We analyze the propagation of waves in unbounded photonic crystals. Waves are described by a Helmholtz equation with x-dependent coefficients, the scattering problem must be completed with a radiation condition at infinity. We develop an outgoing wave condition with the help of a Bloch wave expansion. Our radiation condition admits a 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 show 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.
Accepté le :
DOI : 10.1051/m2an/2018026
Mots-clés : Helmholtz equation, radiation, waveguide, Bloch analysis, outgoing wave condition, photonic crystal, transmission problem, negative refraction
@article{M2AN_2018__52_5_1913_0,
author = {Lamacz, A. and Schweizer, B.},
title = {Outgoing wave conditions in photonic crystals and transmission properties at interfaces},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1913--1945},
publisher = {EDP-Sciences},
volume = {52},
number = {5},
year = {2018},
doi = {10.1051/m2an/2018026},
mrnumber = {3885700},
zbl = {1414.35222},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2018026/}
}
TY - JOUR AU - Lamacz, A. AU - Schweizer, B. TI - Outgoing wave conditions in photonic crystals and transmission properties at interfaces JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 1913 EP - 1945 VL - 52 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2018026/ DO - 10.1051/m2an/2018026 LA - en ID - M2AN_2018__52_5_1913_0 ER -
%0 Journal Article %A Lamacz, A. %A Schweizer, B. %T Outgoing wave conditions in photonic crystals and transmission properties at interfaces %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 1913-1945 %V 52 %N 5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2018026/ %R 10.1051/m2an/2018026 %G en %F M2AN_2018__52_5_1913_0
Lamacz, A.; Schweizer, B. Outgoing wave conditions in photonic crystals and transmission properties at interfaces. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 5, pp. 1913-1945. doi : 10.1051/m2an/2018026. http://archive.numdam.org/articles/10.1051/m2an/2018026/
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