Nanophotonics Class 2 - Surface Plasmon Polaritons

Nanophotonics

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

tzkxkidd

zxeEtzxE 0,,,

tzkxkimm

zxeEtzxE 0,),,(

For propagating bound waves:- kx is real- kz is imaginary

x

z

Derivation of surface plasmon dispersion relation: k()

Wave equation:

Substituting SP wave + boundary conditions leads to the

Dispersion relation: 2/1

"'

dm

dmxxx c

ikkk

2,

2

,0,0,2

t

EE md

mdmdmd

x-direction:

ckNote: in regular dielectric:

2

k

Dispersion relation:

2/1

"'

dm

dmxxx c

ikkk

x-direction:

Bound SP mode: kz imaginary: m + d < 0, kx real: m < 0

so: m < -d

2/12

,,, "'

dm

mmzmzmz c

ikkk

z-direction:

ck

2

k

iim

Ne

E

Nex

E

P p

2

2

20

2

00

1111

0

2

m

Nep

Dielectric constant of metals

Drude model: conduction electrons with damping: equation of motion

with collision frequency and plasma frequency

If << p, then:

3

2

2

2

",1' pp

tieEdt

dxm

dt

xdm e02

2

no restoring force

Measured data and model for Ag:

3

2

2

2

",1' pp

3

2

2

2

",' pp

Drude model:

Modified Drude model:

Contribution of bound electrons

Ag: 45.5

200 400 600 800 1000 1200 1400 1600 1800-150

-100

-50

0

50

Measured data: ' "

Drude model: ' "

Modified Drude model: '

"

Wavelength (nm)

'

Bound SP modes: m < -d

200 400 600 800 1000 1200 1400 1600 1800-150

-100

-50

0

50

Measured data: ' "

Drude model: ' "

Modified Drude model: '

"

Wavelength (nm)

'

bound SP mode: m < -d

-d

p

d

p

1

Re kx

real kx

real kz

imaginary kx

real kz

real kx

imaginary kz

d

xck

Bound modes

Radiative modes

Quasi-bound modes

Surface plasmon dispersion relation:

Dielectric: d

Metal: m = m' +

m"

x

z

'm > 0)

d < 'm < 0)

('m < d)

2/1

dm

dmx c

k

Re kx

d

xck

Surface plasmons dispersion:

large k

small wavelength

Ar laser: vac = 488 nmdiel = 387 nmSP = 100 nmAg/SiO2

3.4 eV(360 nm)

X-ray wavelengthsat optical frequencies

2/1

dm

dmx c

k

2

k

Surface plasmon dispersion for thin filmsDrude model

ε1(ω)=1-(ωp/ω) 2 Two modes appear

L-

L-(symm)

Thinner film:Shorter SP wavelength

Example:HeNe = 633 nm

SP = 60 nm

L+(asymm)

Propagationlengths: cm !!!(infrared)

Cylindrical metal waveguides

k

E

z

rFundamentalSPP modeon cylinder:

E

• Can this adiabatic coupling scheme be realized in practice?

taper theory first demonstrated byStockman, PRL 93, 137404 (2004)

Delivering light to the nanoscale

0.0 0.2 0.4 0.6 0.8 1.01.7

1.8

1.9

2.0

2.1

2.2

2.3

neff =

kSPP/k

0

Waveguide width (µm)

1 µm

1 µm

|E|Field symmetry at tip similar to SPP mode in conical waveguide

E

++++++

+

Ewold Verhagen, Kobus Kuipers

k

E

xz

nanoscaleconfinement

Optics Express 16, 45 (2008)

Concentration of light in a plasmon taper: experiment


Au

Er

Al2O3

λ = 1.5 μm

exc = 1490 nm

PL

Inte

nsi

ty (

counts

/s)

10 µm

Ewold Verhagen, Kobus Kuipers (1

49

0 n

m)

Er3+

ene

rgy

leve

ls

transmission

1 µm

60 nm apex diam.

Nano Lett. 7, 334 (2007)


550 nm

660 nm

• Detecting upconversion luminescence from the air side of the film (excitation of SPPs at substrate side)


Plasmonic hot-spot


k

E

xz

Theory: Stockman, PRL 93, 137404 (2004)


FDTD Simulation: nanofocussing to < 100 nm

z = -35 nm

• Nanofocusing predicted: 100 x |E|2 at 10 nm from tip

• 3D subwavelength confinement: 1.5 µm light focused to 92 nm (/16)

• limited by taper apex (r=30 nm)

n1 = 1

n2 = 1.74

1 µm

1 µm

|E|2

starttip

+ ++++++

E



sym asym

Et, H

Coaxial MIM plasmon waveguides

FIB milling of coaxial waveguides

100 nm 100 nm

• Silica substrates with 250-500 nm thick Ag

• Ring width: 50-100 nm

• Two-step milling process

• ~7° taper angle

<w>=100 nm, L=485 nm <w>=50 nm, L=485 nm

René de Waele, Stanley BurgosNano 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 to power flow

• Negative refractive index of -2

René de Waele, Stanley Burgos

Positive and negative index modes

René de Waele, Stanley Burgos

Plasmonic toolbox: , (), d - Engineer ()

0 200 400 600 800 1000

-1.0

-0.5

0.0

0.5

1.0

Y A

xis

Titl

e

Distance (nm)

thin section

Plasmonic concentrator Plasmonic lens

Plasmonic multiplexer

And much more …..

Plasmonic integrated circuits

Conclusions: surface plasmon polariton

Surface plasmon: bound EM wave at metal-dielectric interface

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

Control dispersion: control (k), losses, concentration

Manipulate light at length scalesbelow the diffraction limit

Nanophotonics Class 2 - Surface Plasmon Polaritons

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