Résumé
Bragg-Berry optical elements combine the bandgap properties of a cholesteric with the spin-orbit properties of birefringent liquid crystals (LCs). By engineering an appropriate LC alignment pattern with surface angle ϕ inside a cholesteric sample, incident circular polarized light with a wavelength inside the cholesteric bandgap will be reflected by this sample and acquire the so-called Pancharatnam-Berry phase ±2ϕ. With different spatial distributions of ϕ, one can therefore obtain various reflective optical elements such as geometric phase lenses [1] or diffractive elements [2,3]. However, topological defects typically appear when ∇ϕ is not uniform, which may affect the optical quality of the realized optical elements. In this work, we study with numerical and theoretical approaches the equilibrium and optical properties of such defects inside Bragg-Berry cholesteric lenses with a rotationally invariant ϕ-pattern. We demonstrate the existence of quantified equilibrium positions for these defects, similar to Grandjean-Cano cholesteric lines in planar wedge samples, and compare this behaviour with experimental realizations of Bragg-Berry lenses done in the LC photonics group at Ghent University. We also study the impact of such defects on the reflective properties of the lens, based on finite-difference time-domain simulations and a simple point-spread-function model.[1] Stebryte, M. “Reflective optical components based on chiral liquid crystal for head-up displays”, Liquid Crystals Today 30, 36-45 (2021).[2] Stebryte, M., Nys, I., Ussembayev, Y., Beeckman, J. & Neyts, K. “Large Angle Forward Diffraction by Chiral Liquid Crystal Gratings with Inclined Helical Axis”, Crystals 10, 807 (2020).[3] Stebryte, M., Nys, I., Beeckman, J. & Neyts, K. “Chiral liquid crystal based holographic reflective lens for spectral detection”, Optics Express 30, 42829 (2022).