Research on the dynamic modeling method of beam control for liquid crystal optical phased array based on the fractional-order generalized Kelvin model

Liquid crystal optical phased array (LCOPA) serves as a core component for non-mechanical beam steering. Their beam response is affected by the viscoelasticity of liquid crystals, exhibiting dynamic hysteresis and nonlinear characteristics, making traditional integer-order models inadequate for describing the beam steering dynamics. This paper proposes a dynamic modeling method based on a fractional-order generalized Kelvin viscoelastic model. By utilizing the memory characteristics of fractional-order derivatives and the multiscale properties of the generalized Kelvin model, a fractional-order constitutive equation for LCOPA elements and a dynamic model relating phase modulation to deflection angles are established, with parameter identification performed using the nonlinear least squares method. Experimental results show that the model outperforms integer-order models in fitting accuracy, better characterizes hysteresis and nonlinearities, and has good generalization capability, providing a foundation for precise LCOPA control and the design of high-performance non-mechanical beam steering systems.