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Photonics Research

Revealing a high-dimensional orbital angular momentum complex spectrum under strong scattering

Chaozhou Xu, Qijian Xiong, Jingjing Wang, Xiaoxue Zhang, Xuefeng Xie, Xiaodong Qiu, Haoxu Guo

Published Jul 24, 2025• 5 citations
Publisher

Abstract

Optical vortex beams carrying orbital angular momentum (OAM) offer unique advantages in high-dimensional optical information processing. However, in the context of free-space links, the full reconstruction of high-dimensional OAM spectra remains challenging due to scattering-induced distortions. Here, we employ a residual convolutional neural network with a custom quantum-state-fidelity loss function (QLF-ResNet) that reconstructs and demultiplexes high-dimensional OAM light fields from a single distorted speckle pattern. Specifically, we achieve an average fidelity of 97.2% for nine-dimensional OAM states and maintain fidelity above 91.9% with only 6.25% of original data, illustrating resilience to information loss, thus enabling robust data encoding and multiplexing. For this, we employ high-dimensional OAM encoding to achieve efficient, high-fidelity transmission of RGB images under strong scattering conditions. These results underscore the promise of our current approach for precise OAM state reconstruction in intricate real-world environments, paving the way for advancements in next-generation optical communications.

DOI
10.1364/prj.569622

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Optical vortex beams carrying orbital angular momentum (OAM) offer unique advantages in high-dimensional optical information processing. However, in the context of free-space links, the full reconstruction of high-dimensional OAM spectra remains challenging due to scattering-induced distortions. Here, we employ a residual convolutional neural network with a custom quantum-state-fidelity loss function (QLF-ResNet) that reconstructs and demultiplexes high-dimensional OAM light fields from a single distorted speckle pattern. Specifically, we achieve an average fidelity of 97.2% for nine-dimensional OAM states and maintain fidelity above 91.9% with only 6.25% of original data, illustrating resilience to information loss, thus enabling robust data encoding and multiplexing. For this, we employ high-dimensional OAM encoding to achieve efficient, high-fidelity transmission of RGB images under strong scattering conditions. These results underscore the promise of our current approach for precise OAM state reconstruction in intricate real-world environments, paving the way for advancements in next-generation optical communications.
Orbital-angular-momentum (OAM) complex-valued spectrum reconstruction routinely necessitates the measurements of a complete set of observables, which is rather time consuming and inefficient for high-dimensional OAM superposition state. Here we break this barrier to realize the full reconstruction of a high-dimensional OAM complex-valued spectrum via only a single-shot measurement, which benefits from the use of a residual convolutional neural network for learning the diffraction behaviors. In our experiment, the high-dimensional OAM states are diffracted by a simple aperture of pentagram that breaks the OAM conjugate symmetry. We achieve fidelity over 97.8% and 92.1% for high-dimensional pure and mixed OAM states (up to d=15d=15d=15), respectively. We also confirm the excellent robustness under strong noise environment. Our method will find potential applications in high-dimensional information encoding, such as large-alphabet communications, quantum imaging, and real-time quantum sensing.
Accurate reconstruction of the complex spectrum of orbital angular momentum (OAM) superposition states is crucial for their application in high-capacity optical communications and quantum information, yet existing methods are often constrained by system complexity, extensive data requirements, or incomplete information retrieval. Here, we propose and experimentally demonstrate an iterative algorithm that enables high-fidelity recovery of the complex OAM spectrum of high-dimensional superpositions from only a few sparsely sampled patterns. The method integrates the Laguerre-Gaussian (LG) modal basis as an a priori constraint, which enables the direct retrieval of spectral coefficients by circumventing intermediate field reconstruction. To validate its performance, we reconstructed a test field composed of a random superposition of 21 LG modes, achieving fidelities of 99.3% in simulation and 97.2% in experiment using only four sparse sampling patterns. This work provides an efficient and robust tool for characterizing high-dimensional structured light, with significant potential in optical communication and quantum science.
A high-dimensional quantum key distribution (QKD), which adopts degrees of freedom of the orbital angular momentum (OAM) states, is beneficial to realize secure and high-speed QKD. However, the helical phase of a vortex beam that carries OAM is sensitive to the atmospheric turbulence and easily distorted. In this paper, an adaptive compensation method using deep learning technology is developed to improve the performance of OAM-encoded QKD schemes. A convolutional neural network model is first trained to learn the mapping relationship of intensity profiles of inputs and the turbulent phase, and such mapping is used as feedback to control a spatial light modulator to generate a phase screen to correct the distorted vortex beam. Then an OAM-encoded QKD scheme with the capability of real-time phase correction is designed, in which the compensation module only needs to extract the intensity distributions of the Gaussian probe beam and thus ensures that the information encoded on OAM states would not be eavesdropped. The results show that our method can efficiently improve the mode purity of the encoded OAM states and extend the secure distance for the involved QKD protocols in the free-space channel, which is not limited to any specific QKD protocol.
As the demand for data capacity continues to grow, optical fiber communication systems are progressively approaching their theoretical limits, thereby motivating the exploration of high-dimensional (HD) degrees of freedom such as orbital angular momentum (OAM). However, strong intermodal coupling in multimode fibers (MMFs) poses substantial challenges for the transmission and recovery of HD optical information. Here, we propose and experimentally demonstrate an HD OAM-array-based multichannel multitask optical communication framework via a single MMF. By encoding different information tasks into HD OAM superposition states across multiple wave-vector (k) channels, the proposed scheme enables the simultaneous transmission of heterogeneous optical information within a unified fiber platform. At the receiver, a residual neural network constrained by a multi-channel quantum-state fidelity loss function directly reconstructs the transmitted signals from single-frame speckle intensity measurements, without requiring phase retrieval or channel inversion. Experiments demonstrate the synchronous communication of multichannel classical image signals and HD mutually unbiased basis states through the same MMF, while maintaining high reconstruction fidelity and low interchannel crosstalk under strong modal mixing conditions. This approach provides a scalable route toward high-capacity hybrid classical–quantum optical communication in fiber systems.
Quantum computing is emerging as a transformative tool for communication systems, offering the potential to overcome long-standing physical limitations. In free-space optical networks, orbital angular momentum (OAM) multiplexing promises massive capacity gains, but its practical use is fundamentally constrained by multiphysics degradations such as atmospheric turbulence, volumetric Mie scattering, and stochastic quantum noise. These effects induce nonlinear modal crosstalk and severe beam distortions, against which classical approaches—most notably convolutional neural networks (CNNs)—provide only partial and non-scalable compensation. To address this gap, we report the first use of variational quantum neural networks (QNNs) for adaptive OAM beam compensation in realistic channels. By embedding parameterized entangling layers into a supervised regression pipeline, our QNN achieves end-to-end reconstruction of distorted Laguerre–Gaussian beams with topological charges l ∈ {1,4,8,12}. Using experimentally validated channel parameters, QNNs achieve mean squared error as low as 4.0 × 10− 6, SSIM above 0.99, and bit-error rates suppressed by > 99.9% (0.0125% BER). To ensure scalability, we introduce the quasi-quantum neural network (QqNN), a classical surrogate that emulates quantum dynamics via tensorial projections, achieving near-optimal performance (0.0375% BER) at reduced complexity. This hybrid framework positions QNNs as a quantum-resilient paradigm for OAM decoding and establishes QqNNs as the first scalable surrogate for near-term deployment.
Abstract High-dimensional (HD) entanglement of photonic orbital angular momentum (OAM) is pivotal for advancing quantum communication and information processing, but its characterization remains significant challenges due to the complexity of quantum state tomography and experimental limitations such as low photon counts caused by losses. Here, we propose a pre-trained physics-informed neural network (PTPINN) framework that enables efficient and rapid reconstruction of HD-OAM entangled states under low photon counts. Experimental results show that the fidelity of five-dimensional OAM entanglement reaches F = 0.958 ± 0.010 even with an exposure time as short as 50 ms. This highlights the capability of PTPINN to achieve high-precision quantum state reconstruction with limited photons, owing to its innovative designs, thus overcoming the reliance on high photon counts typical of traditional methods. Our method provides a practical and scalable solution for high-fidelity characterization of HD-OAM entanglement in environments with low photon numbers and high noise, paving the way for robust long-distance quantum information transmission.