Counterpropagating pattern dynamics: From narrow to broad beams

The development of patterns in counterpropagating (CP) beams in saturable Kerr-like media is investigated in a numerical study, by varying the width of beams. A model of interacting mutually incoherent beams is adopted, with slow local changes in the index of refraction, and a numerical simulation of propagating beams is performed for different values of the driving parameters. Linear stability analysis (LSA) of CP beams is carried out, and a modulational instability threshold for the appearance of side beams is determined. The results of LSA, concerning the instability of plane waves, are compared with the numerical results concerning broad hyper-Gaussian beams whose width is varied. Qualitative agreement is found, due to the similarity between plane waves and flat-top hyper-Gaussian beam profiles. Owing to very slow quasi-steady-state changes in the system during time evolution, the transverse characteristics of beam distributions, determined by LSA, are found to persist for long in the transient evolution of CP beams.