Computation of the modal reflectivity for a partially etched mirror: application for integration of a laser diode and a waveguide.

We demonstrate a fast, accurate for weak waveguiding, approximate solution to the problem of computing the modal reflection and transmission coefficients at a discontinuity between two asymmetric multilayer waveguides together with a rigorous solution to check the validity of the approximate but fast approach. The proposed algorithm is analogous to the widely used approximation proposed by Vassallo [Electron. Lett. 21, 333 (1985)] for the case when the medium after discontinuity is uniform and has a large applicability potential for optoelectronic applications. As an example, the case of optoelectronic integration between an active laser diode and a passive waveguide device is analyzed.