Coupling coefficients of gratings with graded refractive index waveguides

Abstract

In this paper, the effective coupling coefficient κeff and the self-coupling coefficient ζ1 are introduced to describe the characteristic of gratings in a resonant situation when the effects of radiation and other partial waves coupling are considered. The dependence of these two coupling coefficients on grating tooth shapes and depths and the dimensions of graded refractive index (GRIN) waveguides is numerically analysed. The results show that the gratings with linear GRIN waveguides have the largest |κeff|. The possibility of realizing a complex-coupled DFB laser, even a pure gain or loss coupled DFB laser, employing only a real refractive index coupled grating is also discussed.