Pulse evolution in nonlinear optical loop mirrors

In this thesis, a mathematical analysis of the nonlinear Sagnac interferometer switch and degenerate optical parametric oscillator is presented. These all-optical devices have potentially wide applications in fiber-optic communication networks. The nonlinear optical loop mirror is an important component in both of these devices.; In the first part, the interaction of two copropagating pulses with different carrier frequencies in a nonlinear optical loop mirror is described using coupled nonlinear Schrodinger equations. The signal pulse is assumed to propagate as a soliton. The control pulse is assumed to have a Gaussian shape and experience normal group velocity dispersion. Soliton perturbation theory is used to approximate the evolution of the signal pulse in the limit of a strong control pulse and large collision velocity. Control pulse evolution is approximated using a variational method. An integral equation for the frequency shift induced in the signal pulse by control pulse spreading is derived and analyzed asymptotically in the limit of large collision velocity. The analysis suggests that pre-chirping the control pulse before the interaction can significantly reduce the residual frequency shift, and predicts a value for the initial chirp parameter that should be used. Numerical studies confirm the existence of the frequency shift, and demonstrate that the analysis gives a good approximation to the optimal chirp parameter.; The second part is a study of an all-fiber degenerate optical parametric oscillator in which gain is provided by a phase sensitive amplifier based on a nonlinear optical loop mirror. A partial differential equation modeling the evolution of pulses in this device is derived in the limit of small optical path length. The model PDE includes self phase modulation in the cavity and PSA as well as group velocity dispersion in the cavity, but neglects dispersion in the PSA. Results obtained using the PDE model agree well with numerical simulations of the individual DOPO elements. The PDE model is used to study the behavior of the DOPO under various parameter variations. Bistable operation is observed for a range of cavity lengths. The influence of group velocity dispersion on the steady-state pulse shape is investigated.