Outgoing wave conditions in photonic crystals and transmission properties at interfaces
Loading...
Date
2015-08-31
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Alternative Title(s)
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.
Description
Table of contents
Keywords
Helmholtz equation, radiation, Bloch analysis, outgoing wave condition, photonic crystal, transmission problem, negative refraction