Coupled-mode formulations for parallel-laser resonators with application to vertical-cavity semiconductor-laser arrays

Laser resonators, with laterally patterned end mirrors, are considered in the framework of coupled-mode theory. Two distinct coupled-mode formulations are presented. The first is applicable to cavities having high-reflectivity mirrors surrounded by a significantly lower reflectivity background. The second formulation applies to high-reflectivity mirrors with a slightly lower reflectivity background. Unlike coupling between parallel waveguides, the interaction between neighboring elements of the parallel cavities is achieved via diffraction, and the perturbation is of the boundary conditions rather than of the dielectric constant. These formulations are directly applicable to the case of arrays of coupled vertical-cavity semiconductor lasers.