Abstract

Marcuse has used local normal mode theory to calculate general expressions for the coupling coefficients (distributed leakage - DL and distributed feedback - DFB) for asymmetric slab waveguides with corrugated core boundaries.¹ This approach and in general most approaches to this problem^2,3,4 do not give one much feeling for the workings of the diffraction process and are limited in their ability to handle deep and/or metallic groove configurations where higher order diffraction effects can be important.⁵ In this paper, a simple ray optics⁶ technique is outlined which can be used to find approximate values for coupling coefficients in such configurations. In essence, the corrugated waveguide is separated into a planar waveguide and a diffraction grating and each problem is solved separately. The individual solutions are then combined in a manner consistent with the bounce picture of mode propagation. The validity of the technique is proven in the shallow dielectric groove domain by comparing closed form expressions for the DL and DFB coefficients of a sinusoidally corrugated waveguide to the numerical results given in references 2, 3 and 4.

© 1976 Optical Society of America