Outgoing wave conditions in photonic crystals and transmission properties at interfaces

Agnes Lamacz; Ben Schweizer

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arXiv · 1509.00683

Outgoing wave conditions in photonic crystals and transmission properties at interfaces

Agnes Lamacz·Ben Schweizer

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Abstract

We analyze the propagation of waves in unbounded photonic crystals, the waves are described by a Helmholtz equation with $x$-dependent coefficients. The scattering problem must be completed with a radiation condition at infinity, which was not available for $x$-dependent coefficients. We develop an outgoing wave condition with the help of a Bloch wave expansion. Our radiation condition admits a (weak) uniqueness result, formulated in terms of the Bloch measure of solutions. We use the new radiation condition to analyze the transmission problem where, at fixed frequency, a wave hits the interface between free space and a photonic crystal. We derive that the vertical wave number of the incident wave is a conserved quantity. Together with the frequency condition for the transmitted wave, this condition leads (for appropriate photonic crystals) to the effect of negative refraction at the interface.

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Agnes Lamacz, Ben Schweizer. 2017-01-09. Outgoing wave conditions in photonic crystals and transmission properties at interfaces. https://arxiv.org/abs/1509.00683

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