On scattering of waves by the infinite grating of elliptic cylinders

The functional equation derived previously for the scattering by a grating of relatively arbitrary elements is applied to elliptic cylinders. This specifies the problem in terms of an infinite set of linear algebraic equations involving the scattering coefficients of an isolated elliptic cylinder and certain combinations of Schlömilch series. General approximations are obtained by series expansions, and by truncating the sets of equations; we consider both polarizations ( or parallel to the elements), arbitrary angle of incidence, and arbitrary spacing. Explicit results are given for ellipses that are small compared to the wavelength.