Rayleigh-Bloch waves trapped by a periodic perturbation: exact solutions
arXiv:1711.10083 · doi:10.1007/s00033-018-0953-6
Abstract
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.
11 pages, 1 figure