Self-compression of spatially limited laser pulses in a system of coupled light-guides

The self-action features of wave packets propagating in a two-dimensional system of equidistantly arranged fibers are studied analytically and numerically on the basis of the discrete nonlinear Schr\"odinger equation. Self-consistent equations for the characteristic scales of a Gaussian wave packet are derived on the basis of the variational approach, which are proved numerically for powers $\mathcal{P} < 10 \mathcal{P}_\text{cr}$ exceeding slightly the critical one for self-focusing. At higher powers, the wave beams become filamented, and their amplitude is limited due to nonlinear breaking of the interaction between neighbor light-guides. This make impossible to collect a powerful wave beam into the single light-guide. The variational analysis show the possibility of adiabatic self-compression of soliton-like laser pulses in the process of their three-dimensional self-focusing to the central light-guide. However, the further increase of the field amplitude during self-compression leads to the longitudinal modulation instability development and formation of a set of light bullets in the central fiber. In the regime of hollow wave beams, filamentation instability becomes predominant. As a result, it becomes possible to form a set of light bullets in optical fibers located on the ring.