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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: - k x is real - k z is imaginary. EM wave is coupled to the plasma oscillations of the surface charges.

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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)


Cylindrical metal waveguides

E

r

z

k

Cylindrical metal waveguides

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


Concentration of light in a plasmon taper experiment

λ = 1.5 μm

Au

Er

Al2O3

Concentration of light in a plasmon taper: experiment

Ewold Verhagen, Kobus Kuipers


Concentration of light in a plasmon taper experiment1

1 µm

Er3+ energy levels

(1490 nm)

Concentration of light in a plasmon taper: experiment

60 nmapex diam.

transmission

10 µm

PL Intensity (counts/s)

lexc = 1490 nm

Nano Lett. 7, 334 (2007)

Ewold Verhagen, Kobus Kuipers


Concentration of light in a plasmon taper experiment2

E

z

x

k

Concentration of light in a plasmon taper: experiment

  • 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


Fdtd simulation nanofocussing to 100 nm

sym

asym

Et, H

1 µm

E

+

+

+

tip

+

+

+

+

start

FDTD Simulation: nanofocussing to < 100 nm

|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



Fib milling of coaxial waveguides
FIB milling of coaxial waveguides

<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


Narrow channels show negative index
Narrow channels show negative index

  • 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


Positive and negative index modes
Positive and negative index modes

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


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