Liquid crystals are optical materials whose molecules can be oriented via the application of a static or low-frequency electric field. Given the anisotropic optical properties of these materials depending on their orientation, designers can use them to electrically tune the response of a wide class of photonic components including display and communications components including optical switches, couplers, shutters, modulators and beam steering devices. A rigorous Maxwell solver is required to predict the broadband response of photonic components incorporating liquid crystals and when the molecule orientation is varied over wavelength-scale distances.