Geodesic
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

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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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2018026
Classification : 35Q60, 35P25, 35B27
Keywords: Helmholtz equation, radiation, waveguide, Bloch analysis, outgoing wave condition, photonic crystal, transmission problem, negative refraction

Lamacz, A. 1 ; Schweizer, B. 1

1 
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     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://geodesic.mathdoc.fr/articles/10.1051/m2an/2018026/}
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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

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