Authors: Dohnal, Tomáš
Schweizer, Ben
Title: A Bloch wave numerical scheme for scattering problems in periodic wave-guides
Language (ISO): en
Abstract: We present a new numerical scheme to solve the Helmholtz equation in a wave-guide. We consider a medium that is bounded in the x2-direction, unbounded in the x1-direction and ε-periodic for large |x1|, allowing different media on the left and on the right. We suggest a new numerical method that is based on a truncation of the domain and the use of Bloch wave ansatz functions in radiation boxes. We prove the existence and a stability estimate for the infinite dimensional version of the proposed problem. The scheme is tested on several interfaces of homogeneous and periodic media and it is used to investigate the effect of negative refraction at the interface of a photonic crystal with a positive effective refractive index.
Subject Headings: Helmholtz equation
radiation condition
locally periodic media
Bloch waves
negative refraction
Issue Date: 2017-08-01
Appears in Collections:Preprints der Fakultät für Mathematik
Schweizer, Ben Prof. Dr.

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