Abstract: In recent years, nonlocal spatial solitons have attracted a great deal of attention. Optical spatial solitons result from the suppression of beam diffraction by the light-induced perturbed refractive index. For spatial nonlocal solitons, the light-induced perturbed refractive index of medium depends on the light intensity nonlocally, namely, the perturbed refractive index at a point is determined not only by the light intensity at that point but also by the light intensity in its vicinity. Such a spatial nonlocality may originate from heat transfer, like the nonlocal bright solitons in lead glass and dark solitons in liquids or gases. The perturbed refractive index n of lead glass or liquid is direct proportional to the light-induced temperature perturbation t, i.e. n=1t. The proportional coefficient 1 is positive (negative) for lead glass (liquid), and the light-induced temperature perturbation t is determined by the Poisson equation ▽2(t)=-DI, where I is the light intensity and D is a coefficient. In this paper, we investigate another type of thermal nonlinear effect, in which the perturbed refractive index n depends on the light-induced temperature perturbation t in a new way that n=1t+2(t)2. It has been indicated previously that the refractive index of a supercooled aqueous solution depends on the temperature, specifically n(t)=n0-2(t-t0)2, where n0=1.337733 for 501 nm light wave, t0=-0.1℃ and 2=310-6 K-2. So for tt0, the refractive index of aqueous solution increases with temperature rising, while tt0, it decreases with temperature increasing. In this paper, we use the numerical simulation method to investigate the propagation and interaction properties of optical solitons propagating in a supercooled aqueous solution, whose temperature on boundary is maintained at some value below t0, with the aqueous solution placed in a thermostatic chamber. Obviously, the inner temperature of the solution rises, owing to absorbing some optical energies of the light beam propagating in it, and as a consequence the inner refractive index changes according to n(t)=n0-2(t-t0)2. For a soliton with a low power, the inner temperature t of the solution is always kept below t0, so the refractive index at a point with a higher t is larger than that at another point with a lower t. In this case, the solution behaves as a self-focusing medium. A soliton with a higher power has a narrower beam width and a larger propagation constant, and the soliton takes a bell shape. However, for a soliton with a rather high power, the temperature in the core will be higher than t0 while the temperature in the periphery is still below t0. Therefore, the part of the solution in the core behaves as a self-defocusing medium while the part in the periphery behaves as a self-focusing medium. For such a case, the higher the power of the soliton, the larger the radius of the core is and the larger the beam width of the soliton, so the soliton takes a crater shape with a saturated propagation constant. Finally we also investigate the interaction between two solitons in a supercooled aqueous solution. For two neighboring beams with a rather high total power, they cannot maintain their individualities any more during the interaction, but merge into an expanding crater.

Keywords: 
• Schr /
• dinger equation /
• supercooled /
• self-focusing