Nonlocal logarithmic nonlinear optical soliton

The propagation of optical beam in (1 + 2)-dimensional nonlocal logarithmic nonlinear media is studied. The numerical simulation shows that the intensity profiles of solitons undergo a gradual and continuous transition from a Gaussian-shaped function in the general nonlocal media to an approximately hyperbolic secant function in the local case. Due to the nonlocal effect, the stability of solitons increases with the increase of nonlocality degree. Concretely speaking, the quasi-stable solitons can be formed in local and weakly nonlocal (nonlocality degree α < 0.5) logarithmic nonlinear media. In general nonlocal case (0.5 ≤ α≤1), the completely stable solitons can be formed. In special case (α = 1), even the initial power increase largely, the solitons can still exist even the initial power has large change for the saturable nonlinear contract effect. However, when α = 1.1, the solitons cannot be formed at any initial power because nonlinear effect is too small to balance diffraction effect.