Theory of multibeam interactions in strongly nonlocal nonlinear media

Abstract

When beams are interacting with each other in strongly nonlocal nonlinear media, they together induce a graded refractive index profile whose axis is located at the center of mass of the combined field. The center of mass undergoes a straight trajectory whose slope can be steered by the amplitude and/or the phase distribution of the interacting beams. In the comoving reference frame, the propagation of each interacting beam can be regarded as the cross-induced fractional Fourier transform. The intensity patterns of the interacting beams evolve periodically with a period that is inversely proportional to the square root of the total power of the interacting beams. If a beam is shape-invariant in free space, it presents as a breather or a soliton in the interaction case. Every interacting beam undergoes a trajectory that oscillates about the straight line of the center of mass in the one-dimensional case; and in the two-dimensional case the projection of the trajectory on the transverse plane is an ellipse. During propagation, every interacting beam experiences cross-induced phase shift, which is induced not only by the initial transverse spatial momentum and the total power of the combined field, but also by the trajectory and the transverse structure of the interacting beam.