A new publication from Opto-Electronic Advances, 10.29026/oes.2024.240001 discusses robust detection technology of orbital angular momentum of partially coherent vortex light fields in complex environment.

The orbital angular momentum (OAM) carried by the vortex beams is considered as a new set forming the basis of carrier signals that is different from amplitude, phase, polarization, and frequency. By combining with other traditional multiplexing methods, the channel transmission capacity can be greatly expanded. However, during the transmission process, in addition to losing its own energy due to phenomena such as scattering, refraction and absorption, the beam is also affected by atmospheric turbulence disturbance effects such as beam spreading, beam wander and scintillation, as well as obstruction by obstacles, which will seriously affect the performance of its communication system. Partially coherent beams can resist the negative effects caused by turbulent atmosphere or obstacles in the transmission path to some extent. According to research reports, partially coherent vortex light fields with both OAM and partially coherence properties have shown unique advantages in fields such as beam shaping, ghost imaging, optical communications, and information encryption.

How to accurately detect the OAM information of partially coherent vortex beams is a key step in many application fields, such as OAM multiplexing optical communications.

Early researchers used methods such as interference, diffraction, and Fourier analysis to establish a connection between the phase singularities carrying OAM/topological charge and the light intensity distribution. By measuring the light intensity, OAM/topological charge information can be effectively detected. However, the above methods are only suitable for fully coherent beams. As the coherence decreases, the phase singularity of the beam is converted into a spatial coherent structure, and the ability to manipulate the light intensity is lost. Especially under low coherence, OAM/topological charge information cannot be obtained through light intensity. To overcome this limitation, some methods based on measuring the spatially coherent structure have been proposed, including speckle statistics, Hanbury Brown-Twiss method, self-reference holography technology, phase perturbation technology, etc. These methods are all only applicable for measurements under conditions without obstacle perturbation, which excludes measurements in a complex transmission environment. This is because the complex effect of obstacles and the turbulent atmosphere on the vortex phase, results in the chaotic splitting and the destruction of the spatial-coherence structure, and the random annihilation and generation of coherent vortices, which seriously distorts the OAM information and hinders its transmission performance. Therefore, how to accurately measure the orbital angular momentum information carried by partially coherent vortex beams in complex transmission environments has become a key scientific issue and has important application value.

The authors of this article propose a detection scheme based on cross-phase control, achieving accurate measurement of the OAM information of partially coherent vortex beams in complex environments. Robust transmission and far-field detection of topological charge/OAM information was achieved by only relying on the anisotropic control of the spatial coherent structure by cross-phase. The mode conversion property induced by the cross-phase can make the OAM/topological charge information hidden in the coherent structure emerge as a distribution with multiple isolated dark rings. The number of separated dark rings is equal to the magnitude of the topological charge which determines the OAM carried by each photon in the vortex beam. The sign of topological charge is determined by the arrangement direction of separated dark rings, which determines the direction of rotation of the spiral wavefront of the vortex beam. Therefore, by detecting the coherent structure after cross-phase modulation, the far-field topological charge information can be obtained. This method is not only suitable for detection in free space transmission environments, but also for detection in transmission environments with obstructions and atmospheric turbulence disturbances. This is because the improvement in self-healing property induced by the cross-phase is enough to resist the adverse effects caused by complex environments. A schematic of the proposed protocol is illustrated in figure 1.

It is well known that the coherent structure distribution of a partially coherent Laguerre Gaussian beam in the far field consists of a series of concentric dark ring structures, and the number of dark rings is equal to the magnitude of the topological charge. Therefore, the coherent structure can carry information and be used for information transmission and encryption. However, in complex transmission environments, due to the influence of phase disturbance (turbulence), the original circular symmetry structure is obviously distorted [see Figs. 2(a1)-(a4)]. Especially under the joint intervention of amplitude disturbance (obstacle) and phase disturbance (turbulence), the coherent structure is much more severely damaged and becomes speckle-like distribution [see Figs. 2(b1)-(b4)], making it impossible for us to obtain topological charge information. The article points out that under the influence of cross-phase modulation, the coherent structure used to represent topological charge information has a strong ability to resist environmental disturbances. Even under the double perturbations of atmospheric turbulence and obstacles, its structure always remains unchanged and exists stably with a recognizable multiple isolated dark rings distribution [see Figs. 2(c1)-(d4)].

Figure 3 shows the experimental results of measuring the coherent structure/topological charge information of partially coherent vortex beams using the cross-phase. The results show that by modulating the cross-phase, the coherent structure of a partially coherent Laguerre Gaussian beam can still maintain a stable spatial distribution under the effects of atmospheric turbulence and obstacles (see Fig.3). Moreover, the topological charge/OAM information carried by the beam can be effectively and quickly extracted from this separated multi-singularity dark ring structure. To further verify the robustness of this method, the author also conducted corresponding experimental verifications under different turbulence strengths (T=75°C and T=100°C) (see figure 10 of the original article). The high consistency between the experimental and theoretical results strongly proves the effectiveness, accuracy, and robustness of the proposed method. This research method and results have potential application value in optical information encryption and free-space optical communications in complex environments.

Keywords: degree of coherence / orbital angular momentum / cross-phase / topological charge / information transmission
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The Center of Light Manipulation and Applications of Shandong Normal University (http://www.gctk.sdnu.edu.cn) was established in May 2018. The center relies on the Shandong Provincial Engineering and Technical Center of Light Manipulations, Shandong Province Higher Education Laboratory of Multi-dimensional Light Manipulation and Applications, Shandong Provincial Collaborative Innovation Center of Light Manipulation and Applications, Shandong Provincial Key Laboratory of Optics and Photonic Device, and School of Physics and Electronics. The director of the center is Professor Yangjian Cai, winner of the National Science Fund for Distinguished Young Scholars and a fellow of the Optical Society of America. The center now has more than 600 square meters of office and conference space, more than 300 square meters of optical clean rooms. The center is now equipped with large-scale experimental equipment worth more than 50 million yuan, including electron beam exposure systems, femtosecond laser processing systems, Raman spectrum detection systems, laser communication systems, lidar systems and electron beam evaporation coating system, etc. The center closely integrates the major National needs and the limited development areas of Shandong Province's new and old kinetic energy conversion major projects. It mainly carries out light manipulation and its applications in new generation information technologies such as complex environment optical communication, precision optical processing, lidar detection, and optical imaging. Since its establishment, the center has undertaken more than 100 projects of various types, including more than 60 national-level projects. Team members have published more than 300 high-level papers in authoritative journals such as Physics Review Letters, Laser & Photonics Reviews, Nano Letters, ACS Photonics, and Optics Letters.
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Zhang Z, Li GY, Liu YL et al. Robust measurement of orbital angular momentum of a partially coherent vortex beam under amplitude and phase perturbations. Opto-Electron Sci 3, 240001 (2024). doi: 10.29026/oes.2024.240001