Near-field and far-field modeling of surface waves ...

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


Numerical models

Validation


Contents

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ContentsContents

Numerical models

4


Numerical models

Validation



Numerical models

Validation


A-SNOM/TRSTM : principlesA-SNOM/TRSTM : principles

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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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Example of TRSTM deviceExample of TRSTM device

TRSTM devicein developmentin our lab.

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AFM

sample

collecting optic(2 parabolic mirrors)

MCT detector

ContentsContents

Numerical models

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Numerical models

Validation



Numerical models

Validation


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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Numerical models

Validation



Numerical models

Validation


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



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)

vid/SphereT45eva.mpg

ContentsContents


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Numerical models

Validation



Numerical models

Validation


3D computational domain3D computational domain

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Domain of 250 18⨯ 02 cells



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)





Tip : conical tip with a height of 20µm, in dispersive material


Incident wave : gaussian pulse (fully reflected incident wave)


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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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

)


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


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


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°):







Tip : truncated conical tip with a height of 20µm, in tungsten, with a half-apex angle of 18.4° Sphere: dispersive sphere (r=1µm)


Incident wave : gaussian pulse





Tip : truncated conical tip with a height of 20µm, in tungsten, with a half-apex angle of 18.4° Sphere: dispersive sphere (r=1µm)


Incident wave : gaussian pulse

Influence of a small sphereInfluence of a small sphere

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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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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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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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Near-field and far-field modeling of surface waves ...

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