We present a new numerical scheme to solve the Helmholtzequation in a wave-guide. We consider a medium that is bounded inthe x2-direction, unbounded in the x1-direction and ε-periodic for large|x1|, allowing different media on the left and on the right. We suggesta new numerical method that is based on a truncation of the domainand the use of Bloch wave ansatz functions in radiation boxes. We provethe existence and a stability estimate for the infinite dimensional versionof the proposed problem. The scheme is tested on several interfaces ofhomogeneous and periodic media and it is used to investigate the effectof negative refraction at the interface of a photonic crystal with a positiveeffective refractive index.
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