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  • Received: Nov. 4, 2020

    Accepted: Dec. 19, 2020

    Posted: Apr. 1, 2021

    Published Online: Apr. 7, 2021

    The Author Email: Jian Wu (

    DOI: 10.3788/COL202119.071403

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    Cheng Yin, Xuefen Kan, Kun Guo, Tao Wang, Jiangming Xu, Qingbang Han, Jian Wu, Zhuangqi Cao. Highly twisted M-line of a vortex beam due to the coupling of ultrahigh-order modes[J]. Chinese Optics Letters, 2021, 19(7): 071403

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Chinese Optics Letters, Vol. 19, Issue 7, 071403 (2021)

Highly twisted M-line of a vortex beam due to the coupling of ultrahigh-order modes

Cheng Yin1, Xuefen Kan1, Kun Guo2, Tao Wang2, Jiangming Xu2, Qingbang Han1, Jian Wu2,*, and Zhuangqi Cao3

Author Affiliations

  • 1College of Internet of Things Engineering, Hohai University, Changzhou 213022, China
  • 2College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China
  • 3Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China


In modern optics, particular interest is devoted to the phase singularities that yield complicated and twisted phase structures by photons carrying optical angular momentum. In this paper, the traditional M-line method is applied to a vortex beam (VB) by a symmetric metal cladding waveguide chip, which can host numerous oscillating guided modes via free space coupling. These ultrahigh-order modes (UOMs) result in high angular resolution due to the high finesse of the resonant chip. Experiments show that the reflected pattern of a VB can be divided into a series of inner and outer rings, whilst both of them are highly distorted by the M-lines due to the UOMs’ leakage. Taking the distribution of the energy flux into account, a simple ray-optics-based model is proposed to simulate the reflected pattern by calculating the local incident angle over the cross section of the beam. The theoretical simulations fit well with the experimental results, and the proposed scheme may enable new applications in imaging and sensing of complicated phase structures.


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