Polarization properties of twisted nematic liquid crystal

Liquid crystal (LC) layers in TVs are thin films placed between glass substrates and polarizers. By applying electric fields, these layers control the rotation of polarized light, modulating brightness and color for each pixel. Combined with backlights and color filters, they enable high-resolution, vibrant images on TV screens. In this example, we will model a Twisted Nematic LCD (TN-LCD) using STACK solver. For TN-LCD simulation using FDTD solver, see Polarization properties of a helically twisted liquid crystal – Ansys Optics. The results are extracted for use with the LSWM plugin.

Simulation setup

In the absence of an applied voltage, the liquid crystal molecules are arranged so that their director rotates uniformly by 90° from the bottom surface to the top of the LC layer. Light entering the LC with its polarization aligned to the bottom director (e.g. x-axis) will follow this rotation, resulting in the transmitted light being polarized along the top director (e.g. y-axis). When external voltage is applied, the electric field realigns the LC director so that it is uniform and parallel to the direction of propagation. In this state, the polarization of the transmitted light remains unchanged.

To simulate this 90° twist in STACK solver, we use an anisotropic material, and we discretize the LC thickness to several sublayers to define the spatial variation of the director. Assuming a uniform twist through the cell, the director rotates by π/2 (defined by “LC_rot” parameter in the script), across the thickness, so that the rotation angle varies linearly with z as:

$$θ(z) = \frac{z}{thickness}*LC_{rot}$$

The script can be run for multiple theta and phi incident angles and export results to a json file that can be used as input to Speos.

Results

To quantify the polarization conversion induced by the LC layer, we analyze the complex transmission coefficients provided by STACK solver. For an incident p-polarized wave, the transmitted amplitudes are given by t_pp (co-polarized component) and t_ps (cross-polarized component). The corresponding transmitted power fractions are obtained from |t_pp|² and |t_ps|².

Plotting |t_pp|² represents that fraction of incident p-polarized light that remains p-polarized after transmission, while |t_ps|² quantifies the conversion of p-polarized light into s-polarization.

The presence of a non-zero |t_ps|² indicates polarization coupling introduced by the twisted LC.

See also

Polarization properties of a helically twisted liquid crystal, Simple LCD example