Numerical Method for Simulation of Orientation Dynamics of Nematic Liquid Crystals in Electromagnetic Fields

The orientation dynamics of nematic liquid crystals (NLCs) is rotation of the director, i.e. a unit vector representing the preferred direction of orientation of molecules, under the action of elastic forces and an electromagnetic field (EMF). A numerical method for solving the equations of the orientation dynamics is proposed and details of its implementation are discussed. A special attention is paid to coupling of numerical solvers for the orientation dynamics of NLCs and for Maxwell's equations describing the light propagation in an anisotropic non-uniform medium. A numerical solution of the problem of the Freedericksz transition is compared with its analytical solution, other examples of numerical simulations of physical phenomena in liquid-crystalline media interacting with electromagnetic waves are given.