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

The ray-optics approach based on the rigorous coupled wave theory, called rigorous ray-optics method (RROM), is developed for the calculation of backward coupling coefficients of grating waveguide devices. The coupling coefficients of several grating structures, such as rectangular, sinusoidal, triangular, and trapezoidal shapes, are evaluated by the RROM, and they are compared with those obtained by two conventional methods of the ray-optics method (ROM) and the coupled-mode method (CMM). In the case of rectangular gratings, the coupling coefficients are evaluated in more detail by varying grating depth and duty-cycle. We have found that the RROM gives us more exact solutions for the backward coupling coefficients of even arbitrary shapes of diffractive grating waveguides than the other two conventional methods