基于超表面的整数阶和分数阶涡旋拓扑电荷的高精度检测

高昕鹏; 丁双双; 马婧文; 周晓晓; 尚玉立; 范士嵩; 滕树云

doi:10.37188/CO.EN-2025-0037

基于超表面的整数阶和分数阶涡旋拓扑电荷的高精度检测

山东师范大学物理与电子科学学院山东省光操控工程技术中心和山东省光学与光子器件重点实验室, 中国济南 250014

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出版历程
- 收稿日期: 2025-09-11
- 录用日期: 2025-10-20
- 网络出版日期: 2025-12-03

High-precision detection of topological charge of integral and fractional vortices based on metasurface

doi: 10.37188/CO.EN-2025-0037

Shandong Provincial Engineering and Technical Center of Light Manipulations & Shandong Provincial Key Laboratory of Optics and Photonic Device, School of Physics and Electronics, Shandong Normal University, Jinan 250014, China

Funds: Supported by National Natural Science Foundation of China (No. 10874105); Natural Science Foundation of Shandong Province (No. ZR2020KA009)

More Information

Author Bio:
GAO Xin-peng (2001—), Male, native of Yancheng City, Jiangsu Province, China, master's candidate. He graduated from Nanjing University of Posts and Telecommunications in 2023 with a Bachelor of Engineering degree and is currently pursuing a master's degree at Shandong Normal University. His main research focus is on vortex beams. E-mail: 18261299890@163.com

TENG Shu-yun (1971—), Female, Professor of Shandong Normal University, Doctor of Science. She graduated from the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences in 2005, and obtained her doctoral degree. She mainly engages in research in the fields of diffractive optics, micro-nano photonics, micro-optical devices, optical field regulation, and singular optics. E-mail: tengshuyun@sdnu.edu.cn

Corresponding author: tengshuyun@sdnu.edu.cn

摘要

摘要:
在涡旋光束的实际应用中，拓扑荷的高精度检测具有重要意义。针对现有拓扑荷检测方法存在分辨率低、难以同时判别整数阶与分数阶拓扑荷的问题，本文从理论上提出并通过数值模拟验证了一种基于设计超表面的拓扑荷双重判别方法。该超表面产生的内外衍射图样可分别用于判别拓扑荷的数值与符号，且所提方法的检测精度可达0.05。理论分析与仿真结果充分验证了该方法的有效性。与现有方法相比，该方法具有显著优势：采用平面结构设计，无需额外光学元件；无需数据处理，可直接判别；检测精度高。我们认为，此项工作有助于推动拓扑荷检测技术的发展及光学涡旋的实际应用。
- 光学涡旋 /
- 拓扑荷 /
- 超表面
Abstract:
High-precision detection of topological charge is significant for the practical applications of vortex beams. In view of the existing evaluation with low resolution of topological charge and more complexity to judge simultaneously integer and fraction, this paper theoretically proposes and numerically verifies the double judgment method for topological charge based on the designed metasurface. The inner and outer diffraction patterns of metasurface can judge the value and sign of topological charge. The detection precision of the proposed method reaches 0.05. The theoretic and simulated results give the solid verification for the effectiveness of the proposed method. This method has outstanding advantages including planar structure design without additional elements, direct judgment without data processing and high precision over the existing methods. We think this work is beneficial to the detection of topological charge and the applications of optical vortices.
- optical vortex /
- topological charge /
- metasurface

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Figure 1. Schematic diagram of TC measurement based on metasurface (A) and diffraction patterns with the TC taking 1.0, 2.0, 2.5 and 3.5 (B)

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Figure 2. Magnified inner diffraction patterns of optical vortex with TC changing from α=4.0 to α=5.0 with the separation of 0.1 and 0.05, where the scale bar denotes 1μm.

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Figure 3. (A) Inner and (B) outer diffraction patterns with the TC taking ±2.5, ±3.5 and ±4.5, where the scale bar denotes 1μm and the patterns inserted are the right of B are the magnified parts of squared ones.

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Figure 4. Structures of metasurface and diatom (A) and diffraction patterns with the TC taking integers (B) and fractions (C), where the inserted dash lines denote the trajectories of fringes.

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Figure 5. Diffraction patterns as the TC takes negative values (A) with the interval of TC 0.1 and 0.05 (B).

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Table 1. Comparison of works for detecting topological charge of vortex

Works	Principle and Method	Complexity	Precision
Dehnoei Sf et al^[17]	Cross-blade diffraction	Simple	0.1
Shikder A et al^[18]	Hybrid digital-optical correlation	Complex	0.05
Hu Z et al^[19]	Rotational Doppler effect	Additional devices	0.1
Liu Z et al^[20]	Fraunhofer diffraction Deep learning	Additional lens Time-consuming	0.01
This paper	Fresnel diffraction Metasurface	Simple	0.05

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