Rayleigh–Bloch waves trapped by a periodic perturbation: exact solutions

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 quasip...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2018-06, Vol.69 (3), p.1-9, Article 72
Main Authors: Merzon, A., Zhevandrov, P., Romero Rodríguez, M. I., De la Paz Méndez, J. E.
Format: Article
Language:English
Subjects:
Bloch waves
Engineering
Exact solutions
Helmholtz equations
Mathematical analysis
Mathematical Methods in Physics
Periodic variations
Refractivity
Theoretical and Applied Mechanics
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Summary: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.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-018-0953-6