RECTANGULAR CHARACTERISTIC GRATINGS FOR WAVE-GUIDE INPUT AND OUTPUT COUPLING

Normal-incidence planar-optical waveguide-imbedded phase gratings of f inite aperture width and length are analyzed with Svidzinskii's [Sov. J. Quantum Electron. 10, 1103 (1980)] two-dimensional Bragg-diffractio n theory. Svidzinskii's characteristic-grating equations are adapted f or the rectangular-grating case, and an overlap integral is used to ex tend the theory to account for the mode structure of the waveguide. Th e combined theory is used to optimize the throughput of a system compo sed of an input grating coupler, a waveguide, and an output grating co upler for both the highly multimode (thick-waveguide) and the few-mode (thin-waveguide) cases.