Modeling and design of all-optical integrated logic devices using the novel Local Interpolatory Cardinal Spline method

Abstract

A novel numerical method, hereafter called the Local Interpolatory Cardinal Spline (LICS) method, is developed to model and simulate the behavior of optical wave propagation in a nonlinear medium. The architecture of this method is as simple as the finite differences scheme, and it has higher efficiency and accuracy than the widely used Beam Propagation Method. Numerical comparisons between the LICS method and BPM are investigated in the context of solving the Nonlinear Schrodinger Equation. The LICS method is then used to study the phenomena of soliton fusion and steering in a Kerr-type nonlinear medium. In certain particularly simple cases, an analytical approach based on the perturbation method is used for analysis to give a fundamental understanding of the fusion and steering processes for solitons in both the temporal and spatial domains. The analytical expression of a two-soliton fusion and steering system is obtained and the relationships between the fusion process and other factors are determined. For more complicated cases, the LICS method is used to simulate the soliton dynamics. Analysis of this fusion and steering process resulted in the design of an all-optical 1 x 2 switching device. The performance of this switch is analyzed based on power transmission efficiency and control power. The compactness of size, the simple structure, and the switching speed of this device are evident from the design flexibility and the efficient use of fusion phenomena. Furthermore, the design of a one-stage 1 x 4 all-optical switch for time-division demultiplexing application is also presented in the dissertation. Simulations of the device performance are evaluated with the device operating in power-controlled mode. Optimal design parameters and flexibilities of the control-power setting are also demonstrated. In addition, the basic equation governing the fusion and steering for two different-colored solitons in nonlinear planar structures is derived. Possible applications for this phenomenon are discussed.