Highest-quality modes in disordered photonic crystals

We studied the modes of the highest-quality factor Qₘ in disordered photonic crystals. By varying the strength of disorder, we identified five different scaling regimes of the ensemble averaged ⟨Qₘ⟩ with the system size. For sufficiently large systems, ⟨Qₘ⟩ 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 ⟨Qₘ⟩ 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.