| In many applications, the frequency of light produced by the laser is doubled by a crystal with nonlinear optical properties. The presence of such a crystal inside a laser cavity can produce large, irregular fluctuations in the output intensity. This thesis examines nonlinear systems of ordinary differential equations for the longitudinal mode intensities (physical observables) and gains of intracavity doubled lasers. A new system of equations is derived which models the frequency doubling of a general class-B laser with any number of intracavity birefringent elements, and the relevant features of the cavity configuration are reduced to two parameters. General results are also presented on the possible polarization states of the output beam; these polarizations are explicitly included in a dynamical system for the first time. This analysis is also the first to include the possibility of birefringence in the gain medium.; The complete range of behavior of the intensity output is characterized for one, two and three longitudinal modes in this general framework. A novel approach to the linearized stability analysis of the model leads to explicit stability criteria for the cavity parameters, and to several successful predictions of ways to stabilize the laser output. Several experimental laser configurations previously studied prove to be special cases of the general model; all the experimental results confirm the correspondence between the theory and experiment. Extensive numerical integrations also display a wide range of dynamical behavior consistent with experimental observations.; In the specific case of an intracavity doubled Nd:YAG laser, numerical results trace an intermittency route to chaos, with cross saturation as the control parameter. Samples of experimental output are closely matched by numerical integrations. An additional set of rate equations are developed which display dynamics seen in experiments but not in previous numerical results. Still another set of rate equations validates our approximation of the lasing transition in Nd:YAG as a two-level system. The intracavity doubled Nd:YAG laser is found, in theory and experiment, to be a rich source of nonlinear dynamics. |
