Optical textures of a uniform liquid crystal lattice: Monte Carlo simulations with Newton colors and Mueller matrix analysis

The optical textures of a uniform liquid crystal (LC) molecule lattice structure were explored through Monte Carlo (MC) simulations, combined with Mueller matrix (MM) formalism and Newton’s color theory. These simulations utilized a Lebwohl-Lasher (LL) type interacting LC lattice under periodic boundary conditions, generating ensemble-averaged configurations at two temperature regimes (kBT = 0.9 and 1.2), corresponding respectively to nematic and isotropic states. These configurations were then incorporated into the MM framework to evaluate the polarization states of transmitted light. To visually interpret the resulting interference phenomena, we propose a new visualization method based on a modern interpretation of Newton’s color model. The Newton color model was employed to render the emerging patterns on a two-dimensional screen in an intuitive fashion. We further introduce a transmittance saturation model as a function of thickness (Lz ), which provides a good fit to the transmittance data of anisotropic media in a uniform LCM lattice. The model, T(Lz) = T0[1 −exp(−κLz)] , successfully captures how transmittance varies with lattice thickness. Interference hues and texture distributions shifted noticeably with increasing thickness in both nematic and isotropic phases, reflecting the degree and nature of molecular ordering. The nematic textures exhibited a rich, broad color spectrum, whereas the isotropic textures were characterized by fewer chromatic variations. Moreover, increasing thickness significantly enhanced both light intensity and color diversity. The nematic textures appeared more structured and patchy, indicative of partial molecular alignment. These findings underscore the intricate interplay among molecular ordering, optical phase distinctions, and overall LC behavior, offering valuable perspectives for display technologies, optical sensing, and related photonic applications that demand fine control of LCM birefringence.