Radiation patterns of higher azimuthal order spatial modes from a concentric-circle-grating waveguide cavity using the volume-current method

We calculate the surface-emitted scattered radiation from a concentric-circle-grating waveguide cavity. The full vector form of the scattered radiation is calculated using the volume-current method, where the index perturbation caused by the grating is represented as an induced-current driving term in the free-space wave equation for the scattered field. We show intensity patterns and field vector plots for a range of azimuthal modes besides the previously reported fundamental mode, and we find excellent agreement with the observed emission patterns and field polarization from concentric-circle-grating surface-emitting semiconductor lasers.