Abstract
We consider the nonlinear reflection phenomena on the boundary between the vacuum and the semi-infinite dense absorber for an intense plane wave under normal-incidence conditions. A peculiar feature of the problem is that the frequency of the incident field acts within the polariton band gap, in which for the linear case there is a total reflection of light. We show the appearance of a multivalued behavior of the reflectivity on the boundary of the dense absorber for a range of parameters (polariton band-gap width and detuning of resonance) and calculate the critical values for which bistability and multistability occur. We also demonstrate the possibility of optical hysteresis of reflectivity and discover the nature of the instabilities of several branches. The only instabilities found for the range of parameters used are auto-oscillations with periods depending on the crucial variables.
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