Generation Of High-order Orbital Angular Momentum Modes And Its Application In Rotating Image Processing

Angular momentum is divided into spin angular momentum(SAM)and orbital angular momentum(OAM).During its propagation,a photon carrying SAM rotates while a photon carrying OAM orbits in the direction of propagation.OAM modes carry spiral phases of exp(il?)with l being the topological charge,which have infinite dimensionality and orthogonality in principle.These characteristics make OAM modes important in the fields of optical manipulation,quantum information,optical communication,imaging and detection.Laguerre-Gaussian(LG)modes are one of the commonly used high-quality OAM modes.In contrast to the other OAM-carrying modes,LG modes have several unique advantages.For example,as Eigen solutions of the wave equation as well as Eigen modes of laser resonator,LG modes can realize low-loss long-distance transmission.They also feature orthogonality and completeness in the two-dimensional planeSince OAM modes were proposed in 1992,the relative researches have covered various aspects from generations and detections to applications.Especially,the generation of high-order OAM mode is one of the key frontier problems because of high-end applications such as high-capacity optical communication and high-precision optical measurement.In addition,OAM modes has been preliminarily applied in the field of digital imaging in recent years.By analyzing the distribution of OAM modes,one can obtain rotation symmetry of an object,angle and its orientation,and so on.However,in modern industry and scientific research,it still faces great challenges to realize real-time tracking and image processing of high-speed rotating objects such as aero engine,super centrifuge,gas turbine,energy storage flywheel.This paper focuses on the generation of high-order OAM modes and its application in rotating image processing1.The generation of high-order OAM modes through the process of third-harmonic generation based on quasi-phase matching.According to the incident wavelength,LiTaO3 crystals with one-dimensional(1D)quasi-periodic structure and two-dimensional(2D)periodical structure were fabricated by room-temperature electric poling technology.In the 1D quasi-periodically poled LiTaO3 crystals,third-harmonic generation is realized by the coupled second-harmonic generation and sum-frequency generation processes through collinear quasi-phase matching configurations.In 2D periodically poled LiTaO3 crystals,third-harmonic generation is achieved by cascading second-harmonic generation and sum-frequency generation processes through non-collinear quasi-phase matching schemes.Multiple OAM modes along different directions can be generated simultaneously.The experimental results demonstrate that the OAM conservation(i.e.,the topological charge of third-harmonic OAM mode is three times that of incident OAM mode)is well obeyed in the process of third-harmonic generation.Our method provides an efficient way to obtain high-order OAM modes2.Optical image decomposition and noise processing based on LG modes.Due to the complexity of the radial mode expansion,we propose a new method with high efficiency to decompose an optical image in the LG domain,which needs much fewer sampling points in comparison to the existing integral method.Through optimizing the waist and azimuthal and radial truncation orders,and ensuring the effective area of the LG mode to cover the image in both spatial and frequency domain,we realize the high-quality image reconstruction.In addition,the image azimuthal noise reduction based on LG modes is demonstrated,which further proves the advantages of image processing in LG domain3.Laguerre-Gaussian transform for rotating image processing.Due to the spatial rotational symmetry of LG modes,the LG spectrum of a rotating image does not change even the object working at a high speed,which is utilized in real-time rotating image possessing.Similar to the Fourier transform by using an optical lens,the rotation operation provides a feasible method to acquire the LG spectrum.By analyzing the obtained LG spectrum,one can perform image processing such as reconstruction,edge enhancement,and pattern replication.The LG transform provides an effective method for real-time monitoring and analyzing high-speed rotating objects in the field of industry and astronomy.