The additive-pulse modelocked (APM) laser has been traditionally used as an ultrashort pulsed light source, despite being hampered by multiple instabilities, including quasiperiodicity and chaos. Although the system is generally designed to avoid such instabilities, a detailed understanding of these nonlinear phenomena can serve to improve APM operation, as well as provide an excellent system for furthering current experimental chaos study. To this end, this thesis develops a model of the APM laser together with an experimental APM system, both of which display complicated nonlinear dynamics, including period-doubling bifurcations, chaos, and crisis behavior. The APM model is used to simulate the laser under conditions of high nonlinearity, and to explore the dependencies of the dynamics on different APM parameters: fiber length, fiber coupling, and gain. The chaotic regions of operation are characterized by embedding dimension and largest Lyapunov exponent, and some chaotic attractors are plotted in three dimensions. The experimental APM laser system is then developed, optimized with the help of the model, and significant improvements are incorporated to allow experimental observation of detailed chaotic behavior. Saturable Bragg reflector modelocking is demonstrated as a useful starting mechanism for the APM laser, and experimental results are presented. Random noise contributions are also considered in both the APM model and experiment, to allow for realistic comparison. The theoretical and experimental results are then compared graphically, indicating excellent agreement. Further data analysis techniques for confirming the existence of chaos are additionally implemented to strengthen the conclusions. Demonstration of the period-doubling route to chaos, Lyapunov exponent and correlation coefficient quantification of the chaos and the excellent correlation between theory and experiment all represent new accomplishments and valuable insight into the APM laser dynamics.
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