A comparative study of higher order Bragg waveguide gratings using coupled-mode theory and mode expansion modeling

Lamellar diffraction gratings integrated into slab waveguides (so-called Bragg waveguide gratings) found widespread applications in distributed-feedback (DFB) and distributed Bragg-reflector (DBR) lasers, either as edge or as surface emitters. For the numerical simulation of these structures, a large variety of different models exists. In this paper, the modal reflectivity and transmittivity of Bragg waveguide gratings are calculated using models based on the CMT and the bi-directional mode expansion model. Thereby, an approximate solution for the partial waves exploiting the free-space Green's function is corrected and generalized.