Speckle correlation functions applied to surface plasmons

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Speckle correlation functions applied to surface plasmons Frerik van Beijnum Jeroen Sirre Chris Rétif (AMOLF) Martin van Exter

Transcript of Speckle correlation functions applied to surface plasmons

Speckle correlation functions applied to surface plasmons

Frerik van BeijnumJeroen Sirre

Chris Rétif (AMOLF)Martin van Exter

Speckle correlation functions applied to surface plasmons

What is a speckle correlation function?

λ=532 nm, C=1 λ=633 nm, C=0

What is a speckle correlation function?

λ=532 nm, C=1 λ=633 nm, C=0

Averaged change of speckle pattern as a function of

wavelength or angle

The traditional speckle correlation function

3D medium: slab of strongly scattering particles

PRL 64, 2788 (1990)

The traditional speckle correlation function

3D medium: slab of strongly scattering particles

PRL 64, 2788 (1990)

Compared to the complexity of the disorder the correlation

function is simple

Speckle correlation functions applied to surface plasmons

A surface plasmon polariton (SPP)

Image from: Nature 424, 824 (2004)

Surface wave

Suffers from absorption, propagates typically 10-50

µm

Subwavelength holes excite surface plasmons

Surface plasmons in ordered systems

- holes excite surface plasmons- direct transmission- More than ten years of research to understand and apply extraordinary optical transmission

Nature 391, 667 (1998)

Surface plasmons in ordered systems

- holes excite surface plasmons- direct transmission- More than ten years of research to understand and apply extraordinary optical transmission

Nature 391, 667 (1998)

Compared to the simplicity of the structure the understanding the

transmission spectrum is complicated

How to apply correlation functions to surface plasmons?

Interesting and new:

two transmission processes, direct (black) and surface plasmon assisted (red)

Are speckles seen in transmission?

Very faint speckle pattern

Intensity normalized to peak transmissionOL 36, 3666 (2011)

Does the speckle change with wavelength?

Does the speckle change with wavelength?

Does the speckle change with wavelength?

Why do the speckles only change slightly?

Different result than for 3D media

How does the speckle correlation function change with hole density?

Surface plasmon contribution increases with density

Simple model for correlation function

Distance between holes

hole i

hole j

Simple model for correlation function

scattering loss

hole i

hole j

Simple model for correlation function

absorption

hole i

hole j

Simple model for correlation function

phase acquired

hole i

hole j

Simple model for correlation function

hole i

hole j

Correlation width can be separatedin scattering and absorption

Scattering reduces the propagation length by a factor 5

Measured cross section is roughly a fifth of the hole diameter

Absorption agrees with theory

The plasmon contribution vanishes at low density

One parameter fit describes data

Last data point deviates again.

Deviations from model are expected at high densities (hole per squared wavelength).

Conclusions• We applied correlation functions to surface plasmons• Direct and indirect contribution can be separated• Hole density is a crucial parameter• Simple model describes data for medium and low densities

Accepted for publication in PRB