A nonlinear model of flexoelectric liquid crystal diffraction gratings

This paper presents a nonlinear model for flexoelectric liquid crystal (LC) diffraction gratings and compares the results from simulations with those obtained from experiments, providing a more accurate description of the behaviour of the flexoelectric LC grating than that offered by the linear models that have been considered previously. The nonlinear model that is constructed considers both dielectric and flexoelectric coupling and, with the aid of numerical simulations, enables the visualization of the behaviour of the LC director in response to flexoelectric, dielectric, and elastic effects. From the numerical simulations, both in-plane and out-of-plane tilt angles are obtained which are then used to simulate the optical wave propagation and diffraction characteristics for light passing through the LC flexoelectric grating. To compare the results from simulations with experiments, we develop an LC mixture that is capable of forming a flexoelectric LC diffraction grating at room temperature. This mixture allows for real-time manipulation of the periodic splay-bend structure by adjusting the amplitude of the DC electric field, enabling control of the diffraction angle and intensity of light into the different diffraction orders. The consistency observed between our simulation results and experimental data underscores the reliability and accuracy of our proposed models.