Near-field and far-field modeling of surface wavesscattered by an apertureless tip
Application to the Scanning Near-fieldOptical Microscopy
Eurotherm seminar 91Microscale Heat Transfert III
Lemta – "radiative transfer" group
Jérôme Muller, Gilles Parent, David Lacroix
IntroductionIntroduction
Rise of nanotechnology : Expansion of micro and nanostructured materials Importance of surface waves and thermal radiation at the nanoscale
Development of the Scanning Near-field Optical Microscopy applicated to the study of the infra-red thermal near-field (TRSTM)
Weakness of the scattered signal Importance of the influence of the tip (size, shape, material) and the
collecting optics 3D model of a TRSTM device in order to improve the collected signal
Rise of nanotechnology : Expansion of micro and nanostructured materials Importance of surface waves and thermal radiation at the nanoscale
Development of the Scanning Near-field Optical Microscopy applicated to the study of the infra-red thermal near-field (TRSTM)
Weakness of the scattered signal Importance of the influence of the tip (size, shape, material) and the
collecting optics 3D model of a TRSTM device in order to improve the collected signal
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Introduction
ContentsContents
Scanning Near field Optical Microscopy
Numerical models
Validation
A-SNOM/TRSTM, near and far field
Scanning Near field Optical Microscopy
Numerical models
Validation
A-SNOM/TRSTM, near and far field
Contents
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ContentsContents
Numerical models
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Scanning Near field Optical Microscopy
Numerical models
Validation
A-SNOM/TRSTM, near and far field
Scanning Near field Optical Microscopy
Numerical models
Validation
A-SNOM/TRSTM, near and far field
A-SNOM/TRSTM : principlesA-SNOM/TRSTM : principles
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Scanning Near field Optical Microscopy
Use of an apertureless AFM tip: Scattering of the surface waves Collection in the far field
Creation of surface waves: fully reflected incident wave thermal incoherent sources
(surface polaritons) → TRSTM(1)
Use of an apertureless AFM tip: Scattering of the surface waves Collection in the far field
Creation of surface waves: fully reflected incident wave thermal incoherent sources
(surface polaritons) → TRSTM(1)
(1)Y. de Wilde, F. Formanek, R. Carminati, B. Gralak, P.A. Lemoine, K. Joulain, J.P. Mulet, Y. Chen and J.J. Greffet, Thermal Radiation Scanning Tunnelling Microscopy. Nature(London), Vol.444, pp740-743, 2006.
A-SNOM/TRSTM : principlesA-SNOM/TRSTM : principlesA
-SNO
M/TR
STM devic e
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Scanning Near field Optical Microscopy
Example of TRSTM deviceExample of TRSTM device
TRSTM devicein developmentin our lab.
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Scanning Near field Optical Microscopy
AFM
sample
collecting optic(2 parabolic mirrors)
MCT detector
ContentsContents
Numerical models
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Scanning Near field Optical Microscopy
Numerical models
Validation
A-SNOM/TRSTM, near and far field
Scanning Near field Optical Microscopy
Numerical models
Validation
A-SNOM/TRSTM, near and far field
FDTD : Finite Difference Time DomainFDTD : Finite Difference Time Domain
Maxwell's equations:
Additional relations:
Yee's Algorithmnumerical resolution of the Maxwell's eq.
in the space domain in the time domain
Maxwell's equations:
Additional relations:
Yee's Algorithmnumerical resolution of the Maxwell's eq.
in the space domain in the time domain
∇×E=−∂ B∂ t
∇×H= j−∂D∂ t
∇⋅D=ϱ ∇⋅B=0
Yee cell
D= E B= H
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Numerical models
Boundary conditionsBoundary conditions
ABC-Perfectly matched layer: CPML implementation Total Field / Scattered Field
formulation: AFP-TFSF Dispersive media: ADE method Fine geometrical features: CPT
(Yu-Mittra)
NFTFF boundary: storage of surface equivalent currents:
ABC-Perfectly matched layer: CPML implementation Total Field / Scattered Field
formulation: AFP-TFSF Dispersive media: ADE method Fine geometrical features: CPT
(Yu-Mittra)
NFTFF boundary: storage of surface equivalent currents:
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Numerical models
JE=+n×Hnf
JH=−n×Enf
NFTFF transformationNFTFF transformation
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Numerical models
NFTFF (Near-field to far-field) transformation(3,4) based on the surface equivalent theorem, in the frequency domain:
takes into account a surface near to the scattering structure Gives the electric far-field E
ff(ω,r,θ,φ) thanks to the Capoglu and Smith
formalism
NFTFF (Near-field to far-field) transformation(3,4) based on the surface equivalent theorem, in the frequency domain:
takes into account a surface near to the scattering structure Gives the electric far-field E
ff(ω,r,θ,φ) thanks to the Capoglu and Smith
formalism
(3)J. Muller et al., FDTD and Near-field to Far-field transformation in the spectral-domain. Application to scattering objects with complex shape in the vicinity of a semi-infinite dielectric medium - J. Opt. Soc. Am. A , Vol. 28, Issue 5, pp. 868-878 (2011)(4)J. Muller et al., Near-field and Far-field modelling of scattered surface waves. Application to the apertureless scanning near-field optical microscopy. Journal of Quantitative Spectroscopy & Radiative Transfer 112, pp. 1162-1169 (2011)
ContentsContents
Validation
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Scanning Near field Optical Microscopy
Numerical models
Validation
A-SNOM/TRSTM, near and far field
Scanning Near field Optical Microscopy
Numerical models
Validation
A-SNOM/TRSTM, near and far field
Sphere above a plane interfaceSphere above a plane interface
Domain of 250⨯2402 cells
Cubic cells : x=y=z=λ0/100 with λ0=12,5µm
CPML : 10 cells thick
Sample : arbitrary medium (n=1,5)
Sphere : dispersive medium (n=2,4 +0,9i at the wavelength λ=λ0), of 100 cells radius (R=λ0)
Distance sphere/interface : R/10
Incident wave : gaussian pulse (fully reflected incident wave in TE polarization)
Domain of 250⨯2402 cells
Cubic cells : x=y=z=λ0/100 with λ0=12,5µm
CPML : 10 cells thick
Sample : arbitrary medium (n=1,5)
Sphere : dispersive medium (n=2,4 +0,9i at the wavelength λ=λ0), of 100 cells radius (R=λ0)
Distance sphere/interface : R/10
Incident wave : gaussian pulse (fully reflected incident wave in TE polarization)
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Validation
Incidence at 45 degrees: evanescent wave Incidence at 45 degrees: evanescent wave
Sphere above a plane interfaceSphere above a plane interface
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Near-field in the time domain
Far-field in the spectral domain (λ=12,5µm) and comparison with the T-Matrix(2)
Validation
(2)code developed by A. Doicu, T. Wriedt and al. (TPARTSUB code)
ContentsContents
A-SNOM/TRSTM, near and far field
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Scanning Near field Optical Microscopy
Numerical models
Validation
A-SNOM/TRSTM, near and far field
Scanning Near field Optical Microscopy
Numerical models
Validation
A-SNOM/TRSTM, near and far field
3D computational domain3D computational domain
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Domain of 250 18⨯ 02 cells
Cubic cells : x=y=z=λ0/125 with λ0=12,5µm
CPML : 10 cells thick
Sample : 24 cells thick in silicon
Tip : conical tip with a height of 20µm, in dispersive material
Distance tip/interface : 50nm
Incident wave : gaussian pulse (fully reflected incident wave)
Domain of 250 18⨯ 02 cells
Cubic cells : x=y=z=λ0/125 with λ0=12,5µm
CPML : 10 cells thick
Sample : 24 cells thick in silicon
Tip : conical tip with a height of 20µm, in dispersive material
Distance tip/interface : 50nm
Incident wave : gaussian pulse (fully reflected incident wave)
A-SNOM/TRSTM, near and far field
Tungsten tip , with a half-apex angle of 18.4° Incidence at 45 degrees: (behind the critical angle of 17°) TM polarization Far-field in the spectral domain (λ=12,5µm)
Tungsten tip , with a half-apex angle of 18.4° Incidence at 45 degrees: (behind the critical angle of 17°) TM polarization Far-field in the spectral domain (λ=12,5µm)
Tungsten tip: far-fieldTungsten tip: far-field
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A-SNOM/TRSTM, near and far field
Collecting opticsCollecting optics
Modeling of the collecting optics : Modeling of the collecting optics :
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I (λ ,θ)=∫0
2π∣E(λ ,θ ,ϕ)∣2 dϕ
I col.SRO (λ)=∫ΩSRO
R (λ) I (λ ,θ)dΩ
I col.OAP(λ)=∫ΩOAP
R (λ) I (λ ,θ)dΩ
φ
φtip axis (z)
tip axis (z)
collection on the top of the tip by a Schwarzschild reflective
objective (SRO)
collection on the side of the tip by off axis parabolic mirrors
(OAP)interface
azimutalintegration
integrat ion of th e far-fi eld sign al Icol. (λ)over a l arge sp ectrum
(2µm<λ<16µm
)
A-SNOM/TRSTM, near and far field
Collecting opticsCollecting optics
Modeling of the collecting optics : Modeling of the collecting optics :
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I (λ ,θ)=∫0
2π∣E(λ ,θ ,ϕ)∣2 dϕ
φ
φtip axis (z)
tip axis (z)
interface
azimutalintegration
A-SNOM/TRSTM, near and far field
I col.SRO=∫2μ m
16μm∫ΩSRO
R (λ) I (λ ,θ)dΩd λ
I col.OAP=∫2μ m
16μm∫ΩOAP
R (λ) I (λ ,θ)dΩd λ
Influence of the tip shapeInfluence of the tip shape
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Study of different tip shapes (tungsten tip, Silicon sample, θi=45°):
Study of different tip shapes (tungsten tip, Silicon sample, θi=45°):
TE polarization TM polarization
A-SNOM/TRSTM, near and far field
Influence of the tip materialInfluence of the tip material
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Study of different tip materials (Silicon sample, θi=45°):
Study of different tip materials (Silicon sample, θi=45°):
TE polarization TM polarization
A-SNOM/TRSTM, near and far field
Domain of 250 18⨯ 02 cells
Cubic cells : x=y=z=λ0/125 with λ0=12,5µm
CPML : 10 cells thick
Sample : 24 cells thick in silicon
Tip : truncated conical tip with a height of 20µm, in tungsten, with a half-apex angle of 18.4° Sphere: dispersive sphere (r=1µm)
Distance tip/interface : 50nm
Incident wave : gaussian pulse
Domain of 250 18⨯ 02 cells
Cubic cells : x=y=z=λ0/125 with λ0=12,5µm
CPML : 10 cells thick
Sample : 24 cells thick in silicon
Tip : truncated conical tip with a height of 20µm, in tungsten, with a half-apex angle of 18.4° Sphere: dispersive sphere (r=1µm)
Distance tip/interface : 50nm
Incident wave : gaussian pulse
Influence of a small sphereInfluence of a small sphere
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A-SNOM/TRSTM, near and far field
Influence of a small sphereInfluence of a small sphere
Dispersive sphere (SiC) with a radius of 1µm, above a plane silicon sample, and illuminated by an evanescent wave (θ
i=45°):
Dispersive sphere (SiC) with a radius of 1µm, above a plane silicon sample, and illuminated by an evanescent wave (θ
i=45°):
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TE polarization TM polarization
A-SNOM/TRSTM, near and far field
Influence of a small sphereInfluence of a small sphere
Dispersive sphere with a radius of 1µm, above a plane silicon sample, at the extremity of a tungsten tip, and illuminated by an evanescent wave (θ
i=45°):
Dispersive sphere with a radius of 1µm, above a plane silicon sample, at the extremity of a tungsten tip, and illuminated by an evanescent wave (θ
i=45°):
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TE polarization TM polarization
A-SNOM/TRSTM, near and far field
Conclusions and prospectsConclusions and prospects
Conclusions: FDTD and NFTFF models give the angular distribution of the far
field over 4πsr, at numerous wavelengths, with only one numerical simulation in the time domain Models usable with any tip shape and material and any
collecting optics, in order to optimize any A-SNOM device
Prospects: Study of structured and rough surfaces Creation of surface plasmon and phonon polaritons Introduction of thermal incoherent sources (true TRSTM)
Conclusions: FDTD and NFTFF models give the angular distribution of the far
field over 4πsr, at numerous wavelengths, with only one numerical simulation in the time domain Models usable with any tip shape and material and any
collecting optics, in order to optimize any A-SNOM device
Prospects: Study of structured and rough surfaces Creation of surface plasmon and phonon polaritons Introduction of thermal incoherent sources (true TRSTM)
Conclusion
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