A full-vector finite-element beam propagation method in 3-D is introduced for the simulation of light propagation in liquid crystal (LC) devices. The three electric field components are expressed in terms of mixed finite elements, providing the correct enforcement of boundary conditions. Moreover, the optical dielectric tensor of the medium can have all its nine elements nonzero, thus allowing the LC director to have an arbitrary orientation. A photonic crystal fiber with a LC infiltrated core and a homeotropic to multi-domain cell are analyzed. Comparison with other existing simulation techniques is provided, in order to validate the accuracy of the proposed method.

We introduce and develop a new explicit vector beam propagation method, based on the iterated Crank-Nicolson scheme, which is an established numerical method in the area of computational relativity. The proposed approach results in a fast and robust method, characterized by simplicity, efficiency, and versatility. It is free of limitations inherent in implicit beam propagation methods, which are associated with poor convergence or uneconomical use of memory in the solution of large sparse linear systems, and thus it can tackle problems of considerable size and complexity. The advantages offered by this approach are demonstrated by analyzing a multimode interference coupler and a twin-core photonic crystal fiber. A possible wide-angle generalization is also provided.