Abstract
Approximate expressions have been developed for coupling coefficients of gratings on waveguides with nonuniform index profiles. The expressions are particularly suited to utilize the field solutions obtained in closed form for some profiles by setting equal to zero the field at the grating surface. Exact and approximate results are compared for the square and exponential index profiles. New results are presented for the secant hyperbolic squared profile. Comparison is made of the grating coupling coefficients of the three profiles.
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