Computational physics approaches to light transmission through a twisted nematic liquid crystal slab

TL;DR

This paper compares intuitive and Maxwell-based methods for calculating light transmission through twisted nematic liquid crystals, highlighting the limits of simple formulas and evaluating numerical approaches for accuracy and efficiency.

Contribution

It introduces an accurate Maxwell-based solution, compares it with an intuitive approach, and evaluates numerical methods, providing insights into light transmission modeling in liquid crystals.

Findings

Maxwell's equations yield more accurate transmission predictions than simple formulas.

The Gauss-Seidel method converges faster than Euler for numerical calculations.

Conditions for equivalence of the two approaches are identified.

Abstract

We consider light propagation through a twisted nematic liquid crystal. At first, an expression for light transmission is obtained using a rather intuitive approach. Secondly, an accurate solution for light transmission based on Maxwell's equations is derived and compared with the previous one. Both approaches show that when changes in the orientation of the liquid crystal optical axis are small on the scale defined by the optical wavelength (Mauguin limit), the polarization of light approximately follows the optical axis. At the same time, even in this limit, the simple formula for the light transmittance mentioned in some monographs on liquid crystal displays is not necessary accurate. Conditions under which the two approaches give the same expression for the light transmission are found. In addition, two numerical methods for finding the light transmittance are considered. It is demonstrated that the Gauss-Seidel method has much faster convergence rate than the Euler method.