Abstract: We considered a planar dielectric-layer modulated grating. It has been shown that the diffraction problem may be modeled by a Helmholtz equation with periodic coefficients. The diffraction problem may be solved by a Galerkin-spectral method. In this paper, the optimal error estimates and the numerical results for the Galerkin-spectral method are established.

Key words: Helmholtz equation, periodic structure, Galerkin-spectral method