(1+2) dimensional spiraling elliptic spatial optical solitons in the media without anisotropy

Abstract

Starting from the nonlocal nonlinear Schrödinger equation in Cartesian coordinates, we also obtained nonlocal nonlinear Schrödinger equation in a rotating coordinate system.Assuming that the response function of media is Gaussian, we obtain the stable solutions of the solitons of nonlocal nonlinear Schrödinger equation in rotating coordinate system by means ot the imaginary-time evolution method. The propagation properties of the (1+2) dimensional spiraling elliptic spatial optical solitons in the media is discussed in different degrees of the nonlocality by using the split-step Fourier algorithm.The elliptic soliton profiles of the major and the minor axes are Gaussian shaped in a strongly nonlocal case, but not in a weakly nonlocal case. It is suggested that (1+2) dimensional elliptic solitons be highly dependent on the degree of nonlocality. The angular velocity for the change of the ellipticity is very sensitive when the nonlocality is strong,but in the weakly nonlocal case, the change of the angular velocity is very small.The angular velocity depends strongly on weakly nonlocal case to different degrees of ellipticity. Oppositely, in strongly nonlocal case, the value of the angular velocity is almost unchanged. In another way, the critical power for the solitons decreases as the nonlocality decreases in different degrees of ellipticity.Similarly,the critical power for the solitons decreases as the ellipticity decreases in different degrees of nonlocality.