Phase dynamics of high radiance fiber laser arrays with active phase control

The existing model of the LOCSET technique for the active phase synchronization of fiber laser arrays (T. Shay, Opt. Express, 2006) is extended to include relevant physical properties of the system, such as inherent optical path differences (OPD), line-width and group velocity dispersion (GVD), and we also include phase "jitter" of the master oscillator's output in the model, which in experiments is implemented to induce spectral broadening for suppression of nonlinear frequency conversion. Linearization of the phase error signal, which incorrectly predicts convergence to a synchronous equilibrium state, is not performed. Instead, the closed-loop control dynamics are shown to be described by differential equations of Kuramoto type when phase corrector response dynamics are negligible. Linear stability analysis indicates that there is always one and no more than one dynamically stable state. The latter is shown to be normally synchronous, except when strong "jitter" is applied. A Liapounov function is found as subject to the validity of certain symmetry conditions.