Intrinsic localized modes in photonic crystal waveguides composed of a periodic mixed array of linear and Kerr nonlinear dielectric media

Abstract

A theoretical treatment is given of intrinsic localized modes in waveguides and in junctions of waveguides formed inside two-dimensional photonic crystals. Two-dimensional photonic crystals are periodic arrays of parallel-axed dielectric cylinders, and the electromagnetic modes of interest propagate in the plane perpendicular to the cylinder axes. Waveguides are formed inside the photonic crystal by replacement of a row of cylinders. The replacement cylinders are chosen so that the waveguide channels formed bind and conduct electromagnetic energy along the channel in the plane perpendicular to the cylinder axes. In the systems we study, the waveguide channels are composed of a periodic array of linear and Kerr nonlinear media in which both the linear and nonlinear dielectric materials differ from the linear dielectric materials forming the bulk photonic crystal. These waveguides are shown to support intrinsic localized modes. The intrinsic localized modes are studied by determining their scattering properties in waveguide systems. The transmission characteristics of a waveguide formed of linear dielectric media but containing a barrier that is a periodic array of linear and Kerr nonlinear dielectric is studied. Studies are also made of the transmission characteristics of waveguides of linear dielectric media that are connected at a waveguide junction that is composed of co-joined segments containing a periodic array of linear and Kerr nonlinear dielectric media. Transmission anomalies in these two types of waveguide geometries (i.e., barrier and junction geometries), associated with the development of intrinsic localized modes in the barrier or segments composing the waveguide junctions, are identified. This work is an extension of that presented in A.R. McGurn, G. Birkok. Phys. Rev. B 69 (2004) 235105, which treated the scattering characteristics of intrinsic localized modes in barriers and junctions formed solely of Kerr nonlinear dielectric media to treat other types of waveguides that can support intrinsic localized modes.