Stopping and Bending Light in 2D Photonic Structures

Abstract

The problem of light propagating through two dimensional photonic structures with a localized defect is addressed. Examples of potential engineering applications of such structures are rerouting of light pulses or optical memory. The governing mathematical model is the system of Coupled Mode Equations (CME) in two spatial dimensions with addition of potentials which account for the defect. As we briefly explain, unlike the one dimensional model of CME without potentials, the two dimensional (x-uniform grating) one does NOT support stable localized pulses as solutions. Because stable pulses are necessary for any physical application, we add grating also in the x direction making, in effect, a true 2D photonic structure, and as we show numerically, this allows for launching of stable pulses. Next, making sensitive assumptions on the shape of the defect, we first give here a derivation of exact linear defect modes, i.e. solutions to the linear system with potentials, and then outline our future study of whether these linear modes persist into the nonlinear regime. Our next future task is to study the interactions of pulses with the nonlinear defect modes.