Highest-quality modes in disordered photonic crystals

We studied the modes of the highest-quality factor Q(m) in disordered photonic crystals. By varying the strength of disorder, we identified five different scaling regimes of the ensemble averaged <Q(m)> with the system size. For sufficiently large systems, <Q(m)> reaches the maximum at some finite degree of disorder, where its value is comparable to the quality factor of an intentionally introduced single defect at the center of a photonic band gap. Near this optimal degree of disorder, we predict a superexponential increase of <Q(m)> with the system size, due to migration of the frequencies of the highest-quality modes toward the photonic band-gap center. Our result may lead to the design and fabrication of ultralow-threshold random laser.