Ray-optical determination of the coupling coefficients of grating waveguide by use of the rigorous coupled-wave theory

The ray-optics approach based on the rigorous coupled wave theory called ri gorous ray-optics method (RROM), is developed for the calculation of backwa rd coupling coefficients of grating waveguide devices, The coupling coeffic ients of several grating structures, such as rectangular, sinusoidal, trian gular, and trapezoidal shapes, are evaluated by the RROM, and they are comp ared with those obtained by two conventional methods of the ray-optics meth od (ROM) and the coupled-mode method (CMM). In the case of rectangular grat ings, the coupling coefficients are evaluated in more detail by varying gra ting depth and duty-cycle. We have found that the RROM gives us more exact solutions for the backward coupling coefficients of even arbitrary shapes o f diffractive grating waveguides than the other two conventional methods.