Resonant excitation of off-channel localized impurity modes by a photonic crystalwaveguide

Abstract

A theoretical treatment is presented of the electromagnetic transmission properties of aphotonic crystal waveguide that interacts with off-channel dielectric impurities, impurityclusters, neighbouring waveguides, or neighbouring waveguide networks. The photoniccrystal studied is a two-dimensional square lattice array of parallel axis dielectric cylinders(formed of linear dielectric medium) in vacuum, and impurities and waveguides arecreated by cylinder replacement. The waveguide whose transmission is calculated isformed from linear dielectric media, but the off-channel features that it interactswith may be formed from either linear or Kerr nonlinear dielectric media. Theoff-channel features may also be composed of dissipative or amplifying media.Waveguide transmission resonances, associated with resonant scattering fromelectromagnetic modes on the off-channel features, are found. Modes present onoff-channel features formed from linear dielectric media include both propagating andlocalized modes. Modes present on off-channel features formed from Kerr nonlineardielectric media include simple localized and intrinsic localized (soliton-like) modes.