In a recent review published in Chinese Optics Letters (Z. Li, et al., Liquid Crystal Devices for Vector Vortex Beams Manipulation and Quantum Information Applications), the research group led by Prof. Yanqing Lu from Nanjing University discussed the functions and applications of typical Liquid crystal (LC) devices in recent studies on controlling the vector vortex beams (VVBs). They also reviewed the experimental advances on novel photonic applications in the quantum domain enabled by LC devices.
LC is an excellent electro-optic material with an intermediate structure between liquids and crystalline solids. It possesses large optical anisotropy, and its optical properties can be easily modified by moderate external fields, allowing high flexibility of different degrees of freedom of light. One special degree of freedom that has received great interest is that of orbital angular momentum. Light beams carrying orbital angular momentum are well known as vortex beams. Light beams with an azimuthally varying linear polarization surrounding an optical vortex located on the beam axis are called VVBs. They have important applications in particle acceleration, optical sensing, high-resolution imaging, and quantum information processing. LC has been proved to be a versatile tool in the engineering of VVBs, with the advantages of simple configuration, convenient use, low cost, and high conversion efficiency.
Typically used LC-based devices to manipulate VVBs includes geometric phase LC elements such as q-plates and dynamic phase LC elements such as spatial light modulators (SLMs). Patterned nematic LC, patterned cholesteric liquid crystal (CLC), and self-assembled defects can be used to generate q-plates. Usually, they work at the half-wave condition with a small optical thickness, so they are easy to integrate. Nematic LC is a commonly used LC phase, it usually operates at a single wavelength and requires fine-tuning to maximize the conversion efficiency. CLC is a liquid crystalline phase where the rod-like molecules self-assemble into a periodic helical structure. The chiral superstructures exhibit a broadband Bragg reflection with unique circular-polarization (spin) selectivity; thus, it serves as a new platform for broadband reflective geometric phase manipulation. Spontaneously formed LC topological defects under external fields offer a nature-assisted route to the creation of geometric phase optical elements. Compared to patterned nematic or CLC q-plates, extra orientation techniques are not needed in such soft-matter self-organization processes.
VVBs can be obtained by simply using a non-circular polarization input beam passing through a q-plate, and the physics behind that is relatively straightforward. Considering a linearly polarized beam carries zero OAM, the input state can also be written as the supposition of left and right circularly polarized states. After passing through a q-plate, one obtains a nonseparable state of the polarization and OAM degrees of freedom which indicates the generation of VVB.
The concept of classical entanglement or intra-system entanglement is used to describe such property of vector beams, as it is mathematically equivalent to quantum entanglement. However, non-locality isn't involved. With the advantage of their flexible tuning property, LCs have been widely used in the generation of complex entanglement structures and have become important tools for quantum information tasks. Figure 1 shows that combing time-frequency modes (TFM) encoding through a parametric down-conversion process and VVB encoding via a q-plate, a simple yet high-quality source of TFM-VVB hyperentanglement can be generated .
Fig. 1 (a) Sketch of the biphoton hyperentangled state; (b) Experimental setup for state preparation.（Phys. Rev. Res. 2(4), 043350 (2020).）
Besides the applications of LC devices in the field of VVBs engineering, manipulations of other types of vector beams are worth exploring. Novel structures taking advantage of both LC and metasurfaces may lead to promising applications in integrated optics. The collaboration of nonlinear processes would also provide a novel way to achieve dynamic steering of nonlinear structured light.
