Authors: Lamacz, Agnes
Schweizer, Ben
Title: Outgoing wave conditions in photonic crystals and transmission properties at interfaces
Language (ISO): en
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.
Subject Headings: Helmholtz equation
Bloch analysis
outgoing wave condition
photonic crystal
transmission problem
negative refraction
Issue Date: 2015-08-31
Appears in Collections:Preprints der Fakultät für Mathematik
Schweizer, Ben Prof. Dr.

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