Radiation loss coefficients of asymmetric dielectric waveguides with shallow sinusoidal corrugations

Kiselev [10] has solved the boundary equations for an asymmetric slab waveguide with a shallow sinusoidal corrugation, and derived explicit, closed expressions for the TE radiation loss coefficients of various waveguide geometries. For many practical applications in integrated optics, the Rayleigh assumption justifying the boundary-matching procedure and the approximations of linear perturbation analysis employed in this derivation are both satisfied. We have extended this procedure to TM modes and found that the expressions for both TE and TM modes in all of the geometries so treated agree identically with those derived by coupled-mode theory. The dependence of the TM radiation loss coefficient in each waveguide geometry on the grating period, radiation angle, refractive index profile, and mode polarization is illustrated graphically, and compared with its TE counterpart.