A Bloch wave numerical scheme for scattering problems in periodic wave-guides
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Date
2017-08-01
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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.
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Keywords
Helmholtz equation, radiation condition, locally periodic media, Bloch waves, negative refraction