By creating self-induced vortexlike defects in the nematic liquid crystal layer of a light valve, we demonstrate the realization of programable lattices of optical vortices with arbitrary distribution in space. On each lattice site, every matter vortex acts as a photonic spin-to-orbital momentum coupler and an array of circularly polarized input beams is converted into an output array of vortex beams with topological charges consistent with the matter lattice. The vortex arrangements are explained on the basis of light-induced matter defects of both signs and consistent topological rules.

Quantum walks are powerful tools for quantum applications and for designing topological systems. Although they are simulated in a variety of platforms, genuine two-dimensional realizations are still challenging. Here we present an innovative approach to the photonic simulation of a quantum walk in two dimensions, where walker positions are encoded in the transverse-wavevector component of a single light beam. The desired dynamics is obtained by means of a sequence of liquid-crystal devices, which apply polarization-dependent transverse “kicks” to the photons in the beam. We engineer our quantum walk so that it realizes a periodically driven Chern insulator, and we probe its topological features by detecting the anomalous displacement of the photonic wavepacket under the effect of a constant force. Our compact, versatile platform offers exciting prospects for the photonic simulation of two-dimensional quantum dynamics and topological systems.

By sending circularly polarized light beams onto a homeotropic nematic liquid crystal cell with a photosensitive wall, we are able to locally induce spontaneous matter vortices that remain, each, stable and trapped at the chosen location. We discuss the dual light-matter nature of the created vortices and demonstrate the ability of the system to create optical vortices with opposite topological charges that, consistent with angular momentum conservation, both derive from the same defect created in the liquid crystal texture. Theoretically, we identify a self-stabilizing mechanism for the matter vortex, which is provided by the concurrency of light-induced gradients and anisotropy of the elastic constants that characterize the deformation of the liquid crystal medium.

Optical vortices are attracting much attention because of their applications in various fields of optical processing, communications, enhanced imaging systems, and bio-inspired devices. Different methods to generate optical vortices have been devised to date. Among them, several are based on the exploitation of light–matter interaction in liquid-crystal media. This review focuses on the main mechanisms of vortex generation in liquid crystals, in particular on vortex generation induced by umbilics, that is, defects arising in homeotropically aligned nematic cells, which act as topological matter templates able to realize the conversion from spin to orbital angular momentum of an incoming Gaussian beam. Optical vortex induction in a photosensitive light valve is presented as a self-stabilizing mechanism leading to reconfigurable and programmable vortex arrays. On each lattice site, every matter vortex acts as a photonic spin-to-orbital momentum coupler, converting input arrays of circularly polarized beams into output arrays of vortex beams with topological charges consistent with the matter lattice symmetry.

A Berry phase is revealed for circularly polarized light when it is Bragg reflected by a chiral liquid-crystal medium of the same handedness. By using a chiral nematic layer we demonstrate that if the input plane of the layer is rotated with respect to a fixed reference frame, a geometric phase effect occurs for the circularly polarized light reflected by the periodic helical structure of the medium. Theory and numerical simulations are supported by an experimental observation, disclosing novel applications in the field of optical manipulation and fundamental optical phenomena.

The success of nematic liquid crystals in displays and optical applications is due to the combination of their optical uniaxiality, fluidity, elasticity, responsiveness to electric fields and controllable coupling of the molecular orientation at the interface with solid surfaces. The discovery of a polar nematic phase opens new possibilities for liquid crystal-based applications, but also requires a new study of how this phase couples with surfaces. Here we explore the surface alignment of the ferroelectric nematic phase by testing different rubbed and unrubbed substrates that differ in coupling strength and anchoring orientation and find a variety of behaviors – in terms of nematic orientation, topological defects and electric field response – that are specific to the ferroelectric nematic phase and can be understood as a consequence of the polar symmetry breaking. In particular, we show that by using rubbed polymer surfaces it is easy to produce cells with a planar polar preferential alignment and that cell electrostatics (e.g. grounding the electrodes) has a remarkable effect on the overall homogeneity of the ferroelectric ordering.