Effects of spatial inhomogeneities on the dynamics of cavity solitons in quadratically nonlinear media - art. no. 036610

We study the dynamics of cavity solitons under the influence of spatial inh omogeneities and derive generalized equations of motions. For perturbations large compared to the soliton size we find the modulus of the soliton velo city to be proportional to the gradient of the respective perturbation and that the proportionality coefficient changes sign when the soliton peak pow er drives the cavity beyond the resonance. For short scale perturbations so litons may be trapped at the extrema of the inhomogeneities. Shape and stab ility of these trapped solitons can be quasianalytically described by means of a perturbation theory. If both types of perturbations act solitons are either trapped or move depending on the strength of the respective perturba tion. In the framework of a quasiparticle approach this dynamics is governe d by a differential equation that holds for particle motion in a strongly v iscous fluid under the action of a constant and harmonically varying force. We also show that in addition to acquiring a velocity the very existence c onditions of the solitons (hysteresis curve) are affected by both kinds of perturbations. We find good quantitative agreement between our analytical r esults and numerical findings, which were obtained for a two wave interacti on in a cavity filled with a quadratically nonlinear material.