Abstract
In the current work, the nonlinear problem of electromagnetic wave propagation in a Nematic Liquid Crystal (NLC) cell is solved numerically. The LC is sandwiched between two glass layers of finite thickness and a linearly polarized beam is obliquely incident to the cell. The dielectric properties of N-LCs depend on the tilt angle of the directors. When the excitation beam enters the cell, and providing the incident intensity is above the Fréedericksz threshold, the directors reorient themselves changing the LC's relative permittivity tensor. In turn, this affects beam propagation throughout the crystal. The electromagnetic field is modeled by the time-harmonic Maxwell equations whereas the director field is governed by a nonlinear ordinary differential equation (ODE). Our solution method is iterative, consistently taking into account this interaction between the excitation beam and the director field. The Maxwell equations are solved employing the Mode-Matching Technique (MMT). The solution of the nonlinear differential equation for the director field is obtained with the aid of a finite difference (FD) scheme.
Original language | English |
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Title of host publication | Application of Mathematics in Technical and Natural Sciences - 4th International Conference, AMiTaNS 2012 |
Subtitle of host publication | Memorial Volume devoted to Prof. Christo I. Christov |
Pages | 288-295 |
Number of pages | 8 |
Volume | 1487 |
DOIs | |
Publication status | Published - 2012 |
Event | 4th International Conference on Application of Mathematics in Technical and Natural Sciences: Memorial Volume devoted to Prof. Christo I. Christov, AMiTaNS 2012 - St. Constantine and Helena, Bulgaria Duration: 11 Jun 2012 → 16 Jun 2012 |
Other
Other | 4th International Conference on Application of Mathematics in Technical and Natural Sciences: Memorial Volume devoted to Prof. Christo I. Christov, AMiTaNS 2012 |
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Country/Territory | Bulgaria |
City | St. Constantine and Helena |
Period | 11/06/12 → 16/06/12 |
Keywords
- finite differences
- Fréedericksz transition
- Mode-Matching
- nematic liquid crystals
- nonlinear electromagnetic waves