| This thesis describes the occurrence of electromagnetic Bloch waves in lossy photonic crystals that are periodically embedded with two-level transition electric dipole resonators, and are under uniform incoherent pumping. These nonlinear Bloch waves emerge above a specific pumping threshold, when an intricate balance between gain and loss is reached. This balance determines the amplitude of the nonlinear Bloch wave. The nonlinear waves present a laser-like behaviour with pumping and provide an underpinning for laser activity in strongly scattering dielectric photonic crystals (PCs). A related system of practical importance is the case of metallic backbone PCs. We demonstrate that, in spite of background losses, a metallic PC filament may exhibit nonlinear Bloch waves, under strong incoherent (by thermal or electrical sources) pumping. These intense nonlinear waves, excited through localized surface resonances, propagate through an optical pass band, below the effective plasma frequency of the structured metal. This result may be relevant to high efficiency light bulb filaments in which the electrical power is funneled preferentially toward specific frequencies over and above the standard blackbody spectrum.;We present a novel self-consistent iterative method for obtaining nonlinear Bloch waves in a strongly scattering periodic dielectric or metal, with nonlinear, frequency-dependent, and complex dielectric function. This is based on an integral equation formulation of the nonlinear-wave equation. We give numerical results for several illustrative cases of two-dimensional PCs doped with resonant dipoles (two-level atoms) describing colloidal quantum dots, localized surface plasmons, or other resonators. We show that the nonlinear integral equation which was developed initially for strictly positive dielectric functions can be generalized to treat metals with large negative dielectric functions. |
