  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.
