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    High-capacity hybrid encryption with topological lemniscate knots in the longitudinal component

    Jia-Hao Zhao1, Yue Li1, Qiang Wang1,2,*, Xuan Zhang1, Yong-Nan Li1, and Cheng-Hou Tu1,†

    • 1School of Physics and Key Laboratory of Weak Light Nonlinear Photonics, Nankai University, Tianjin 300071, China
    • 2Department of Physics, College of Science, Shantou University, Shantou 515063, China

    • *Contact author: qiangwang@stu.edu.cn
    • †Contact author: tuchenghou@nankai.edu.cn

    Phys. Rev. Applied 25, 064055 – Published 16 June, 2026

    DOI: https://doi.org/10.1103/qcc9-xqxg

    Abstract

    Escalating data volumes and security demands challenge traditional encryption, necessitating high-capacity, robust optical solutions. While optical knots offer topological protection, current constructions are restricted to simple torus knots. We overcome this limitation by introducing a framework for lemniscate knots, a generalized family that unlocks a rich variety of topologies through novel geometric control. Distinct from conventional realizations in the transverse component, we experimentally realize these knots within the longitudinal component—a largely unexplored polarization subspace—using inverse design. Crucially, we exploit the inherent faintness under paraxial conditions to establish an intrinsically covert topological carrier. Furthermore, we demonstrate a hybrid encryption scheme integrating these knots with the Advanced Encryption Standard. This scheme achieves hexadecimal encoding that provides multilayered protection, simultaneously expanding information capacity and bolstering cryptographic security. This work expands the topological toolkit and unlocks the longitudinal dimension for robust, high-capacity, and secure optical information processing.

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