We report a theoretical and experimental work on the nematicon in the planar cell containing the nematic liquid crystal with negative dielectric anisotropy, aligned homeotropically in the presence of an externally applied voltage. The formation of th
e soliton is resulted from the balance between the linear difrraction and the nonlocal nonlinearity due to molecular reorientation.
In this paper, several proposals of optically simulating Yang-Baxter equations have been presented. Motivated by the recent development of anyon theory, we apply Temperley-Lieb algebra as a bridge to recast four-dimentional Yang-Baxter equation into
its two-dimensional counterpart. In accordance with both representations, we find the corresponding linear-optical simulations, based on the highly efficient optical elements. Both the freedom degrees of photon polarization and location are utilized as the qubit basis, in which the unitary Yang-Baxter matrices are decomposed into combination of actions of basic optical elements.
