### Abstract

This paper presents a robust numerical method for the analysis of wave propagation in nematic liquid crystals. The structure is excited by a plane wave incident at an oblique angle with respect to the normal to the liquid-crystal cell. The underlined formulation is based on an eigenvalue problem which is solved analytically in order to obtain the governing field expressions inside a homogeneous, thin crystal layer. The liquid-crystal cell is comprised of N such layers. Enforcing the continuity of the tangential electric and magnetic fields at the interfaces formed by the various layers, a matrix system is generated. Solution of the linear system of equations results in the light intensity inside the liquid crystal, which is coupled to a non-linear differential equation for the director tilt angle. This equation is solved using either an explicit or implicit finite-difference scheme. An iteration process continues until convergence is reached for the coupled problem. The proposed numerical method was validated against published results that were generated by approximate analytical methods. Further simulations and studies were conducted emphasizing on the physics of the problem and related interesting phenomena.

Original language | English |
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Pages (from-to) | 10643-10654 |

Number of pages | 12 |

Journal | Applied Mathematics and Computation |

Volume | 219 |

Issue number | 22 |

DOIs | |

Publication status | Published - 2013 |

### Keywords

- Finite difference method
- Fréedericksz transition
- Maxwell equations
- Modal analysis
- Mode-matching technique
- Nematic liquid crystals
- Nonlinear differential equations