The Proper Orthogonal Decomposition for Dimensionality Reduction in Mode-Locked Lasers and Optical Systems

The onset of multi-pulsing, a ubiquitous phenomenon in laser cavities, imposes a fundamental limit on the maximum energy delivered per pulse. Managing the nonlinear penalties in the cavity becomes crucial for increasing the energy and suppressing the multi-pulsing instability. A Proper Orthogonal Decomposition (POD) allows for the reduction of governing equations of a mode-locked laser onto a low-dimensional space. The resulting reduced system is able to capture correctly the experimentally observed pulse transitions. Analysis of these models is used to explain the sequence of bifurcations that are responsible for the multi-pulsing instability in the master mode-locking and the waveguide array mode-locking models. As a result, the POD reduction allows for simple and efficient way to characterize and optimize the cavity parameters for achieving maximal energy output.