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Nanophotonics Class 2 Surface plasmon polaritons

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Nanophotonics

Class 2

Surface plasmon polaritons

Surface plasmon polariton: EM wave at metal-dielectric interface

z

x

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

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

Derivation of surface plasmon dispersion relation: k()

Wave equation:

Substituting SP wave + boundary conditions leads to the

Dispersion relation:

x-direction:

Note: in regular dielectric:

Dispersion relation:

x-direction:

z-direction:

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

so: m < -d

Dielectric constant of metals

Drude model: conduction electrons with damping: equation of motion

with collision frequencyg and plasma frequency

If g << wp, then:

no restoring force

Measured data and model for Ag:

Drude model:

Modified Drude model:

Contribution of bound electrons

Ag:

Bound SP modes: m < -d

-d

bound SP mode:m< -d

z

x

Dielectric: ed

Metal: em = em' + em"

Surface plasmon dispersion relation:

w

Radiative modes

real kx real kz

(e'm > 0)

wp

Quasi-bound modes

imaginary kx real kz

(-ed < e'm < 0)

real kx imaginary kz

Bound modes

(e'm < -ed)

Re kx

Surface plasmons dispersion:

w

large k

small wavelength

3.4 eV

(360 nm)

X-ray wavelengths

at optical frequencies

Ar laser:

vac = 488 nm

diel = 387 nm

SP = 100 nm

Ag/SiO2

Re kx

Surface plasmon dispersion for thin films

Drude model

ε1(ω)=1-(ωp/ω) 2

Two modes appear

Thinner film:

Shorter SP

wavelength

Propagation

lengths: cm !!!

(infrared)

Example:

HeNe = 633 nm

SP = 60 nm

L-

L+(asymm)

L-(symm)

E

r

z

k

E

Fundamental

SPP mode

on cylinder:

- Can this adiabatic coupling scheme be realized in practice?

taper theory first demonstrated by

Stockman, PRL 93, 137404 (2004)

E

+

+

+

+

+

+

+

E

|E|

z

1 µm

x

k

1 µm

Delivering light to the nanoscale

nanoscale

confinement

Field symmetry at tip similar to SPP mode in conical waveguide

Optics Express 16, 45 (2008)

Ewold Verhagen, Kobus Kuipers

λ = 1.5 μm

Au

Er

Al2O3

Ewold Verhagen, Kobus Kuipers

1 µm

Er3+ energy levels

(1490 nm)

60 nmapex diam.

transmission

10 µm

PL Intensity (counts/s)

lexc = 1490 nm

Nano Lett. 7, 334 (2007)

Ewold Verhagen, Kobus Kuipers

E

z

x

k

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

550 nm

660 nm

Plasmonic hot-spot

Theory: Stockman, PRL 93, 137404 (2004)

Optics Express 16, 45 (2008)

Ewold Verhagen, Kobus Kuipers

sym

asym

Et, H

1 µm

E

+

+

+

tip

+

+

+

+

start

|E|2

z = -35 nm

n1 = 1

1 µm

n2 = 1.74

- Nanofocusing predicted: 100 x |E|2at 10 nm from tip
- 3D subwavelength confinement: 1.5 µm light focused to 92 nm (/16)
- limited by taper apex (r=30 nm)

Optics Express 16, 45 (2008)

Ewold Verhagen, Kobus Kuipers

<w>=50 nm, L=485 nm

<w>=100 nm, L=485 nm

100 nm

100 nm

- Silica substrates with 250-500 nm thick Ag
- Ring width: 50-100 nm
- Two-step milling process
- ~7° taper angle

Nano Lett. 9,in press (2009)

René de Waele, Stanley Burgos

- Excitation above resonance, w>wsp
- 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

René de Waele, Stanley Burgos

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

Plasmonic multiplexer

Plasmonic integrated circuits

Plasmonic lens

Plasmonic concentrator

thin section

Andmuch more …..

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 scales

below the diffraction limit