Modeling of molecular reorientation in nematic liquid crystals - Sala, Filip; Bujok, Maksymilian; Karpierz, Mirosław (Photonics Letters of Poland, 2016)
In this paper modeling of molecular reorientation in nematic liquid crystals is described. The theoretical model bases on Frank-Oseen elastic theory. By minimizing the equation on free energy the equation describing molecular reorientation is obtained. To get a solution two numerical methods (Successive Over-Relaxation and multigrid) are employed and are compared for numerical results of director orientation and computation time. Full Text: PDF References G. Assanto, M.A. Karpierz, "Nematicons: self-localised beams in nematic liquid crystals", Liq. Cryst. 36, 1161 (2009). CrossRef G.D. Ziogos, E.E. Kriezis, "Modeling light propagation in liquid crystal devices with a 3-D full-vector finite-element beam propagation method", Opt. Quant. Electron. 40, 10 (2008). CrossRef M. Kwaśny, U.A. Laudyn, F.A. Sala, A. Alberucci, M.A. Karpierz, G. Assanto, "Self-guided beams in low-birefringence nematic liquid crystals", Phys. Rev. A 86, 013824 (2012). CrossRef M.A. Karpierz, "Solitary waves in liquid crystalline waveguides", Phys. Rev. E 66, 036603 (2002). CrossRef A. Walczak, "Soliton like solutions and subsurface behaviour of the nematic layer", Proc. SPIE 4759, 327 (2002). CrossRef F.A. Sala, M.A. Karpierz, "Chiral and nonchiral nematic liquid-crystal reorientation induced by inhomogeneous electric fields", J. Opt. Soc. Am. B 29, 1465 (2012). CrossRef F.A. Sala, M.A. Karpierz, "Modeling of molecular reorientation and beam propagation in chiral and non-chiral nematic liquid crystals", Opt. Express 20, 13923 (2012). CrossRef D.M. Young, Iterativemethods for solving partial difference equations of elliptical type, Ph.D. thesis (Harvard University, 1950). D. Kincaid, W. Cheney, Numerical Analysis: Mathematics of Scientific Computing (American Mathematical Society, 2002). W.L. Briggs, V.E. Henson, S.F. McCormick, A Multigrid Tutorial (Society for Industrial and Applied Mathematics, 2000). A. Brandt, O. Livne, Multigrid Techniques (Society for Industrial and Applied Mathematics, 2011).