Objective  Nematic liquid crystals have excellent electro-optical properties, significant optical nonlinearity, and the adjustable nonlocality and nonlinearities. So, it has become an ideal material for the study of non-local solitons. In 2017, JUNG P S et al. proposed a non-local model in which both molecular orientation and thermal effects coexist in the nematic liquid crystals. So far, there are few literature reports on the propagation of (1+2)-dimensional bright solitons and (1+2)-dimensional dipole solitons in this model. For this purpose, the propagation properties of (1+2)-dimensional solitons in nematic liquid crystals with competing nonlocal nonlinearities are investigated based on this model. The results can provide a theoretical basis for competing (1+2)-dimensional spatial optical soliton interactions in nonlocalized media, as well as potential applications in areas such as all-optical information processing and optical switching device preparation.

Methods  The critical power of (1+2)-dimensional ground-state bright solitons and dipole solitons in nematic liquid crystals with competing nonlocal nonlinearities are obtained by the variational method. Subsequently, the propagation properties of the (1+2)-dimensional bright soliton and dipole soliton with competing nonlocal nonlinearities are obtained using the beam propagation method. The conditions for stable transmission of (1+2)-dimensional bright and dipole solitons in nematic liquid crystals with competing nonlocal nonlinearities are given.

Results and Discussions  It is found that when the degree of reorientational nonlocality and the thermal nonlinearity coefficient is fixed, the critical power of optical solitons increases monotonically with the increase of the degree of thermal nonlocality. When the degree of thermal nonlocality increases to a certain value, the power of the upper branch increases monotonically with the increase of the degree of thermal nonlocality, and the power of the lower branch decreases monotonically with the increase of the degree of thermal nonlocality, and the power of the upper branch increases faster than the decrease of the power of the lower branch (Fig.1). When the degree of thermal nonlocality and the thermal nonlinearity coefficient are fixed, the increase of the degree of reorientational nonlocality, the critical power of optical solitons is first divided into two power branches, and the power of the upper branch decreases monotonically with the increase of the degree of reorientation nonlocality, while the power of the lower branch increases monotonically with the increase of the degree of reorientational nonlocality. When the value of the degree of reorientation nonlocality increases to a certain value, the critical power of optical solitons branches coincide into one, and the critical power of optical solitons decreases monotonically with the increase of the degree of reorientational nonlocality (Fig.2). When the degree of reorientational nonlocality and the degree of thermal non-locality are fixed, the increase of the thermal nonlinearity coefficient, the critical power of optical solitons is first divided into two branches, and the upper branch decreases monotonically with the increase of the thermal nonlinearity coefficient, while the lower branch increases monotonically with the increase of the thermal nonlinearity coefficient. When the thermal nonlinearity coefficient increases to a certain value, the critical power of optical solitons branches coincide into one, and the critical power of optical solitons decreases monotonically with the increase of the thermal nonlinearity coefficient (Fig.3). Finally, the beam propagation method shows that only the (1+2) dimensional solitons corresponding to the points on the unequal power branch can be stable propagation, and the solitons corresponding to the points with the equal power of the two branches cannot be stable propagation (Fig.4).

Conclusions  According to the model proposed by JUNG P S et al, the propagation characteristics of (1+2) dimensional optical solitons in nematic liquid crystals with competing nonlocal nonlinearities are studied. The analytical expression of the critical power of the soliton is given by the variational method, and it is found that the critical power of the soliton is related to the degree of reorientational nonlocality, the degree of thermal non-locality and the thermal nonlinearity coefficient of the material. The beam propagation method shows that only optical solitons and dipole solitons corresponding to the points on the unequal power branch can propagate stably in competing nematic liquid crystals, and optical solitons and dipole solitons corresponding to the points with the equal power of the two branches cannot be stable propagation.