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Sub- metallic surfaces : a microscopic analysis Philippe Lalanne INSTITUT d'OPTIQUE, Palaiseau - France Haitao Liu (Nankai Univ. Jean-Paul Hugonin

Sub- l metallic surfaces : a microscopic analysis

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Sub- l metallic surfaces : a microscopic analysis. La TEO a été decouverte il y a une dixaine d'annees. Elle est rapidement devenue un phénomène emblématique de la plasmonique qui a suscites des querelles, des polémiques, des passions souvent trop fortes pour expliquer. Philippe Lalanne - PowerPoint PPT Presentation

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Page 1: Sub- l  metallic surfaces : a microscopic analysis

Sub- metallic surfaces : a microscopic analysis

Philippe Lalanne

INSTITUT d'OPTIQUE, Palaiseau - France

Haitao Liu (Nankai Univ.)Jean-Paul Hugonin

Page 2: Sub- l  metallic surfaces : a microscopic analysis

z

exp(-1z)

exp(-2z)

z

x

SPPs are localized electromagnetic modes/ charge density oscillations at the interfaces, which

exponentially decay on both sides

c

dm

dm( )1/2

kSP=

x

Dielectric

Metal

Surface plasmon Surface plasmon polaritonpolariton

Page 3: Sub- l  metallic surfaces : a microscopic analysis

Dielectricx

Drude model : |2

z

kSP

exp(-z/1)

= 1/2/2 >>

Surface plasmon polariton

k

Re(/c)

p/2

=ck

kSP

exp(-z/2)

= 1/2/2 cte

Page 4: Sub- l  metallic surfaces : a microscopic analysis

1.The emblematic example of the EOT-extraordinary optical transmission (EOT)-limitation of classical "macroscopic" grating theories-a microscopic pure-SPP model of the EOT

2.SPP generation by 1D sub- indentation-rigorous calculation (orthogonality relationship)-slit example-scaling law with the wavelength

3.The quasi-cylindrical wave-definition & properties-scaling law with the wavelength

4.Multiple Scattering of SPPs & quasi-CWs-definition of scattering coefficients for the quasi-CW

Page 5: Sub- l  metallic surfaces : a microscopic analysis

The extraordinary optical transmission

T. W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio and P.A. Wolff, Nature 391, 667 (1998).

Page 6: Sub- l  metallic surfaces : a microscopic analysis

1/(µm-1)

k//

transmittance (,k//)

Two branches

EOT peak

SPP of the flat interface

minimum

Page 7: Sub- l  metallic surfaces : a microscopic analysis

T (

%)

(nm)

0

1

2

800640 720

Black : experiment red : Fano fitC. Genet et al. Opt. Comm. 225, 331 (2003)

The extraordinary optical transmission

Page 8: Sub- l  metallic surfaces : a microscopic analysis

The extraordinary optical transmission

T. W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio and P.A. Wolff, Nature 391, 667 (1998).

?

Page 9: Sub- l  metallic surfaces : a microscopic analysis

The extraordinary optical transmission

a grating scattering problem

=

Page 10: Sub- l  metallic surfaces : a microscopic analysis

Phil. Mag. 4, 396-402 (1902).

What is learnt from grating theory?

Page 11: Sub- l  metallic surfaces : a microscopic analysis

Wire grid polarizer

Inductive-capacitive grids

•Hertz (1888) first used a wire grid polarizer for testing the newly discovered radio wave.•J.T. Adams and L.C. Botten J. Opt. (Paris) 10, 109–17 (1979).•R. Ulrich, K. F. Renk, and L. Genzel, IEEE Trans. Microwave Theory Tech. 11, 363 (1963).•C. Compton, R. D. McPhedran, G. H. Derrick, and L. C. Botten, Infrared Phys. 23, 239 (1983).

Nearly 100% of the incident energy is transmitted at resonance frequencies for TM polarization

Page 12: Sub- l  metallic surfaces : a microscopic analysis

Poles and zeros of the Poles and zeros of the scattering matrixscattering matrix

d

tF

700 750 8000

0.1

0.2

(nm)

|tF|2

E. Popov et al., PRB 62, 16100 (2000).

tF -z

-prF

-Global analysis.-Why does the pole exist? Why does the zero exist? Why are they close or not to the real axis?

Page 13: Sub- l  metallic surfaces : a microscopic analysis

tF =tA

2 exp(ik0nd)rA

2 exp(2ik0nd)

The surface-mode interpretation

L. Martín-Moreno, F. Garcia-Vidal & J. Pendry, Phys. Rev. Lett. 86, 1114 (2001).

Resonance-assisted tunneling

650 700 750 8000

10

20

30

(nm)

rA

drA

tA

tF

Page 14: Sub- l  metallic surfaces : a microscopic analysis

1/

P. Lalanne, J.C. Rodier and J.P. Hugonin , J. Opt. A 7, 422 (2005).

k//

Mode of the perforated interface = pole of rA or tA

The surface-mode interpretation

SPP of the flat interface

|Hy|

Hybrid character

Page 15: Sub- l  metallic surfaces : a microscopic analysis

tF =tA

2 exp(ik0nd)rA

2 exp(2ik0nd)

The surface-mode interpretation

L. Martín-Moreno, F. Garcia-Vidal & J. Pendry, Phys. Rev. Lett. 86, 1114 (2001).

Resonance-assisted tunneling

650 700 750 8000

10

20

30

(nm)

rA reinforcement of the initial vision of a SPP assisted effect

drA

tA

tF

Page 16: Sub- l  metallic surfaces : a microscopic analysis

Theory :J. Pendry, L. Martín-Moreno & F. Garcia-Vidal, Science 305, 847 (2004).

Experimental verification :P. Hibbins et al., Science 308, 670 (2004).

The surface-mode also exists as

perfectconductor

"SPOOF" SPP

Page 17: Sub- l  metallic surfaces : a microscopic analysis

tF =tA

2 exp(ik0nd)rA

2 exp(2ik0nd)

Weaknesses of classical grating theories

-The resonance of tF is explained by the resonance of another scattering coefficients.-In reality, nothing is known about the waves that are launched in between the hole and that are responsible for the EOT

L. Martín-Moreno, F. Garcia-Vidal & J. Pendry, Phys. Rev. Lett. 86, 1114 (2001).

Resonance-assisted tunneling

rA

650 700 750 8000

10

20

30

(nm)

rA

Page 18: Sub- l  metallic surfaces : a microscopic analysis

M. C. Hutley and D. Maystre, “Total absorption of light by a diffraction grating,” Opt. Commun. 19, 431-436 (1976).D. Maystre, General study of grating anomalies from electromagnetic surfacemodes, in: A.D. Boardman (Ed.), Electromagnetic Surface Modes, Wiley, NY,1982, (chapter 17).

/30

R(,)=0r -z

-p

Page 19: Sub- l  metallic surfaces : a microscopic analysis
Page 20: Sub- l  metallic surfaces : a microscopic analysis

r

xt k( )

xk( )

xk( )

xt k( )

xk( )

Microscopic pure-SPP model

H. Liu, P. Lalanne, Nature 452, 448 (2008).

Page 21: Sub- l  metallic surfaces : a microscopic analysis

SPP coupled-mode equations

Coupled-mode equations

• An = w1w2…wn (kx) + unAn1 + unBn+1

• Bn = w1w2…wn (kx) + un+1Bn-1 + unAn1

• cn = w1w2…wn t(kx) + unAn-1 + un+1Bn+1

with un = exp(ikSPan) , wn = exp(ikxan)

Periodicity is Periodicity is not needed!not needed!

Page 22: Sub- l  metallic surfaces : a microscopic analysis

only non-resonant quantities

drA

tA

tF

tF =tA

2 exp(ik0nd)

1- rA2 exp(2ik0nd)

tA = t +2

u-1 (+)rA =

22

u-1 (+)

Microscopic pure-SPP model

Page 23: Sub- l  metallic surfaces : a microscopic analysis

A 1

2αβ

(ρ τ)t t

u

2

A 1

(ρ τ)r r

u

|u|1u=exp(ikSPa) |u |-1 slightly larger than 1

||1 slightly smaller than 1

resonance conditionRe(kSP)a+arg() 0 modulo 2

SPP coupled-mode equations (kx=0)

Microscopic interpretation

Page 24: Sub- l  metallic surfaces : a microscopic analysis

holes slits holes slits

tF =tA

2 exp(ik0nd)rA

2 exp(2ik0nd)

•n complex•|exp(2ik0nd)| <<1•pole of tF = pole of rA (for k0d>>1)

•n real•|exp(2ik0nd)|=1•no relation between the pole of tF and that of rA

FP condition: arg(rA)+k0nd=2m

Page 25: Sub- l  metallic surfaces : a microscopic analysis

holes slits holes slits

tF =tA

2 exp(ik0nd)rA

2 exp(2ik0nd)

1 1.20

10

20

30

/a

|rA|

1 1.20

1

/a

|rA|

Page 26: Sub- l  metallic surfaces : a microscopic analysis

A 1

2αβ

(ρ τ)t t

u

2

A 1

(ρ τ)r r

u

|u|1u=exp(ikSPa) |u |-1 slightly larger than 1

||1 slightly smaller than 1

resonance conditionRe(kSP)a+arg() 0 modulo 2

SPP coupled-mode equations (kx=0)

Microscopic interpretation

Page 27: Sub- l  metallic surfaces : a microscopic analysis

resonance condition :

Re(kSP)a + arg() kxa (modulo 2

Microscopic interpretation

the macroscopic surface Bloch mode

superposition of many elementary SPPs scattered by individual hole chains that fly over adjacent chains and sum up constructively

Page 28: Sub- l  metallic surfaces : a microscopic analysis

=0°

0.95 1 1.05 1.1 1.15

0

0.1

0.2

a=0.68 µm

a=0.94 µm

a=2.92 µm

Tra

nsm

itta

nce

/a

RCWASPP model

Influence of the metal conductivity

H. Liu & P. Lalanne, Nature 452, 448 (2008).