Pitch-controlled reorientational nonlinearity in chiral nematic liquid crystals: a reduced-order model for self-focusing and soliton formation
We present a reduced-order semi-analytical model for reorientational nonlinearity in chiral nematic liquid crystals, showing that the chiral pitch acts as the dominant physical length scale governing the onset of nonlinear self-focusing and soliton formation. Starting from the full Frank-Oseen equation, we derive a closed-form expression for the optically induced molecular rotation that captures the essential saturable response of the medium while reducing computational cost by more than two orders of magnitude compared with standard relaxation-method solvers. Despite its simplicity, the model reproduces the essential features of the numerically obtained nonlinear refractive index, the onset of self-localization, and the transition from discrete to continuous solitons in one and two dimensions. It further predicts the formation of fully localized astigmatic nematicons with only minor shifts in the self-localization threshold due to the neglect of nonlocal effects. The proposed model provides direct physical insight into light-matter interactions with soft matter media and offers a computationally efficient tool for the design and optimization of nonlinear photonic devices.