Switchable 3D liquid crystal grating generated by periodic photo-alignment on both substrates

A planar liquid crystal (LC) cell is developed in which two photo-alignment layers have been illuminated with respectively a horizontal and a vertical diffraction pattern of interfering left- and right-handed circularly polarized light. In the bulk of the cell, a complex LC configuration is obtained with periodicity in two dimensions. Remarkably, the period of the structure is larger than the period of the interference pattern, indicating that lowering of the symmetry allows a reduction in the elastic energy. The liquid crystal configuration depends on the periodicity of the alignment but also on the thickness of the cell. By applying a voltage over the electrodes, the power going into the different diffracted orders can be tuned. Finite element (FE) simulations based on Q-tensor theory are used to find the 3D equilibrium director distribution, which is used to simulate the near-field transmission profile based on the Jones calculus. A 2D Fourier transform is performed for both the x- and y-component of the transmitted wave to find the diffraction efficiency.