Different regimes of the Purcell effect in disordered photonic crystals

We demonstrate that disorder in photonic crystals could lead to pronounced modification of spontaneous emission rate in the frequency region corresponding to the photonic band gap (PBG). Depending on the amount of disorder, two different regimes of the Purcell effect occurs. We provide statistical analysis of Purcell coefficient on the frequency of the emitter and its position within the sample. For the moderate disorder, an enhancement of spontaneous emission occurs at the edge of PBG due to the modification of properties of the edge state. This effect is responsible for recently observed mirrorless lasing in photonic crystals at the edge of PBG. When the level of disorder increases, the spontaneous emission rate enhances within the PBG due to the appearance of the high quality factor states. This effect is likely responsible for a superlinear dependence of emissions on pumping observed in synthetic opals.