Self-pulsing and bistability in nonlinear Bragg gratings

International audienceWe present a full characterization of Hopf bifurcations ruling self-pulsing of spatially varying fields in a Bragg grating with Kerr nonlinear response. Our analysis permits, inside the stopband, to distinguish between the fully unstable region and the region where stable high transmission mediated by localized waves is achievable dynamically. Outside the stop-band, it reveals a complex behavior where islands of stability are interspersed between regions of self-pulsing and bistability. Beam propagation simulations validate our linear stability analysis and illustrate the dynamics