Efficiency of diffraction of light by a sinusoidally corrugated interface

A method is developed for the calculation of the efficiency of light scattering in an arbitrary diffraction order by a phase grating whose period and depth are comparable with the wavelength of light. The example of a sinusoidally corrugated interface is used to study numerically the convergence of the solution in respect of the expansion parameter 2πσ/λ (σ is the corrugation amplitude and λ is the wavelength of light).