Exact solutions describing the Rayleigh–Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction and of finite support in the other. These solutions are quasiperiodic along the structure and exponentially decay in the orthogonal direction. A simple formula for the dispersion relation of these waves is obtained.
Zeitschrift für angewandte Mathematik und Physik – Springer Journals
Published: May 23, 2018
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