Nonlinear Dynamics of Arrays of Coherent Laser Beams

The final report of the project FA8655-10-1-3069 presents the combined results of the project including: introduction of the key mathematical models governing optical field propagation in the multiple-core fibres, study of the steady state propagation regimes, study of the modulation instability in multiple-core fibres, investigation of the nonlinear stage of the instability and energy transfer. We have determined theoretically thresholds of the modulation instability in the 2D infinite array of discrete waveguides, and in 2-, 3- and 4-core array systems. We have found stationary solutions in the ring configurations with a central core and N symmetrically surrounding cores and discovered in the array with non-equal cores (e.g. with the central core) the phase matching and stable steady-state propagation is possible only in the nonlinear regime. We have determined theoretically thresholds of the modulation instability in the ring configuration. The important prediction of the theory is a level of nonlinear oscillations resulting from the development of modulation instability. We studied modulation instability of such solutions in the ring configurations with a central core and N symmetrically surrounding cores. All the obtained theoretical results have been verified using numerical simulations.
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