Spatial solitons interaction in liquid crystalline waveguides

Nematic liquid crystals are excellent medium for nonlinear optics, both in three-dimensional bulk systems [1-2] as well as in waveguide structures [3-4]. The main contribution to nonlinear optical phenomena in liquid crystals arises from thermal and reorientational processes. While the thermal effect is similar to that observed in other materials, the reorientational effect is characteristic only in the liquid crystalline phase. Reorientational nonlinearity in nematic liquid crystals can also form spatial solitons [5]. Experimental results showed that for light power of the order of only a few mW it could be achieved self-trapped beams at distances of the order of a few mm. The stability of such beams can be controlled by external fields or by state of the light polarization. The experiments showed the existence of the self-focused light beams inside liquid crystals in capillaries [6-9], in planar cells [10], and in planar waveguides [11]. In this paper, the collisions of the optical solitons in planar waveguides are analyzed theoretically. Such solitons were previously observed experimentally and analyzed theoretically in a thin layer with homeotropically-aligned nematics [11]. By controlling the state of polarization of the incident light the stable self-trapped beams were obtained. They were named spatial soliton, but in fact only their stability were proved. In the exact definition, solitons need to be stable and need to maintain their properties after the collision with another solitons. Obtained results in this paper show that analyzed self-trapped beams are rather solitary waves than solitons. They are stable during the propagation but the interaction between two such beams can destroy them.