Mode-locked Pulses in Passive Coherent Beam Combining Fiber Laser Arrays

We present a dynamic model for simultaneously passive coherent beam combining and mode locking with the Nonlinear Schrödinger equation (NLSE). As a result of spectral beating, most longitudinal modes disappear except for the array modes which are the common ones for all channels. The array mode separation is inversely proportional to the fiber length difference. The density of modes decreases with the increase of array size, however, a nice output pulse packet is still possible when channel lengths are commensurate. Dissipative solitons in normal dispersion are more robust to wave breaking than conventional solitons. Coherent beam combining naturally leads to a frequency comb of the array modes, and produces a pulse train of dissipative solitons to carry higher pulse energy with a high and tunable repetition rate. Incommensurate fiber lengths result in an amplitude modulation on the pulse train, which otherwise have uniform amplitude with commensurate lengths. Used widely in beam combining, a directional coupler places two parallel fiber cores together to allow power exchange through frustrated internal total reflection (FTIR). The power tunnels into the other channel by evanescent waves in the cladding gap. Both the lateral Goos-Hanchen shift and the group delay in FTIR constitute the contributions from energy dwell time and self-interference time. None of them relates to "superluminal" propagation.