FIELD ANALYSIS OF 2-DIMENSIONAL INTEGRATED OPTICAL GRATINGS

A method to determine the field scattered by a two-dimensional rectangular grating of finite length is developed. Both periodic or aperiodic and lossy or lossless structures can be treated. The grating is built up as a finite sequence of two alternating types of waveguide sections connected by means of step discontinuities. The mode-matching method is employed to determine the field scattered by a single step. In combining the scattering properties of the separate steps and waveguide sections to describe the entire grating, the scattering matrix formalism was employed. With the proposed method we have examined the 10- and the 20-period configurations described by Shigesawa and Tsuji [IEEE Trans. Microwave Theory Tech. 37, 3-14 (1989)] and by Liu and Chew [IEEE Trans. Microwave Theory Tech. 39, 422-430 (1991)], which show good agreement. Furthermore, we have successfully extended these configurations to gratings with 100 periods.