Nanophotonics class 2 - surface plasmon polaritons

Class 2 Surface plasmon polaritons... Surface plasmon dispersion for thin films... Concentration of light in a plasmon taper: experimentEwold Verhagen, Kobus Kuipers Au Er Al2O3 λ = 1.5

Class 2

Surface plasmon polaritons

Surface plasmon polariton: EM wave at metal-dielectric interface

EM wave is coupled to the plasma oscillations of the surface charges



k x k z t

i m

 ,0)

, ,



For propagating bound waves:

- kx is real

- kz is imaginary

xz

Derivation of surface plasmon dispersion relation: k()

Wave equation:

Substituting SP wave + boundary conditions leads to the

Dispersion relation:

2 / 1

d

m x

x x

c

ik k

2 ,

0 ,

0 ,

Dispersion relation:

2 / 1

d

m x

x x

c

ik k

, ,

m m

z m

z m

z

c

ik k

Ne E

Nex E

2

0 0

1 1

1 1

Dielectric constant of metals

Drude model: conduction electrons with damping: equation of motion

with collision frequency  and plasma frequency

2

"

, 1

t i

eE dt

dx m

Measured data and model for Ag:

2

"

, 1

imaginary kx real kz

real kx imaginary kz

'm > 0)

d < 'm < 0)

('m < d)

2 / 1

d

m x

m x

Surface plasmon dispersion for thin films

Cylindrical metal waveguides

taper theory first demonstrated by

Stockman, PRL 93, 137404 (2004)

Delivering light to the nanoscale

E

+ ++

+ + + +

Ewold Verhagen, Kobus Kuipers

k

E

x z

nanoscale confinement

Optics Express 16, 45 (2008)

Concentration of light in a plasmon taper: experiment

Ewold Verhagen, Kobus Kuipers

Au Er

Al2O3

λ = 1.5 μm

Theory: Stockman, PRL 93, 137404 (2004)

Concentration of light in a plasmon taper: experiment

Coaxial MIM plasmon waveguides

FIB milling of coaxial waveguides

René de Waele, Stanley Burgos

Nano Lett 9, in press (2009)

Narrow channels show negative index

• Excitation above resonance, >sp

• 25 nm-wide channel

in Ag filled with GaP

• Simulation shows negative phase velocity with respect

Positive and negative index modes

René de Waele, Stanley Burgos

Plasmonic toolbox: , (), d - Engineer ()

And much more …

Plasmonic integrated circuits

Conclusions: surface plasmon polariton

Dispersion: (k) diverges near the plasma resonance: large k, small 

Control dispersion: control (k)) , losses, concentration

Manipulate light at length scales below the diffraction limit