Generation And Detection Of Vortex Arrays Based On Coherent Superposition Of Laguerre-Gaussian Beams/Hermite-Gaussian Beams

Vortex beam is a special beam existing in optics,which can also be called vortex light field or optical vortex,its essence is that the optical field carries helical phase wavefront.Compared with the traditional fundamental mode Gaussian beam,vortex beam carries orbital angular momentum and has a doughnut-shaped ring spot structure.Therefore,vortex beams can play a unique advantage in applications such as particle micro-manipulation,optical communication,chiral material micro-fabrication,and microscopy super-resolution imaging.With the development of micro-control technology,vortex beams with single singularities no longer meet the scientific research needs of researchers.In order to pursue the simultaneous control of multiple particles（such as multi-well optical tweezers）,breaking the limitation of singularities located only at the center of the light beam,satisfying the applicability of vortex beams in different scenarios,people focus their attention on vortex arrays with multiple singularities in order to improve the degree of freedom of particle manipulation..Researchers have discovered two ways to generate vortex arrays:Obtaining high-quality vortex arrays by overlaying vortex beams with different singularities outside the cavity;direct output of high-power and high stability vortex array through intra-cavity modulation.In this paper,this article focuses on the superposition of Laguerre-Gaussian(LG_0l)vortex beams and Hermite-Gaussian(HG_mn)beams,A multi singularity vortex array was obtained by stacking degenerate HG_mn beams with different modes inside the cavity.The main research content is as follows:1.Generation of large topological charge number vortex beams by cascaded multiple spiral phase plates.The characteristics of vortex beams passing through n SPPs are analyzed theoretically.In experiments,1064 nm and 532 nm fundamental mode Gaussian beam are modulated by multiple cascaded SPPs,respectively,to produce LG_0n vortex beams with large TC.The TC of the generated vortex beam was detected using three different methods:inclined lens method,off-axis interference method,and spherical wave interference method.The advantages and disadvantages of various detection methods were compared,indicating that off-axis interference method is more suitable for detecting large quantities of TC.2.Generation of rotationally symmetric vortex arrays by superimposing high order LG_0lvortex beam outside the cavity.The petal shaped vortex array is generated by the coaxial interference of LG_0l,and the vortex array with rotational symmetry is generated by superposition of LG_0l beam based on two different interference devices,namely,Mach–Zehnder interferometer（MZI）and Sagnac interferometer.The distribution of singularities in the vortex array is detected using off-axis interferometry.The results show that the number of central singularities of the vortex array generated by the coaxial superposition of two LG_0lbeams（with topological charges of l₁ and l₂,respectively）is the smaller value of the TC of the two beams,and|l₂-l₁|single vortices with topological charges of（l₂-l₁）/|l₂-l₁|are uniformly distributed in the outer circle.The vortex array exhibits good rotational symmetry.3.The generation of multi singularity vortex arrays is achieved based on the superposition of different degenerate HG modes in the resonant cavity.In the experiment,a laser with a flat cavity structure using Nd:YVO₄as the working medium was pumped by a large annular spot.By introducing an asymmetric distribution on the pump light and adjusting the inclination angle of the output coupling mirror in a small angle range,a variety of multi-mode HG superposition states vortex arrays were obtained.The effects of pump power,cavity length and other parameters on the number of singularities in vortex arrays were experimentally studied.Theoretical analysis was conducted using the coherent superposition of transverse mode degenerate HG modes,and the numerical simulation results were consistent with the experimental results,confirming that the vortex array is generated by the superposition of different degenerate HG modes.