Study On The Theory And Method Of Optical Vortex Field Customization With Fiber Laser Arrays

Optical vortex(OV)fields possess exotic intensity distributions,phase structures,and dynamic properties,which hold great promise for widespread applications,including information transmission,particle manipulation,and industrial processing.In terms of the generation and manipulation of OV fields,the current techniques present the bottlenecks in both power enhancement and high-speed mode switching,and the customization of high-power,mode-flexibly switchable OV fields is currently an international challenge in the research regime of structured light.Addressing this challenge,using the fiber laser array system as the platform to tailor OV fields based on coherent laser beam combining offers a promising technical solution,which spurs substantial research interests worldwide.However,this technical route is still in its infancy in terms of theoretical model construction and control method exploration,and there are many research gaps in the performance evaluation criterions and optimization methods for the system.This paper conducts a comprehensive study on the theory and method of vortex optical fields customization based on fiber laser arrays,and the key issues including the laser array design,spatial mode characteristics of customized optical field,the theory of mode control,intelligent control techniques,and the performance evaluation and optimization of the tailored optical field are systematically analyzed.1.The theoretical model of laser array design for tailoring OV fields is established.The two design guidelines including “forward design” and “reverse design” are proposed.According to the forward design guideline of laser arrays,the customization of single vortex beam is explored in detail.The laser array design methods based on discrete piston phases fitting and spiral line arrangement are introduced,and the feasibility of tailoring OV fields with higher azimuthal modes is validated.According to the reverse design guideline,the customization of multiple optical vortices is investigated.The method for tailoring OV arrays based on laser arrays is proposed and verified theoretically.The results offer the general guidance on the laser array design for tailoring structured light fields.2.The spatial mode characteristics of the OV fields tailored by fiber laser arrays is studied in detail.According to the definitions of orbital angular momentum(OAM)mode purity and OAM spectrum,the OAM mode components and the mode distributions of the OV field tailored by the laser array are characterized and analyzed.The optical field of the laser array is revisited in the view of angular domain.After transforming the Cartesian coordinates representation to Polar coordinates representation,the optical field of laser array is azimuthally decomposed.The formation of the mainlobe and sidelobes of the combined optical field is analyzed based on the results of azimuthal decomposition,and the theoretical basis of the intuitive design experience for the filling of laser array emitting aperture is elucidated.Based on the findings,the spatial mode extraction of the laser array is explored,and the mode extraction method for laser array based on spatial filtering is proposed,which enables the mode purification of combined OV field.Furthermore,the customization of OV fields with higher radial modes based on the spatial filtering of laser array is demonstrated.3.The theoretical model for the mode control of OV fields generated from fiber laser arrays is constructed.The complex control difficulty for the OV field tailored by the fiber laser array is illustrated.The limitation of directly employing the phase control method in conventional coherent fiber laser beams combination regimes to manipulate the mode of OV field is pointed,and the necessity for developing mode control methods in the aspects of dynamic phase noises compensation and flexible mode switching is explained.The concepts of cost function extraction at the non-focal plane and power-in-the generalized “bucket” cost function are proposed,and the mode control method based on the non-focal plane optical field information is further proposed.The feasibility of the proposed method for the mode stabilization of vortex optical fields under dynamic phase noise perturbation is theoretically verified.Then,incorporated by the knowledge for the spatial mode characteristics of laser arrays,the mode control method based on the OAM mode sorting assistance is proposed.The results indicate that by employing the mode sorting into phase control system,the differences between the intensity patterns detected by the control module that correspond to different OAM states are magnified at the determined position,thus ensuring the efficient compensation of dynamic phase noises and flexible mode switching of the generated OV field at the same time.4.The deep learning(DL)based phase control technique for fiber laser arrays is investigated,which offers the new solution for the programmable mode control of combined OV fields.The theoretical model of convolutional neural network(CNN)based DL phase control is constructed.The non-focal plane optical field information based DL phase control technique is proposed,and the core idea is utilizing the non-focal plane optical field information as the sample data to efficiently avoid the data confliction difficulty of the CNN.The utility of the proposed technique for phase errors estimation and compensation is numerically verified in 7-element and 19-element fiber laser array systems.Multi-spatial domain optical field information integrated,two-stage phase control scheme is proposed,which combines the utility of DL method in the avoidance of undesired optimum converging and the advantage of conventional gradient descent optimization algorithm in the phase-locking accuracy enhancement,thus ensuring the accurate compensation of phase noises and the programmable mode control of combined OV field.The dimension of optical field information mining is extended in the angular domain perspective,and the angular domain optical field information based DL phase control technique is further proposed.The feasibility of training the CNN by using the OAM demultiplexed intensity patterns as the sample data is demonstrated,and the analysis exhibits the compatibility enhancement of the two-stage control.Furthermore,the array elements extensibility of the proposed phase control technique is explored and discussed.5.The performance evaluation and optimization methods for the OV fields tailored by fiber laser arrays is systematically studied.By employing the OAM of light,the physical concept of “Airy patterns” is extended to “Higher-order Airy patterns”.Then,based on the concept of higher-order Airy pattern,the appropriate performance metric and the evaluation method for the OV fields tailored by fiber laser arrays are proposed.According to the proposed performance metric and evaluation method.The influences of design parameters and properties of the laser source module,emitting array module,and dynamic control module in the fiber laser array system on the performance of the generated OV field is comprehensively analyzed,which provides references on system design and perturbation tolerance evaluation.To fulfill the performance improvement of tailored OV fields,the optimization methods for the system are proposed in terms of the definition of higher-order Airy patterns,geometric fractal structure,and complex wavefront control.