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.
Employing a Fox-Li approach, we derived the cold-cavity mode structure and a coupled mode theory for a phased array of N single-transverse-mode active waveguides with feedback from an external cavity. We applied the analysis to a system with arbitrary laser lengths, external cavity design and coupling strengths to the external cavity. The entire system was treated as a single resonator. The effect of the external cavity was modeled by a set of boundary conditions expressed by an N-by-N frequency-dependent matrix relation between incident and reflected fields at the interface with the external cavity. The coupled mode theory can be adapted to various types of gain media and internal and external cavity designs.
We propose a systematic approach that may apply to many complex interactive networks, such as biological or
electronic neural assemblies, which was partly inspired by mathematical features of phased laser arrays. Using an
appropriate quasi-logarithmic transformation, a Fox-Li integral equation of linearly coupled phased laser arrays is
mapped to a semi-equivalent coupled oscillator description, of which the interaction term is decomposed into
orthogonal projections. Based on traditional ideas of symmetry, orthogonality, completeness, and the physical
concept of criticality, techniques are proposed for the description of the dynamics and organization of massively
nonlinearly interconnected networks, which may serve as memories, or perform computational operations in
biological neuron assemblies, or models of evolution, pathology, ecological and social networks, individual and
collective behavior, etc.
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