Grating coupled surface emitting distributed feedback lasers are analysed by our recently developed model. The model takes into account spontaneous emission, the longitudinal variation of carrier concentration and that of photon density, calculated by a self-consistent technique. The emission spectrum and near and far field radiation patterns are determined as a function of the injection current and external optical feedback. It is found that a single lobed far field radiation pattern is favoured by asymmetric coating of the facets. In addition, the phase margin to achieve a single lobed radiation profile can be increased by increasing the amplitude of the reflection.