Curvature instability and localized structures in passive diffractive resonators

Summary form only given. Stationary localized structures (LS) and localized patterns have been predicted in passive resonators in regimes where the homogeneous steady states exhibit a subcritical Turing (or modulational) instability. These solutions consist of bright or dark spots in the transverse profile of the intracavity field amplitude. They can be either spatially independent and randomly distributed or clusters forming well-defined spatial patterns in the transverse plane orthogonal to the propagation axis. We consider an optical cavity with plane mirrors filled with resonant two-level atoms and driven by a coherent plane-wave injected signal. We focus on the purely absorptive limit where the two-level atoms are in resonance with the injected field. In this system, two type of LS may be generated, depending on the magnitude of the critical wave number associated with the modulational instability: circular localized bright spots or a stationary localized single stripe. Both types of LS can form for the same value of parameters.