Dynamic counterpropagating vector solitons in saturable self-focusing media

We display rich spatial and temporal dynamics of light fields counterpropagating in a saturable self-focusing medium numerically, and analyze instabilities that counterpropagating solitons experience. An expression for the maximum length that the medium must not exceed for the solitons to be stable is derived and connected to the coupling strength of beam interaction. The instability can lead to periodic or irregular temporal dynamics of the light beams. By considering mutually incoherent counterpropagating beams, we show that differences to the copropagating case are due to the different boundary conditions.