A comparative study of higher order Bragg gratings: coupled-mode theory versus mode expansion modeling

The modal reflectivity and loss of lamellar diffraction gratings to be used in distributed-feedback and distributed-Bragg reflector lasers were computed in dependence of wavelength, duty cycle and Bragg order. Different methods based on the approximate coupled-mode theory and and the exact bidirectional mode expansion modeling were compared and a good mutual agreement was found. The slab Green´s function needed to compute the coupling coefficients can be approximated by that of a homogeneous unbounded medium with sufficient accuracy.