Fractional orbital angular momentum(OAM) vortex beams present a promising way to increase the data throughput in optical communication systems. Nevertheless, high-precision recognition of fractional OAM with different...Fractional orbital angular momentum(OAM) vortex beams present a promising way to increase the data throughput in optical communication systems. Nevertheless, high-precision recognition of fractional OAM with different propagation distances remains a significant challenge. We develop a convolutional neural network(CNN)method to realize high-resolution recognition of OAM modalities, leveraging asymmetric Bessel beams imbued with fractional OAM. Experimental results prove that our method achieves a recognition accuracy exceeding 94.3% for OAM modes, with an interval of 0.05, and maintains a high recognition accuracy above 92% across varying propagation distances. The findings of our research will be poised to significantly contribute to the deployment of fractional OAM beams within the domain of optical communications.展开更多
Orbital angular momentum(OAM), as a new degree of freedom, has recently been applied in holography technology.Due to the infinite helical mode index of OAM mode, a large number of holographic images can be reconstruct...Orbital angular momentum(OAM), as a new degree of freedom, has recently been applied in holography technology.Due to the infinite helical mode index of OAM mode, a large number of holographic images can be reconstructed from an OAM-multiplexing hologram. However, the traditional design of an OAM hologram is constrained by the helical mode index of the selected OAM mode, for a larger helical mode index OAM mode has a bigger sampling distance, and the crosstalk is produced for different sampling distances for different OAM modes. In this paper, we present the design of the OAM hologram based on a Bessel–Gaussian beam, which is non-diffractive and has a self-healing property during its propagation. The Fourier transform of the Bessel–Gaussian beam is the perfect vortex mode that has the fixed ring radius for different OAM modes. The results of simulation and experiment have demonstrated the feasibility of the generation of the OAM hologram with the Bessel–Gaussian beam. The quality of the reconstructed holographic image is increased, and the security is enhanced. Additionally, the anti-interference property is improved owing to its self-healing property of the Bessel-OAM holography.展开更多
We investigate the ground states of spin-orbit coupled spin-1 Bose-Einstein condensates in the presence of Zeeman splitting.By introducing the generalized momentum operator,the linear version of the system is solved e...We investigate the ground states of spin-orbit coupled spin-1 Bose-Einstein condensates in the presence of Zeeman splitting.By introducing the generalized momentum operator,the linear version of the system is solved exactly,yielding a set of Bessel vortices.Additionally,based on linear solution and using variational approximation,the solutions for the full nonlinear system and their ground state phase diagrams are derived,including the vortex states with quantum numbers m=0,1,as well as mixed states.In this work,mixed states in spin-1 spin-orbit coupling(SOC)BEC are interpreted for the first time as weighted superpositions of three vortex states.Furthermore,the results also indicate that under strong Zeeman splitting,the system cannot form localized states.The variational solutions align well with numerical simulations,showing stable evolution and meeting the criteria for long-term observation in experiments.展开更多
A general technique to obtain simple analytic approximations for the first kind of modified Bessel functions. The general procedure is shown, and the parameter determination is explained through the applications to th...A general technique to obtain simple analytic approximations for the first kind of modified Bessel functions. The general procedure is shown, and the parameter determination is explained through the applications to this particular case I1/6(x)and I1/7(x). In this way, it shows how to apply the technique to any particular orderν, in order to obtain an approximation valid for any positive value of the variable x. In the present method power series and asymptotic expansion are simultaneously used. The technique is an extension of the multipoint quasirational approximation method, MPQA. The main idea is to look for a bridge function between the power and asymptotic expansion of the I1/6(x), and similar procedure for I1/7(x). To perform this, rational functions are combined with hyperbolic ones and fractional powers. The number of parameters to be determined for each case is four. The maximum relative errors are 0.0049 for ν=1/6, and 0.0047 for ν=7. However, these relative errors decrease outside of the small region of the variables, wherein the maximum relative errors are reached. There is a clear advantage of this procedure compared with any other ones.展开更多
The Bessel beam,characterized by its unique non-diffracting properties,holds promising applications.In this paper,we provide a detailed introduction and investigation into the theory and research of the Bessel beam,wi...The Bessel beam,characterized by its unique non-diffracting properties,holds promising applications.In this paper,we provide a detailed introduction and investigation into the theory and research of the Bessel beam,with a special focus on its generation and applications in the near-field region.We provide an introduction to the concepts,properties,and foundational theories of the Bessel beam.Additionally,the current study on generating Bessel beams and their applications is categorized and discussed,and potential research challenges are proposed in this paper.This review serves as a solid foundation for researchers to understand the concept of the Bessel beam and explore its potential applications.展开更多
In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = ...In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = （α,β）） of the q-case, associated generalized q-wavelets and generalized q-wavelet transforms are developed for the new context. Reconstruction and Placherel type formulas are proved.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.12174338 and 11874321)。
文摘Fractional orbital angular momentum(OAM) vortex beams present a promising way to increase the data throughput in optical communication systems. Nevertheless, high-precision recognition of fractional OAM with different propagation distances remains a significant challenge. We develop a convolutional neural network(CNN)method to realize high-resolution recognition of OAM modalities, leveraging asymmetric Bessel beams imbued with fractional OAM. Experimental results prove that our method achieves a recognition accuracy exceeding 94.3% for OAM modes, with an interval of 0.05, and maintains a high recognition accuracy above 92% across varying propagation distances. The findings of our research will be poised to significantly contribute to the deployment of fractional OAM beams within the domain of optical communications.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.62375140 and 62001249)the Open Research Fund of the National Laboratory of Solid State Microstructures (Grant No.M36055)。
文摘Orbital angular momentum(OAM), as a new degree of freedom, has recently been applied in holography technology.Due to the infinite helical mode index of OAM mode, a large number of holographic images can be reconstructed from an OAM-multiplexing hologram. However, the traditional design of an OAM hologram is constrained by the helical mode index of the selected OAM mode, for a larger helical mode index OAM mode has a bigger sampling distance, and the crosstalk is produced for different sampling distances for different OAM modes. In this paper, we present the design of the OAM hologram based on a Bessel–Gaussian beam, which is non-diffractive and has a self-healing property during its propagation. The Fourier transform of the Bessel–Gaussian beam is the perfect vortex mode that has the fixed ring radius for different OAM modes. The results of simulation and experiment have demonstrated the feasibility of the generation of the OAM hologram with the Bessel–Gaussian beam. The quality of the reconstructed holographic image is increased, and the security is enhanced. Additionally, the anti-interference property is improved owing to its self-healing property of the Bessel-OAM holography.
基金supported by the Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515110198)the Natural Science Foundation of Guangdong Province,China(Grant Nos.2024A1515030131 and 2021A1515010214)+2 种基金the National Natural Science Foundation of China(Grant Nos.12274077,11905032,and 12475014)the Research Fund of the Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology(Grant No.2020B1212030010)the Israel Science Foundation(Grant No.1695/22).
文摘We investigate the ground states of spin-orbit coupled spin-1 Bose-Einstein condensates in the presence of Zeeman splitting.By introducing the generalized momentum operator,the linear version of the system is solved exactly,yielding a set of Bessel vortices.Additionally,based on linear solution and using variational approximation,the solutions for the full nonlinear system and their ground state phase diagrams are derived,including the vortex states with quantum numbers m=0,1,as well as mixed states.In this work,mixed states in spin-1 spin-orbit coupling(SOC)BEC are interpreted for the first time as weighted superpositions of three vortex states.Furthermore,the results also indicate that under strong Zeeman splitting,the system cannot form localized states.The variational solutions align well with numerical simulations,showing stable evolution and meeting the criteria for long-term observation in experiments.
文摘A general technique to obtain simple analytic approximations for the first kind of modified Bessel functions. The general procedure is shown, and the parameter determination is explained through the applications to this particular case I1/6(x)and I1/7(x). In this way, it shows how to apply the technique to any particular orderν, in order to obtain an approximation valid for any positive value of the variable x. In the present method power series and asymptotic expansion are simultaneously used. The technique is an extension of the multipoint quasirational approximation method, MPQA. The main idea is to look for a bridge function between the power and asymptotic expansion of the I1/6(x), and similar procedure for I1/7(x). To perform this, rational functions are combined with hyperbolic ones and fractional powers. The number of parameters to be determined for each case is four. The maximum relative errors are 0.0049 for ν=1/6, and 0.0047 for ν=7. However, these relative errors decrease outside of the small region of the variables, wherein the maximum relative errors are reached. There is a clear advantage of this procedure compared with any other ones.
文摘The Bessel beam,characterized by its unique non-diffracting properties,holds promising applications.In this paper,we provide a detailed introduction and investigation into the theory and research of the Bessel beam,with a special focus on its generation and applications in the near-field region.We provide an introduction to the concepts,properties,and foundational theories of the Bessel beam.Additionally,the current study on generating Bessel beams and their applications is categorized and discussed,and potential research challenges are proposed in this paper.This review serves as a solid foundation for researchers to understand the concept of the Bessel beam and explore its potential applications.
文摘In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = （α,β）） of the q-case, associated generalized q-wavelets and generalized q-wavelet transforms are developed for the new context. Reconstruction and Placherel type formulas are proved.
