Nonlinear Bloch waves in metallic photonic band-gap filaments

We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals PCs . These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequencydependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional 2D metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin 10–50 nm layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic silver and tungsten PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell’s equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten suitably microstructured filament.