Interaction of two spatially separated light beams in a nonlinear Kerr medium

The evolution of two spatially separated light beams in a nonlinear Kerr medium described by a system of coupled nonlinear Schrödinger equations is studied. An analytic solution is found for the variational problem. It is shown that when two crossed beams interact, a bound state can develop in which the distance between the centers of the beams and their radii vary periodically. Here the mutual curvature of the trajectories of the centers of the beams causes the beams to bend into a helical structure whose parameters (pitch and diameter) are also periodic functions. The threshold power for mutual trapping is determined and the period of the oscillations is found.