Nonlinear transverse modes of large-aspect-ratio homogeneously broadened lasers: I. Analysis and numerical simulation.

TLDR: This work provides direct numerical evidence for weakly turbulent behavior of a 2D Raman laser where Eckhaus and zigzag phase instabilities act in concert to spontaneously nucleate topological defects and ridgelike illuminated regions.

Abstract: Transverse pattern evolution is investigated in single-longitudinal-mode two-level and Raman lasers with flat end reflectors, subjected to uniform transverse pumping. The natural nonlinear modes of the laser are identified as spatially homogeneous when the detuning from the gain peak is negative and as ``local'' plane traveling waves when the detuning is positive. The latter correspond to an off-axis emission of the laser. Stability characteristics of the underlying patterns are predicted to be quite different for one-dimensional and two-dimensional (2D) lasers. As an illustration, we provide direct numerical evidence for weakly turbulent behavior of a 2D Raman laser where Eckhaus and zigzag phase instabilities act in concert to spontaneously nucleate topological defects and ridgelike illuminated regions. Our numerics also confirm that the complicated patterns persist for finite transverse pumping as long as the characteristic width of the pump source contains a sufficient number of selected pattern wavelengths.