Variational approach to orthogonally-polarized optical soliton interaction with cubic and quintic nonlinearities

A reduced variational technique is developed to describe the interaction of opposite-handed, circularly-polarized, d-dimensional solitons propagating in an isotropic material with both cubic and quintic nonlinearities. Dynamical equations for the simultaneous collapse and interaction of the two solitons are developed and are shown to be analogous to a particle in a (d + 2)-dimensional. potential well. This potential simultaneously describes the dynamics of the interaction as well as the self- and cross-focusing of the two solitons. Stability and escape velocity formulas are derived and compared to analytic and numerical results. The possibility of a "slingshot" interaction is revealed, even for d = 1 dimensional solitons, and its dynamics are illustrated by direct integration of the variational state equations.