sub- l metallic surfaces : a microscopic analysis
DESCRIPTION
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 PresentationTRANSCRIPT
Sub- metallic surfaces : a microscopic analysis
Philippe Lalanne
INSTITUT d'OPTIQUE, Palaiseau - France
Haitao Liu (Nankai Univ.)Jean-Paul Hugonin
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
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
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
The extraordinary optical transmission
T. W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio and P.A. Wolff, Nature 391, 667 (1998).
1/(µm-1)
k//
transmittance (,k//)
Two branches
EOT peak
SPP of the flat interface
minimum
T (
%)
(nm)
0
1
2
800640 720
Black : experiment red : Fano fitC. Genet et al. Opt. Comm. 225, 331 (2003)
The extraordinary optical transmission
The extraordinary optical transmission
T. W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio and P.A. Wolff, Nature 391, 667 (1998).
?
The extraordinary optical transmission
a grating scattering problem
=
Phil. Mag. 4, 396-402 (1902).
What is learnt from grating theory?
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
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?
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
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
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
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
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
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
r
xt k( )
xk( )
xk( )
xt k( )
xk( )
Microscopic pure-SPP model
H. Liu, P. Lalanne, Nature 452, 448 (2008).
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!
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
A 1
2αβ
(ρ τ)t t
u
2
A 1
2α
(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
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
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|
A 1
2αβ
(ρ τ)t t
u
2
A 1
2α
(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
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
=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).