The electromagnetic wave interactions in a sinusoidally corrugated dielectric waveguide are analyzed for the oblique incidence case.
The coupled mode equations which govern the interactions are derived by the sigular perturbation method for the TE-TE mode coupling. The results are compared with those of Wagatsuma et al.'s normal mode analysis and Stegeman et al.'s total field analysis. Comparison with the results of Seshadri's analysis on the planar dielectric waveguide with a sinusoidally modulated refractive index gives the conversion relation between the two modulation indices.
Also, beam splitting phenomena in a two dimensionally corrugated dielectric waveguide which were observed experimentally by A. Yi-Yan et al. are analyzed quantitatively. 3-wave coupled equations which govern the interactions among the incident and the two reflected waves are derived by the singular perturbation method. The diffraction efficiencies are also calculated for the two types of grating structures, reflection and transmission types.
