Analysis of grating couplers in planar waveguides for waves at oblique incidence

A grating coupler is investigated for the case when the incident direction of a guided wave in a planar waveguide is inclined, within the guide plane, to the direction of a grating vector. The coupling and conversion between a TE, or TM, guided mode and the TE and TM radiative and nonradiative modes are considered in a weakly corrugated guide. The amplitude transport equation and the expressions for the leakage parameter, and the phase correction to a wave number of an unperturbed waveguide, are deduced using a quasi-optical technique. The power-conservation relation of a grating coupler for obliquely incident waves is established, and the coupling and conversion efficiencies are examined. It has been found that significant differences exist for excitation, or scattering, of waves at the normal and oblique incidences.