Generation And Application Of Higher-order Laguerre-Gaussian Beams Based On Liquid-Crystal Spatial Light Modulators

Higher-order Laguerre-Gaussian (LG) beams are characterized by carrying angular momentum and having ring-shape, therefore, contain more information. LG beams have been extensively studied in recent years and have an irreplaceable advantages in parametric down-conversion entanglement, quantum cryptography, gravitational wave detection, particles manipulate, optical tweezers, optical spanner, optical communication, material processing and so on. Hence, the generation of high-order LG beams becomes particularly important. There are several ways to produce high-order LG beams at present, such as using spatial light modulator, spiral phase plate, cylindrical lens, hologram forked grating, diffractive optical elements (DOE) etc. However, Spatial light modulators (SLMs) have the advantages of wide spatial bandwidth, high resolution and small pixel size. In particular, they can control each pixel dynamically and in real-time. Thus, SLMs is usually used in generating high-order LG beams.This article studies the generation of high-order LG beams based on liquid crystal spatial light modulator and its application. This research is mainly focus on the following aspects:1. The generation of high-order LG beams. We theoretically calculate and simulate the purity of the generated LG beam. Programs utilized to extract the phase hologram of LG beam are designed by Matlab. In experiments, LG beams with purities of 83.97%(LG0,5),74.03%(LG1,5) and 54.98%(LG3,3) are obtained, respectively. We also prove that the LG beams possess spiral phase structure as observed in the experiments.2. Optimization of the generated LG beams. Analysis the performance of helical LG mode and sinusoidal LG mode in triangular mode cleaner (MC) and liner mode cleaner, and prove the triangular MC can’t transmit helical LG mode. Further design liner MC and optimize the experimental generated LG beams, and the fidelity of LG0,1 reached to 91.5%.3. The application of high-order LG beams in continuous-variable spatial multi-mode entanglement and phase measurement. Analysis the principle of generated of continuous-variable hyper-entanglement and polarization entanglement by type-Ⅱ OPO. Also, study the principle of phase measurement by high-order LG mode.