Collisions between Optical Spatial Solitons Propagating in Opposite Directions

We formulate the theory describing the evolution and interactions between optical spatial solitons that propagate in opposite directions. We show that coherent collisions between counterpropagating solitons give rise to a new focusing mechanism resulting from the interference between the beams, and that interactions between such solitons are insensitive to the relative phase between the beams.

Figure 1

Interactions between spatial solitons that propagate in opposite directions.

Figure 2

(a)–(c) Coherent interactions between the counterpropagating (a),(c) forward and (b) backward solitons. (d)–(f) Incoherent interactions between the counterpropagating (d),(f) forward and (e) backward solitons. For comparison, interactions between coherent in-phase (g) and $\pi$ out of phase (h), and incoherent (i) copropagating solitons. The plots show absolute values of the field amplitudes. The arrow indicates the propagation direction of each beam. The column to the right is a contrast bar indicating normalized intensities between 0 and 1.

Figure 3

Coherent (a),(b) and incoherent (c),(d) interactions between almost-counterpropagating solitons. The plots show absolute values of the field amplitudes, and the arrows indicate the propagation directions.