Electric Field and Polarizer Angle-Dependent Optical Response of a Planar Liquid Crystal Cell Using Monte Carlo Simulations and Mueller matrix Analysis

We investigate the optical response of a planar nematic liquid crystal (LC) cell under varying electric fields and polarizer orientations using a combination of Monte Carlo (MC) simulations and Mueller matrix formalism. The LC molecular configurations are generated using a Lebwohl–Lasher-type lattice model with periodic boundary conditions, electric field coupling, and surface anchoring interactions. These configurations are incorporated into a Mueller matrix framework to calculate the spectrally dependent transmittance through a crossed-polarizer setup for three primary wavelengths: red (λR=700 nm), green (λG=546.1 nm), and blue (λB=435.8 nm), corresponding to simply the RGB color channels, respectively. By systematically varying the polarizer azimuthal angle (𝛼=0⁰, -22.5⁰, and -45⁰), we demonstrate that both the transmitted intensities and the resulting color maps are strongly modulated by changes in electric field and crossed polarizer’s azimuthal angle. To visualize these effects, RGB-based color maps are constructed, providing an intuitive representation of the optical response as a function of system parameters. The results reveal a strong dependence of output intensity and color on the LC molecular orientation, confirming the capability of this simulation-based approach for designing tunable LC optical elements and display technologies.