Resonant nonlinear dielectric response in a photonic band gap material.

We study the dielectric response of impurity two-level atoms in a photonic band gap (PBG) to an applied laser field. In this system, the atoms may exchange energy coherently by resonance dipoledipole interaction (RDDI) which is assumed to be strong compared to the spontaneous emission rate. When the applied Rabi frequency exceeds the RDDI energy scale, nonlinear saturation of the absorptive part of the susceptibility occurs while the real part of the nonlinear susceptibility remains large. This suggests that doped PBG materials may act as nearly lossless, but highly nonlinear dielectrics.