Nonlinear dynamics of the additive-pulse modelocked laser

We have modeled the additive-pulse modelocked (APM) laser with a set of four nonlinear difference equations, that describe the transit of optical pulses through the main cavity and through an external cavity containing a single-mode optical fiber. Simulating the system under several parameter variations, including fiber length, gain, and fiber coupling, we have observed period-doubling bifurcations into chaos. In addition, the model predicted large regimes of quasiperiodicity, and crisis transitions between different chaotic regions. We have used the method of nearest neighbors, Lyapunov exponents, and attractor reconstruction to characterize the chaotic regimes and the different types of bifurcations. We have included bandwidth-limiting and monitoring provisions to prevent non-physical solutions. To our knowledge, this is the first such characterization of chaos in the APM laser, as well as the first evidence of crisis behavior.