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Optics Letters

High-fidelity orbital angular momentum spectrum reconstruction via sparse intensity measurements

Jingjing Zhang, Xiao Wang, Guangdong Ma, Ruifeng Liu, Yongtao Zhao, Pei Zhang, Fuli Li

Published Oct 20, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1364/ol.578190

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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.
Superpositions of orbital angular momentum (OAM) eigenstates form a continuous state space characterized by the complex coefficients of the constituent modes. When such OAM superposition states propagate through a random medium, they produce speckle patterns. The random granular speckle patterns encode the complete information of the original superposition states. This work demonstrates that the complex coefficients of an arbitrary OAM superposition can be retrieved from a single-shot speckle image. The extraction is performed using custom-designed regression model and is validated through both experimental measurements and numerical simulations. The method remains effective for superpositions of high-dimensional OAM eigenstates, including intensity-degenerate states, demonstrating that speckle can serve as a robust information carrier for state characterization.
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.
The orbital angular momentum (OAM) of light is an infinite-dimensional degree of freedom of light with several applications in both classical and quantum optics. However, to fully take advantage of the potential of OAM states, reliable detection platforms to characterize generated states in experimental conditions are needed. Here, we present an approach to reconstruct input OAM states from measurements of the spatial intensity distributions they produce. To obviate issues arising from intrinsic symmetry of Laguerre-Gauss modes, we employ a pair of intensity profiles per state projecting it only on two distinct bases, showing how this allows to uniquely recover input states from the collected data. Our approach is based on a combined application of dimensionality reduction via principal component analysis, and linear regression, and thus has a low computational cost during both training and testing stages. We showcase our approach in a real photonic setup, generating up-to-four-dimensional OAM states through quantum walk dynamics. The high performance and versatility of the demonstrated approach make it an ideal tool to characterize high-dimensional states in quantum information protocols.
Abstract The rich structure of transverse spatial modes of structured light has facilitated their extensive applications in quantum information and optical communication. The Laguerre–Gaussian (LG) modes, which carry a well-defined orbital angular momentum (OAM), consist of a complete orthogonal basis describing the transverse spatial modes of light. The application of OAM in free-space optical communication is restricted due to the experimentally limited OAM numbers and the complex OAM recognition methods. Here, we present a novel method that uses the advanced deep learning technique for LG modes recognition. By discretizing the spatial modes of structured light, we turn the OAM state regression into classification. A proof-of-principle experiment is also performed, showing that our method effectively categorizes OAM states with small training samples and the accuracy exceeds 99% from three-dimensional (3D) to fifteen-dimensional (15D) space. By assigning each category a classical information, we further apply our approach to an image transmission task, achieving a transmission accuracy of 99.58%, which demonstrates the ability to encode large data with low OAM number. This work opens up a new avenue for achieving high-capacity optical communication with low OAM number based on structured light.
High-dimensional (HD) entanglement enables an encoding of more bits than in the two-dimensional case and promises to increase communication capacity over quantum channels and to improve robustness to noise. In practice, however, one of the central challenges is to devise efficient methods to quantify the HD entanglement explicitly. Full quantum state tomography is a standard technology to obtain all the information about the quantum state, but it becomes impractical because the required measurements increase exponentially with the dimension in HD systems. Hence, it is highly anticipated that a new method will be found for characterizing the HD entanglement with as few measurements as possible and without introducing unwarranted assumptions. Here, we present and demonstrate a scan-free tomography method independent of dimension, which only requires two measurements for the characterization of two-photon HD orbital angular momentum (OAM) entanglement. Taking Laguerre-Gaussian modes of photons as an example, the density matrices of OAM entangled states are experimentally reconstructed with very high fidelity. Our method is also generalized to the mixed HD OAM entanglement. Our results provide realistic approaches for quantifying more complex OAM entanglement in many scientific and engineering fields such as multiphoton HD quantum systems and quantum process tomography.
Photons with a spiral phase will carry orbital angular momentum (OAM), which can serve as a valuable resource for constructing high-dimensional Hilbert spaces due to its orthogonality and unbounded dimensionality. However, the fast measurement of high-dimensional OAM spectra remains a challenge. While intensity detection is relatively straightforward, full characterization requires phase retrieval. Although quantum state tomography allows full reconstruction, it demands a number of measurements scaling quadratically with the d2 of dimension (d), leading to a “curse of dimensionality” as the dimension d increases. Thus, there is an urgent need for efficient and simple methods for extracting phase information from high-dimensional OAM spectra. Here, we propose a generalized Poincaré sphere model with analog Stokes-like parameters, enabling full phase measurement of a d-dimensional OAM spectrum using only 4d measurements, significantly reducing the data acquisition requirement. We experimentally validated the method by performing intensity and phase measurements on 8-, 16-, and 32-dimensional OAM comb spectra. The results show excellent agreement with theoretical predictions, with measured fidelities ranging from 0.9829 to 0.9965. This approach facilitates an efficient characterization of high-dimensional OAM spectra and contributes to advancing their practical applications.