中国物理B ›› 2023, Vol. 32 ›› Issue (10): 104208-104208.doi: 10.1088/1674-1056/acc1d0

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Theoretical analysis of the optical rotational Doppler effect under atmospheric turbulence by mode decomposition

Sheng-Jie Ma(马圣杰)1,2, Shi-Long Xu(徐世龙)1,2,†, Xiao Dong(董骁)1,2, Xin-Yuan Zhang(张鑫源)1,2, You-Long Chen(陈友龙)1,2, and Yi-Hua Hu(胡以华)1,2,‡   

  1. 1 State Key Laboratory of Pulsed Power Laser Technology, National University of Defense Technology, Hefei 230037, China;
    2 Key Laboratory of Electronic Restriction of Anhui Province, National University of Defense Technology, Hefei 230037, China
  • 收稿日期:2022-08-20 修回日期:2023-02-02 接受日期:2023-03-07 出版日期:2023-09-21 发布日期:2023-09-27
  • 通讯作者: Shi-Long Xu, Yi-Hua Hu E-mail:xushi1988@yeah.net;skl_hyh@163.com
  • 基金资助:
    Project supported by the Research Plan Project of the National University of Defense Technology (Grant No. ZK18-01-02), the National Natural Science Foundation of China (Grant No. 61871389), the State Key Laboratory of Pulsed Power Laser Technology (Grant No. KY21C604), and the Postgraduate Scientific Research Innovation Project of Hunan Province (Grant Nos. CX20220007 and CX20230024).

Theoretical analysis of the optical rotational Doppler effect under atmospheric turbulence by mode decomposition

Sheng-Jie Ma(马圣杰)1,2, Shi-Long Xu(徐世龙)1,2,†, Xiao Dong(董骁)1,2, Xin-Yuan Zhang(张鑫源)1,2, You-Long Chen(陈友龙)1,2, and Yi-Hua Hu(胡以华)1,2,‡   

  1. 1 State Key Laboratory of Pulsed Power Laser Technology, National University of Defense Technology, Hefei 230037, China;
    2 Key Laboratory of Electronic Restriction of Anhui Province, National University of Defense Technology, Hefei 230037, China
  • Received:2022-08-20 Revised:2023-02-02 Accepted:2023-03-07 Online:2023-09-21 Published:2023-09-27
  • Contact: Shi-Long Xu, Yi-Hua Hu E-mail:xushi1988@yeah.net;skl_hyh@163.com
  • Supported by:
    Project supported by the Research Plan Project of the National University of Defense Technology (Grant No. ZK18-01-02), the National Natural Science Foundation of China (Grant No. 61871389), the State Key Laboratory of Pulsed Power Laser Technology (Grant No. KY21C604), and the Postgraduate Scientific Research Innovation Project of Hunan Province (Grant Nos. CX20220007 and CX20230024).

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摘要： The optical rotational Doppler effect associated with orbital angular momentum provides a new means for rotational velocity detection. In this paper, we investigate the influence of atmospheric turbulence on the rotational Doppler effect. First, we deduce the generalized formula of the rotational Doppler shift in atmospheric turbulence by mode decomposition. It is found that the rotational Doppler signal frequency spectrum will be broadened, and the bandwidth is related to the turbulence intensity. In addition, as the propagation distance increases, the bandwidth also increases. And when $C_{n}^{2} \le 5\times 10^{-15}$ m$^{-2/3}$ and $2z\le 2$ km, the rotational Doppler signal frequency spectrum width $d$ and the spiral spectrum width $d_{0}$ satisfy the relationship $d=2d_{0} -1$. Finally, we analyze the influence of mode crosstalk on the rotational Doppler effect, and the results show that it destroys the symmetrical distribution of the rotational Doppler spectrum about $2l\cdot \varOmega /2\pi$. This theoretical model enables us to better understand the generation of the rotational Doppler frequency and may help us better analyze the influence of the complex atmospheric environment on the rotational Doppler frequency.

关键词: optical rotational Doppler effect, atmospheric turbulence, vortex beam, mode decomposition, mode crosstalk

Abstract: The optical rotational Doppler effect associated with orbital angular momentum provides a new means for rotational velocity detection. In this paper, we investigate the influence of atmospheric turbulence on the rotational Doppler effect. First, we deduce the generalized formula of the rotational Doppler shift in atmospheric turbulence by mode decomposition. It is found that the rotational Doppler signal frequency spectrum will be broadened, and the bandwidth is related to the turbulence intensity. In addition, as the propagation distance increases, the bandwidth also increases. And when $C_{n}^{2} \le 5\times 10^{-15}$ m$^{-2/3}$ and $2z\le 2$ km, the rotational Doppler signal frequency spectrum width $d$ and the spiral spectrum width $d_{0}$ satisfy the relationship $d=2d_{0} -1$. Finally, we analyze the influence of mode crosstalk on the rotational Doppler effect, and the results show that it destroys the symmetrical distribution of the rotational Doppler spectrum about $2l\cdot \varOmega /2\pi$. This theoretical model enables us to better understand the generation of the rotational Doppler frequency and may help us better analyze the influence of the complex atmospheric environment on the rotational Doppler frequency.

Key words: optical rotational Doppler effect, atmospheric turbulence, vortex beam, mode decomposition, mode crosstalk

中图分类号:  (Atmospheric turbulence effects)

  • 42.68.Bz
92.10.Lq (Turbulence, diffusion, and mixing processes in oceanography) 42.79.Qx (Range finders, remote sensing devices; laser Doppler velocimeters, SAR, And LIDAR)