Nonlinear dynamics of circular-grating distributed-feedback semiconductor devices

We report numerical results for the spatiotemporal dynamics of circular-grating distributed-feedback devices with an intensity-dependent refractive index. For the specific geometry and range of variables considered, we find that modulational instabilities do not propagate in these structures. This is due to the 1/r intensity distribution associated with cylindrical waves, which reduces the effectiveness of the self- and cross-phase-modulation nonlinearities.