Plasmonic waves  allow perfect transmission through sub-wavelength metallic gratings

Guy Bouchitté; Ben Schweizer

doi:10.3934/nhm.2013.8.857

Article Contents

2013, Volume 8, Issue 4: 857-878. Doi: 10.3934/nhm.2013.8.857

This issue Previous Article Asymptotic periodicity of flows in time-depending networks Next Article On the passage from atomistic systems to nonlinear elasticity theory for general multi-body potentials with p-growth

Plasmonic waves allow perfect transmission through sub-wavelength metallic gratings

Guy Bouchitté^1, and
Ben Schweizer^2,

1.
Université de Toulon, IMATH, EA 2134, 83957 La Garde
2.
Technische Universität Dortmund, Fakultät für Mathematik, Vogelpothsweg 87, D-44227 Dortmund

Received: November 2012

Revised: July 2013

Published online: November 2013

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Abstract

We investigate the transmission properties of a metallic layer with narrow slits. Recent measurements and numerical calculations concerning the light transmission through metallic sub-wavelength structures suggest that an unexpectedly high transmission coefficient is possible. We analyze the time harmonic Maxwell's equations in the $H$-parallel case for a fixed incident wavelength. Denoting by $\eta>0$ the typical size of the complex structure, effective equations describing the limit $\eta\to 0$ are derived. For metallic permittivities with negative real part, plasmonic waves can be excited on the surfaces of the channels. When these waves are in resonance with the height of the layer, the result can be perfect transmission through the layer.

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Mathematics Subject Classification: Primary: 78M40, 35J05; Secondary: 35P25.

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