A periodic knitting problem for the Helmholtz equation

We study a diffraction of a plane wave incident to a periodic surface separating two dielectric materials with different real dielectric coefficients. Existence and uniqueness of solution to a periodic knitting problem for the Helmholtz equation is proved. Moreover we prove that the solution can be approximated by linear combinations of reflected and transmitted waves (the Rayleigh method). (C) 1997 Academic Press.