Numerical modeling of wave propagation in nonlinear photonic crystal fiber

In this dissertation, we propose numerical techniques to explain physical phenomenon of nonlinear photonic crystal fiber (PCF). We explain novel physical effects occurred in PCF subjected to very short duration pulses including soliton. To overcome the limitations in the analytical formulation for PCF, an accurate and efficient numerical analysis is required to explain both linear and nonlinear physical characteristics. A vector finite element based model was developed to precisely synthesize the guided modes in order to evaluate coupling coefficients, nonlinear coefficient and higher order dispersions of PCFs. This finite element model (FEM) is capable of evaluating coupling length of directional coupler implemented in dual core PCF, which was supported by existing experimental results. We used the parameters extracted from FEM in higher order coupled nonlinear Schrodinger equation (HCNLSE) to model short duration pulses including soliton propagation through the PCF. Split-step Fourier Method (SSFM) was used to solve HCNLSE.;Recently, reported experimental work reveals that the dual core PCF behaves like a nonlinear switch and also it initiates continuum generation which could be used as a broadband source for wavelength division multiplexing (WDM). These physical effects could not be explained by the existing analytical formulae such as the one used for the regular fiber. In PCF the electromagnetic wave encounters periodic changes of material that demand a numerical solution in both linear and nonlinear domain for better accuracy. Our numerical approach is capable of explaining switching and some of the spectral features found in the experiment with much higher degree of design freedom. Numerical results can also be used to further guide experiments and theoretical modeling.