%0 Journal Article
%T Nonlinear Coherent Directional Coupler: Coupled Mode Theory and BPM Simulation
%A Dharmadas Kumbhakar
%J International Journal of Optics
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/173250
%X Finite difference beam propagation method is an accurate numerical procedure, used here to explore the switching dynamics of a nonlinear coherent directional coupler. The coupling lengths derived from this simulation are compared with coupled mode theories. BPM results for the critical power follow the trend of the coupled mode theories, but it lies in between two coupled mode theories. Coupled mode theory is sensitive to numerical approximations whereas BPM results practically do not depend on grid size and longitudinal step size. Effect of coupling-region-width and core-width variations on critical power and coupling length is studied using BPM to look at the aspects of optical power-switch design. 1. Introduction Beam propagation method [1] is a versatile tool to investigate or model various optical phenomena in photonic devices. Earlier, the method was popular to find the guided modes in dielectric waveguide structures [2]; even in microstructure fibers like holey fibers it can be used to find the modes [3]. With suitable boundary conditions, it gave proper estimates of the propagation constant in leaky structures like arrow waveguides [4]. The method was used in linear directional couplers to simulate switching of a CW signal and filtering TE/TM mode signals [5]. With growing interest in nonlinear fibers, it was the only tool to model the pulse propagation [6] in conjugation with split-step Fourier transform. It has been also used to model various other nonlinear phenomena like second harmonic generation [7], leakage loss in buried silicon substrate [8], and so forth. Beam propagation method can be incorporated either in the finite element or finite difference framework. In cases where the interfaces are parallel to the axes, the two methods are almost the same in terms of accuracy, but the latter is sometimes preferred due to its simplicity in implementation. Nonlinear directional coupler (NLDC) is a very useful device in photonic circuits; it can be used as all optical modulator, switches, logic gates, and so forth. Jenson [9] first showed that total power exchange in a linear coherent coupler is lost in a nonlinear coherent coupler above a critical input power in one guide. This fact was used to design power-controlled all optical switches [10, 11]. The device can also be used as phase-controlled switches [12] and optical modulator [13]. So, the knowledge of the dependence of the critical power and phase variations on the NLDC parameters is important. There are numerous studies on this device; analytic methods include coupled mode theory [9,
%U http://www.hindawi.com/journals/ijo/2012/173250/