Swing effect of spatial soliton in second order material

Spatial solitons are self-trapped optical beams that propagate without changing their spatial shape, since the diffraction and the nonlinear refraction balance each other in a self-focusing medium. In this paper we study the behavior of a soliton beam in a second order material and in a waveguide which, in the plane between the cladding and the substrate, has a distribution of refractive index that follows a Gaussian curve, where the initial position of the maximum of the intensity of the soliton is shifted with respect to the maximum of the index profile. In this situation the beam is attracted towards the center of the index profile, acquiring a certain velocity that allows it to pass this point and to continue to move forward to the other side of the index profile, decreasing its velocity