Analysis of grating surface emitting lasers

An approach to the analysis of grating-coupled semiconductor lasers is presented. It is shown that there are only two resonant solutions when the grating has infinite extent. The solutions are either symmetric or antisymmetric about the center of the longitudinal coordinate system where the antisymmetric solution is nonradiating. The field in the grating layer is expressed in terms of grating eigenfunctions and rigorously matched to the boundary conditions at the waveguide interface. Solutions to the finite-length grating problem are expressed as linear combinations of the infinite-length solutions. It is shown that the two diffraction parameters in the coupled-wave equations are composed of sums and differences of the eigenvalues from the infinite-length problem