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 Tsuji [ IEEE Trans. Microwave Theory Tech. 37, 3– 14 ( 1989)] and by Liu 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.
© 1995 Optical Society of America
Original Manuscript: July 29, 1994
Revised Manuscript: November 28, 1994
Manuscript Accepted: December 6, 1994
Published: May 1, 1995
P-P. Borsboom and H. J. Frankena, "Field analysis of two-dimensional integrated optical gratings," J. Opt. Soc. Am. A 12, 1134-1141 (1995)