Speckle correlation functions applied to surface plasmons

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  • Speckle correlation functions applied to surface plasmonsFrerik van BeijnumJeroen SirreChris Rtif (AMOLF)Martin van Exter

  • Speckle correlation functions applied to surface plasmons

  • What is a speckle correlation function?=532 nm, C=1 =633 nm, C=0

  • What is a speckle correlation function?=532 nm, C=1 =633 nm, C=0 Averaged change of speckle pattern as a function of wavelength or angle

  • The traditional speckle correlation function3D medium: slab of strongly scattering particles

    PRL 64, 2788 (1990)

  • The traditional speckle correlation function3D 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 m

    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 transmissionNature 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 transmissionNature 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 functionDistance between holeshole ihole j

  • Simple model for correlation functionscattering losshole ihole j

  • Simple model for correlation functionabsorptionhole ihole j

  • Simple model for correlation functionphase acquired hole ihole j

  • Simple model for correlation functionhole ihole j

  • Correlation width can be separatedin scattering and absorptionScattering 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 densityOne parameter fit describes data

    Last data point deviates again.

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

  • ConclusionsWe applied correlation functions to surface plasmonsDirect and indirect contribution can be separatedHole density is a crucial parameterSimple model describes data for medium and low densitiesAccepted for publication in PRB