We consider numerical modeling of the optical properties of devices typical of beam-steering devices based on liquid-crystal materials: two-dimensional, anisotropic and inhomogeneous dielectric properties, periodic in one dimension. A mathematical formulation of the system of second-order partial differential equations for the components of the time-harmonic electric field is discretized by using a finite-element method based on curl-conforming edge elements. The discrete equations are also interpreted as equivalent finite-difference equations. It is shown how the resulting large sparse complex system of linear algebraic equations can be solved by an iterative method with convergence accelerated by a preconditioner based on fast Fourier transforms. Benchmarking results and the application to a realistic problem are reported. The practical limitations of the approach and its advantages and disadvantages compared with other approaches are discussed.
© 2004 Optical Society of America
(050.1970) Diffraction and gratings : Diffractive optics
(160.3710) Materials : Liquid crystals
(230.3720) Optical devices : Liquid-crystal devices
(260.1180) Physical optics : Crystal optics
(260.2110) Physical optics : Electromagnetic optics
Nandana D. Amarasinghe, Eugene C. Gartland, Jr., and Jack R. Kelly, "Modeling optical properties of liquid-crystal devices by numerical solution of time-harmonic Maxwell equations," J. Opt. Soc. Am. A 21, 1344-1361 (2004)