Self-pulsing and bistability in nonlinear Bragg gratings

We characterize the Hopf bifurcations that rule self-pulsing of spatially varying fields in distributed feedback structures with Kerr nonlinear response. Our analysis allows us to distinguish, inside the stop band, between fully unstable regions and those where stable high transmission mediated by localized waves is achievable dynamically. Outside the stop band, the grating reveals a complex behavior where islands of stability are interspersed between regions of self-pulsing and bistability. Numerical integration of the time-dependent coupled-mode equations validates our linear stability analysis and illustrates the dynamics.