
Wavelength (nm)
Confinement
❑ Confinement (LSPR) – redistribution (blue shift) of the main spectral features due to intrabandtransitions (material properties, q and linked via Kramers-Kronig relations)
Phase adjustment: spectral features redistribution
LPS
IntrabandInterband
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
450 500 550 600 650 700 750 800 850-3,0x10
-3
-2,0x10-3
-1,0x10-3
0,0
1,0x10-3
2,0x10-3
3,0x10-3
Calculated
Disks 100 nm
Pol S
q
Pol P
q
An
gle
(ra
d)
Wavelength (nm)
400 500 600 700 800 900 1000 1100 1200-8,0x10
-3
-6,0x10-3
-4,0x10-3
-2,0x10-3
0,0
2,0x10-3
4,0x10-3
6,0x10-3
8,0x10-3
Disks 100 nmPol S
q
Pol P
q
EMA Calculated (f = 0.1)
An
gle
(ra
d)
Wavelength (nm)
500 1000 1500 2000 2500-4,0x10
-3
-3,0x10-3
-2,0x10-3
-1,0x10-3
0,0
1,0x10-3
2,0x10-3
3,0x10-3
4,0x10-3
Ni film
Pol S
q
Pol P
q
An
gle
(ra
d)
Wavelength (nm) 500 1000 1500 2000 2500-1,0x10
-2
-8,0x10-3
-6,0x10-3
-4,0x10-3
-2,0x10-3
0,0
2,0x10-3
4,0x10-3
6,0x10-3
8,0x10-3
1,0x10-2
NF Calculated (n=1.125)
Pol S
q
Pol P
q
Disks 100 nm
An
gle
(ra
d)
Wavelength (nm)
Confinement
Substrate
❑ Confinement (LSPR) – redistribution (blue shift) of the main spectral features (material properties, qand linked via Kramers-Kronig relations)
❑ Substrate – reduction of MOKE contrast and slight additional blue shift of the spectral features
Step 1
Step 2 Step 3
Let’s have a look at the individual steps
LPS
IntrabandInterband
Phys. Rev. Lett. 111, 167401 (2013); Phys. Status Solidi A 211, 1067-75 (2014)
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
MM
450 600 750 900
Wavelength (nm)
100 nm
ErEr
MM
450 600 750 900
Wavelength (nm)
100 nm
ErEr
qkk
qk
k
PhaseAmplitude
Wavelength
Summary for an individual magnetic nano-antenna
The concerted action of LSPRs and MO activity allows for the controlled
manipulation of Kerr rotation/ellipticity of ferromagnetic nanostructures
(beyond intrinsic material properties).
MO-LSPR
pEr
Er
EiEi
t
PMO
PO
t
PMO
PO
lG lR
Phase delay tuning
lR
lG
Phys. Rev. Lett. 111, 167401 (2013)
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Control of magneto-optics via magnetoplasmonic anisotropy
Nano Letters 14, 7207 (2014)
L-MOKE
170/240 nm; t = 30 nm
“Magnetoplasmonic design rules for active magneto-optics”
Shape engineeringActive tuning
MO enhancement (3D structures)
Enhancement by a factor of 20
450 600 750 900 1050-0.14
-0.07
0.00
0.07
0.14
qK (
mra
d)
Wavelength (nm)
E
45°
@ 800nm
0
1
-1
0° 90°
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
LPRS phase-sensitivity in the reflected/transmitted light polarization
N. Maccaferri et al., Nature Commun. 6, 6150 (2015)
Extin
ctio
nE
xtin
ctio
nE
xtin
ctio
n
Wavelength
Wavelength
Wavelength
Extinction
Min l detectable ~ 0.5 nm
of PA-6.6MLtMin10
1=
ALD deposition Talk by N. Maccaferri
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
LPRS phase-sensitivity in the reflected/transmitted light polarization
Extin
ctio
nE
xtin
ctio
nE
xtin
ctio
n
Wavelength
Wavelength
Wavelength
Extinction
Min l detectable ~ 0.5 nm
of PA-6.6MLtMin10
1=
ALD deposition
R. Verre et al. Nanoscale 8, 10576 (2016)
Au dimers
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Near field interactions: Magnetoplasmonic ruler
Plasmon ruler is an emerging concept where strong near-field coupling of plasmon nanoantenna
elements is employed to obtain the structural information at the nanoscale (nanoscale distances).
Magnetoplasmonic ruler concept
MP ruler: two orders of
magnitude higher precision
compared to the state-of-the-art
plasmon rulers.
Nano Letters 15, 3204 (2015)
Kerr
q (
rad)
4.0
3.0
2.0
1.0
0.0
x 10-4
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
NANOANTENNAs COMBINING MAGNETIC AND PLASMONIC FUNCTIONALITITES
➢ Localized surface plasmons & Magneto-optical Kerr effects (MOKE): Introduction
➢ Physical picture and modeling
➢ LSPR-based sensing: Towards molecular sensing
➢ Photonics technology: control of the non-reciprocal light propagation
MAGNETOPLASMONIC METAMATERIALS
➢ Surface lattice resonances in arrays of nanoantennae
➢ Arrays of elliptical nanoantennae
➢ Magnetoplasmonic gratings: arrays of antidots
CONCLUSIONS
Outline
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Ordered arrays of metallic nano-antennas (MNAs) placed in symmetric or quasi-
symmetric refractive index environment exhibit surface lattice resonances
(SLRs) which arise from diffraction-induced coupling between LSPRs of the
MNAs.
This coupling may result in significant reduction of plasmon radiative damping,
and therefore, narrowing of plasmon resonance, which is of interest for plasmon
based sensors.
Reduced plasmon radiative damping – Fano-like resonance
Ex
MNAs
l = dy * n
dy
l = dy * n
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Ordered arrays of metallic nano-antennas (MNAs) placed in symmetric or quasi-
symmetric refractive index environment exhibit surface lattice resonances
(SLRs) which arise from diffraction-induced coupling between LSPRs of the
MNAs.
This coupling may result in significant reduction of plasmon radiative damping,
and therefore, narrowing of plasmon resonance which is of interest for plasmon
based sensors.
MNAs
Ey
l = dx * n dx
l = dx * n
Reduced plasmon radiative damping – Fano-like resonance
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Ordered arrays of metallic nano-antennas (MNAs) placed in symmetric or quasi-
symmetric refractive index environment exhibit surface lattice resonances
(SLRs) which arise from diffraction-induced coupling between LSPRs of the
MNAs.
This coupling may result in significant reduction of plasmon radiative damping,
and therefore, narrowing of plasmon resonance which is of interest for plasmon
based sensors.
Arrays of magnetoplasmonic nanoantennas
Magnetic
MNAs
Ei
M
x
lMO = dx * n
dy
dx
lO = dy * n
l = dy * n
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
From random to ordered arrays: Polarizability
l = d * n
600 800 1000 1200
0.1
0.2
0.3
0.4
0.5
Im[a
lph
a]
(no
rm)
Wavelength (nm)
Periodic
Random
Ni
100 nm
30 nm
400 nm
n = 1.5
400 nm
500 600 700 800 900 1000-5000
0
5000
10000
15000
S (
m
-3)
Wavelength(nm)
Re[S]
Im[S]
l =d * n
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
550 600 650
-1
0
1
2
3
Wavelength (nm)
S-p
ha
se
(ra
d)
0
5000
10000
15000
20000
S-a
mp
litud
e (
m-3)
600 800 1000 1200
0.1
0.2
0.3
0.4
0.5
Im[a
lph
a]
(no
rm)
Wavelength (nm)
Periodic
Random
500 600 700 800 900 1000-5000
0
5000
10000
15000
S
(m
-3)
Wavelength(nm)
Re[S]
Im[S]
The S coupling factor shows
a suddend and large phase
change around l*.
Constructive/destructive
interference.l* =d * n
On the origin of SLMs
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
l ≈d * n
]1Im[]Im[
]Re[]1Re[
]Im[
Im
Re
2Im
2Re
Im*
a
a
a
−=
−=
+
=
S
S
]Im[]Im[ * aa
]Im[]Im[ * aa <<
500 600 700 800-10000
-5000
0
5000
10000
15000
S,
/a
m
-3]
Wavelength (nm)
Re[S]
Re[1/a] Im
*1
]Im[
=a
500 600 700 800-10000
-5000
0
5000
10000
15000
S,
/a
m
-3]
Wavelength (nm)
Im[S]
Im[1/a]
]Im[]Im[ * aa
600 800 1000 1200
0.1
0.2
0.3
0.4
0.5
Im[a
lpha] (n
orm
)
Wavelength (nm)
Periodic
Random
On the origin of SLMs
Resonance position mainly determined
by crossing points of real parts.
Strength of resonance determined by
difference between imaginary parts
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Material: Py; Lattice parameters: px 400 nm py 400 -500 nm
From random to ordered arrays: MP crystals
Refractive index matching oil (n = 1.5)
M. Kataya et al., Nat. Commun. 6, 7072 (2015)
py
40
0 -
50
0 n
m
px 400 nm
Exct.
qK
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Rectangular arrays
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
ll=d*n
Relative position of the LSPR and the diffractive interference
Resonance lineshape evolution varying the relative position
of the LSPR with respect to the Rayleigh’s anomaly
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
N. Maccaferri et al., Nano Lett. 16, 2533 (2016)
LA
LA SA
SA
Enhanced and tunable O and MO-Anisotropy
MOA = 22KK q + MOALA-MOASA
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
N. Maccaferri et al., Nano Lett. 16, 2533 (2016)
Experiment
Enhanced and tunable O and MO-Anisotropy
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Py
Py
Py
Py
Au Au
AuAu
Ei
Checkerboard hybrid arrays of Py and Au nanoantennae
Efficient radiative far-field coupling between the
magnetic and noble-metal components
M. Kataia et al., Opt. Express 24, 3652 (2016)
Integrating MO active
and pure plasmonic
nanostructures:
combination of intense
optical resonances with
strong MO activity.
Ni
50%Ni 50%Au
50%Ni
50%Au
Ni
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
LSMs with hybrid nanostructures
Another common strategy toovercome the excess ofdamping is to develop hybridstructures consisting of noblemetals and ferromagnets.
Banthí et. al Adv. Opt. Mat. 24,
OP36 (2012).
Dimers
Ni
Au
SiO2
Mikko Kataja, Pourjamal Sara &Sebastiaan van Dijken
Aalto, Finland
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
➢ Concerted action of LSPRs (or SPPs) and MO-coupling can beexploited to achieve a controlled manipulation of the MO response(control Kerr rotation/ellipticity) beyond what is offered by intrinsicmaterial properties.
Patterning magnetic nanostructures for resonant interaction with light: Magnetoplasmonic Crystals
➢ Magnetically tunable plasmonic crystal based on the excitation ofFano-like lattice surface modes in periodic arrays.
✓ Highly tunable and amplified magneto-optical effects as comparedto disordered systems.
➢ Two-dimensional magnetoplasmonic crystals supporting surfaceplasmon polariton modes and displaying a two-dimensional photonicband structure.
✓ Design of metamaterials with tailored and enhanced magneto-optical response by engineering the plasmonic band structure vialattice engineering.
Concluding remarks
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Other directions explored: magneto-plasmonics with SPP s
SPPs are localized electromagnetic
modes/charge density oscillations at
the interface of two media with
dielectric constants of opposite
signs, e.g. a metal and a dielectric,.
s ↔ p-polarization coversion!!
p-polarization only
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
SP resonance: coupling with a grating (conservation of momentum)
ki
θ
ki sin(θ)kg
kSP
kSP = ki sin(θ) - kg
ki θ
ki sin(θ) kg
kSP
kSP = ki sin(θ) + kg
+1 order coupling -1 order coupling
grating
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
Magntoplasmonic gratings: MOKE enhancement due to resonant coupling with SPPs
Magnetic diffraction grating
Antidot array (square lattice ):
material Py (Fe20Ni80), thickness = 80 nm,
lattice parameter = 405 nm,
hole diameter = 265 nm
by deep-UV photolithography
(Prof. A. Adeyeye, Singapore)
N. Maccaferri et al., ACS Photonics 2, 1769 (2015)
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
k||
kSSP1
(-1,+1)kSSP2
k||(-1,0)
kSSP(-1,-1)
Gx
Gy
k||
kSSP1
kSSP2
k||
kSSP
(-1,0)(-1,-1)
(0,-1)
Gx
Gy
SPP band structure: perturbative approach
= 45°
= 0°
Type II
k|| = k0Sinq
Type I
Type IIType I
(-1,-1) (-1,0)
(0,-1)
Type II:
both p- and s-pol
Type I:
only p-pol
Key property
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
500 600 700 8000.2
0.3
0.4
0.5
0.6
R
Wavelength (nm)
“Generalized scattering-matrix approach for magneto-optics in periodically patterned multilayer systems”
B. Caballero, A. García-Martín, and J. C. Cuevas, Phys. Rev. B 85, 245103 (2012)
Reflectivity maps: full calculations (antidots size and cross section)
Rpp (f = 0o )
Rpp (f = 45o ) Rss (f = 45o )
Rss (f = 0o )
(-1,0)&(0,-1)(-1,0)&(0,-1)
(+1,0)&(0,+1)
(-1,-1)
(+1,0)&(0,+1)
(-1,-1)&(-1,+1)(0,+1)&(0,-1)(0,+1)&(0,-1) (-1,-1)&(-1,+1)
(-1,0)
(+1,0)
Type I Type II
No channels for sp
conversion in the VIS
1 channel for sp
conversion in the VIS
Rss
Rpp
400 500 600 700 800
0.5
0.6
0.7
0.8
Wavelength (nm)
Rss
Rpp
R
G(-1,0)
G(0,-1)
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
400 500 600 700 800
0.2
0.4
0.6
0.8
Wavelength (nm)
MO activity enhancement mechanism (L-MOKE)
(-1,0)&(0,-1)
(-1,-1)
(-1,0)&(0,-1)
= 45°
q = 30°
Plasmonic channel “open” for resonant MO
induced polarization conversion.
= 0°
q = 30°
500 600 700 8000.1
0.2
0.3
0.4
0.5
0.6
Wavelength (nm)
Rss Rpp
Rss
Rpp
rps-rsp x 1000
rps-rsp x 1000
(-1,0)
(L-MOKE and P-MOKE involve s p polarization conversion
T-MOKE p p: no polarization conversion,)
N. Maccaferri et al., ACS Photonics 2, 1769 (2015)
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
450 525 600 675 750
0.5
1.0
1.5
2.0
2.5
30
45 60
(-1,0)
(0,-1)
(-1,-1)400 500 600 700 800
0.3
0.4
0.5
0.6
0.7
|rp
p|2
Wavelength (nm)
p-polarization
500 575 650 725 800
0.4
0.8
1.2
1.6
30
45
60
(-1,0)
400 500 600 700 800
0.3
0.4
0.5
0.6
0.7
|rp
p|2
Wavelength (nm)
p-polarization
Experimental MO-activity
500 600 700 800
0.4
0.8
1.2
1.6 30°
45°
60°
MO
A p
_pol (m
rad)
Wavelength (nm)
MO
A (
mra
d)
MO
A (
mra
d)
= 0° = 45°
Film
N. Maccaferri et al., ACS Photonics 2, 1769 (2015)
MOA = 22KK q +
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
mra
d = 45°
q = 30°
Rotation and ellipticity
N. Maccaferri et al., ACS Photonics 2, 1769 (2015)
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
SPP band structure engineering
(-1,-1) & (-1,+1)
(0,-1) & (0,+1)
(-1,0)
MO
activ
ity
Rectangular array:
two SPPs channels
Square array:
one SPP chasnnel
MO
activ
ityOne SPP assisted
MO enhancement
Two SPPs assisted
MO enhancement
Black dashed lines:
MO-active SPPs
Modes of different nature
bandgap opening
Resonant-antiresonant
lineshape
film
film
N. Maccaferri et al., ACS Photonics 2, 1769 (2015)
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
SPPs
Au
Ni
Zhou Xue & Adekulne O. Adeyeye
National University of Singapore
P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
➢ Concerted action of LSPRs (or SPPs) and MO-coupling can beexploited to achieve a controlled manipulation of the MO response(control Kerr rotation/ellipticity) beyond what is offered by intrinsicmaterial properties.
Patterning magnetic nanostructures for resonant interaction with light: Magnetoplasmonic Crystals
➢ Magnetically tunable plasmonic crystal based on the excitation ofFano-like lattice surface modes in periodic arrays.
✓ Highly tunable and amplified magneto-optical effects as comparedto disordered systems.
➢ Two-dimensional magnetoplasmonic crystals supporting surfaceplasmon polariton modes and displaying a two-dimensional photonicband structure.
✓ Design of metamaterials with tailored and enhanced magneto-optical response by engineering the plasmonic band structure vialattice engineering.
Concluding remarks