Transmission through Kerr Media Barriers within Waveguidesand Circuits

摘要

The transmission properties of a barrier composed of Kerr nonlinear media contained within a photonic crystal waveguide or within circuits formed of photonic crystal waveguides is studied theoretically. The photonic crystal is a two-dimensional array of linear media dielectric cylinders, waveguides are formed in the photonic crystal by replacing a row of photonic crystal cylinders with linear media replacement dielectric cylinders, and the barrier is formed by replacing a finite number of waveguide cylinders with cylinders containing Kerr nonlinear dielectric media. The transmission maxima of the circuits, for an incident waveguide mode into the circuits, are determined as functions of two parameters characterizing the Kerr nonlinear media in the barrier. The resulting two-dimensional plot in the Kerr parameter space gives a complex pattern with features that are identified with Fabry-Perot excitations, intrinsic localized modes, and dark soliton modes resonantly excited within the barrier. Circuits treated are straight waveguides, waveguides with bends, and waveguides with side couplings. The theory is based on a difference equation approach developed for nonlinear barriers in Phys Rev B 69, 235105(2004) and Phys Rev B 77, 115105(2008).