Bistable Solitary Waves and Switching Waves with a Hexagonal Pattern in Semiconductor Planar Resonators

Since many years it is well-known that planar resonators filled with a nonlinear material may exhibit bistability and various kinds of instabilities [1]. Two-dimensional patterns and stationary localized structures (SLS) could be observed provided that transverse effects were taken into account. SLS attract a great deal of interest because it is believed that their particle-like behavior can be potentially exploited in future data processing and storage systems. SLS were found in media with saturable dispersive focusing as well as saturable absorptive nonlinearities [2,3]. Hitherto, it is common believe that in dispersive defocusing media only switching waves rather than SLS may exist. Unfortunately, highly nonlinear materials, as e.g. semiconductors operated near the band gap exhibit a defocusing nonlinearity. The aim of this paper is to show that even in these materials SLS are allowed to exist due to an interplay of transverse effects (diffraction, diffusion), saturation and nonlinearity.