Optical bistability and phase transitions in a doped photonic band-gap material.

We discuss the nonlinear response of impurity two-level atoms in a pseudophotonic band gap ~PBG! to an applied laser field. It is shown that in the case when the variance of resonant dipole-dipole interaction ~RDDI! is much larger than its average value and the spontaneous emission rate, a nonequilibrium second-order phase transition occurs when the applied field strength parameter exceeds the variance of RDDI. This situation arises when the atomic density is low and the resonance frequency is near the center of a wide PBG. At this threshold the system changes from glassy phase to ferroelectric phase. In the case when the average value of RDDI is larger than its variance and spontaneous emission decay rate, this phase transition becomes first order, leading to optical bistability. This situation arises when the atomic density is high or when the photon localization length within the PBG extends over many optical wavelengths. The influence of RDDI fluctuation on bistability is discussed. These results suggest that disordered, impurity-doped, PBG materials may exhibit very low threshold switching properties. @S1050-2947~96!02111-7#