Diffraction coupling of radiation into a thin-film waveguide

A thin-film optical waveguide with a sinusoidally corrugated surface is considered. This waveguide acts as a phase diffraction grating. The relationships between the waveguide parameters and the parameters of the exciting beam, ensuring the most effective coupling of the radiation into a specified waveguide mode, are determined for an arbitrary ratio of the grating period to the wavelength of light and for a relatively weak depth of modulation of the film thickness (i.e., for relatively weak coupling conditions).