Nonlinear combining of laser beams

We propose to combine multiple laser beams into a single diffraction-limited beam by the beam self-focusing (collapse) in the Kerr medium. The beams with the total power above critical are first combined in the near field and then propagated in the optical fiber/waveguide with the Kerr nonlinearity. Random fluctuations during propagation eventually trigger strong self-focusing event and produce diffraction-limited beam carrying the critical power.Comment: 5 pages, 5 figure

Multi-mode correlations and the entropy of turbulence

We suggest a new focus for turbulence studies -- multi-mode correlations -- which reveal the hitherto hidden nature of turbulent state. We apply this approach to shell models describing basic properties of turbulence. The family of such models allows one to study turbulence close to thermal equilibrium, which happens when the interaction time weakly depends on the mode number. As the number of modes increases, the one-mode statistics approaches Gaussian (like in weak turbulence), the occupation numbers grow, while the three-mode cumulant describing the energy flux stays constant. Yet we find that higher multi-mode cumulants grow with the order. We derive analytically and confirm numerically the scaling law of such growth. The sum of all squared dimensionless cumulants is equal to the relative entropy between the full multi-mode distribution and the Gaussian approximation of independent modes; we argue that the relative entropy could grow as the logarithm of the number of modes, similar to the %mutual information and entanglement entropy in critical phenomena. Therefore, the multi-mode correlations give a new way to characterize turbulence states and possibly divide them into universality classes

Self-Similarity and Universality in Rayleigh-Taylor, Boussinesq Turbulence

We report and discuss case study simulations of the Rayleigh-Taylor instability in the Boussinesq, incompressible regime developed to turbulence. Our main focus is on a statistical analysis of density and velocity fluctuations inside of the already developed and growing in size mixing zone. Novel observations reported in the manuscript concern self-similarity of the velocity and density fluctuations spectra inside of the mixing zone snapshot, independence of the spectra of the horizontal slice level, and universality showing itself in a virtual independence of the internal structure of the mixing zone, measured in the re-scaled spatial units, of the initial interface perturbations.Comment: 10 pages, 11 figure

Non-Gaussian Statistics of Multiple Filamentation

We consider the statistics of light amplitude fluctuations for the propagation of a laser beam subjected to multiple filamentation in an amplified Kerr media, with both linear and nonlinear dissipation. Dissipation arrests the catastrophic collapse of filaments, causing their disintegration into almost linear waves. These waves form a nearly-Gaussian random field which seeds new filaments. For small amplitudes the probability density function (PDF) of light amplitude is close to Gaussian, while for large amplitudes the PDF has a long power-like tail which corresponds to strong non-Gaussian fluctuations, i.e. intermittency of strong optical turbulence. This tail is determined by the universal form of near singular filaments and the PDF for the maximum amplitudes of the filaments