Exact derivation of the coupling coefficient in corrugated waveguides with arbitrary cross-section: application to optical fibers

Expressions for the coupling coefficient in corrugated waveguides with rectangular tooth shape are derived based on local mode expansion. The expressions are exact to first order in the tooth height (or index difference) for any waveguide cross-section. When applied to slab waveguides, the familiar expressions are obtained. Specializing to weakly guiding fibers, with step index profile, result in simple expressions in terms of the fiber parameters, which are compatible with the effective index method