Skip to main content
Log in

Single-shot phase retrieval for randomly fluctuated and obstructed vortex beams

  • Article
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

Vortex beams with orbital angular momentum play a crucial role in increasing the information capacity in optical communications. The magnitude of orbital angular momentum determines the ability of information encoding. In practice, a vortex beam can encounter random objects or turbulence during free-space propagation, resulting in information damage. Therefore, accurately measuring the orbital angular momentum of a randomly fluctuated and obstructed vortex beam is a considerable challenge. Herein, we propose a single-shot method for the phase retrieval of a randomly fluctuated and obstructed vortex beam by combining the phase-shift theorem and self-reference holography. Experimental results reveal that the sign and magnitude of the initial orbital angular momentum can be simultaneously determined based on their quantitative relation with the number of coherence singularities on the observation plane, thus addressing the effects of random occlusion and atmospheric turbulence. The proposed method considerably improved the accurate decoding of orbital angular momentum information in nonideal freespace optical communications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).

    Article  CAS  PubMed  ADS  Google Scholar 

  2. A. Forbes, M. de Oliveira, and M. R. Dennis, Nat. Photon. 15, 253 (2021).

    Article  CAS  ADS  Google Scholar 

  3. H. Zhang, J. Zeng, X. Lu, Z. Wang, C. Zhao, and Y. Cai, Nanophotonics 11, 241 (2022).

    Article  CAS  ADS  Google Scholar 

  4. H. Zang, Z. Miao, M. Wang, Q. Fan, L. Wei, C. Wang, W. Zhou, Y. Hua, L. Cao, X. Xue, and H. Guo, Sci. China-Phys. Mech. Astron. 65, 294212 (2022).

    Article  ADS  Google Scholar 

  5. J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photon. 6, 488 (2012).

    Article  CAS  ADS  Google Scholar 

  6. J. Fang, Z. Xie, T. Lei, C. Min, L. Du, Z. Li, and X. Yuan, ACS Photonics 5, 3478 (2018).

    Article  CAS  Google Scholar 

  7. J. Wang, Sci. China-Phys. Mech. Astron. 62, 034201 (2018).

    Article  ADS  Google Scholar 

  8. H. Zhang, X. Li, H. Ma, M. Tang, H. Li, J. Tang, and Y. Cai, Opt. Express 27, 22930 (2019).

    Article  CAS  PubMed  ADS  Google Scholar 

  9. J. Hu, Y. Lan, H. Fan, W. Ye, P. Zeng, Y. Qian, and X. Li, Appl. Phys. Lett. 121, 221103 (2022).

    Article  CAS  ADS  Google Scholar 

  10. Y. Yang, Y. X. Ren, M. Chen, Y. Arita, and C. Rosales-Guzmán, Adv. Photon. 3, 034001 (2021).

    Article  CAS  ADS  Google Scholar 

  11. M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, Science 341, 537 (2013).

    Article  CAS  PubMed  ADS  Google Scholar 

  12. Y. Ren, S. Qiu, T. Liu, and Z. Liu, Nanophotonics 11, 1127 (2022).

    Article  Google Scholar 

  13. X. Fang, H. Ren, and M. Gu, Nat. Photon. 14, 102 (2020).

    Article  CAS  ADS  Google Scholar 

  14. F. Feng, J. Hu, Z. Guo, J. A. Gan, P. F. Chen, G. Chen, C. Min, X. Yuan, and M. Somekh, ACS Photon. 9, 820 (2022).

    Article  CAS  Google Scholar 

  15. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).

    Article  CAS  PubMed  ADS  Google Scholar 

  16. B. Mao, Y. Liu, W. Chang, L. Chen, M. Feng, H. Guo, J. He, and Z. Wang, Nanophotonics 11, 1413 (2022).

    Article  Google Scholar 

  17. H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, Y. Wang, J. Tang, and Z. Nie, Opt. Lett. 42, 135 (2017).

    Article  PubMed  ADS  Google Scholar 

  18. Q. Zhao, M. Dong, Y. Bai, and Y. Yang, Photon. Res. 8, 745 (2020).

    Article  CAS  Google Scholar 

  19. J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).

    Article  CAS  PubMed  ADS  Google Scholar 

  20. B. Pinheiro da Silva, G. H. dos Santos, A. G. de Oliveira, N. Rubiano da Silva, W. T. Buono, R. M. Gomes, W. C. Soares, A. J. Jesus-Silva, E. J. S. Fonseca, P. H. Souto Ribeiro, and A. Z. Khoury, Optica 9, 908 (2022).

    Article  CAS  ADS  Google Scholar 

  21. V. V. Kotlyar, A. A. Kovalev, and A. P. Porfirev, Appl. Opt. 56, 4095 (2017).

    Article  PubMed  ADS  Google Scholar 

  22. Z. Liu, S. Yan, H. Liu, and X. Chen, Phys. Rev. Lett. 123, 183902 (2019).

    Article  CAS  PubMed  ADS  Google Scholar 

  23. G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).

    Article  PubMed  ADS  Google Scholar 

  24. Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, Phys. Rev. Lett. 120, 193904 (2018).

    Article  CAS  PubMed  ADS  Google Scholar 

  25. A. D’Errico, R. D’Amelio, B. Piccirillo, F. Cardano, and L. Marrucci, Optica 4, 1350 (2017).

    Article  ADS  Google Scholar 

  26. J. Pinnell, V. Rodríguez-Fajardo, A. Forbes, S. Chabou, K. Mihoubi, and A. Bencheikh, Phys. Rev. A 102, 033524 (2020).

    Article  CAS  ADS  Google Scholar 

  27. Y. Shen, S. Pidishety, I. Nape, and A. Dudley, J. Opt. 24, 103001 (2022).

    Article  ADS  Google Scholar 

  28. X. Li, L. Ma, J. Zeng, Z. Dong, L. Liu, F. Wang, B. J. Hoenders, Y. Cai, and X. Liu, Appl. Phys. Lett. 117, 251103 (2020).

    Article  CAS  ADS  Google Scholar 

  29. A. V. Falits, V. V. Kuskov, and V. A. Banakh, J. Quant. Spectr. Radiat. Transfer 302, 108568 (2023).

    Article  CAS  Google Scholar 

  30. E. E. Elsayed, B. B. Yousif, and M. Singh, Opt. Quant. Electron. 54, 116 (2022).

    Article  Google Scholar 

  31. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, New York, 2007).

    Google Scholar 

  32. M. Dong, C. L. Zhao, Y. J. Cai, and Y. J. Yang, Sci. China-Phys. Mech. Astron. 64, 224201 (2021).

    Article  ADS  Google Scholar 

  33. B. B. Yousif, E. E. Elsayed, and M. M. Alzalabani, Opt. Commun. 436, 197 (2019).

    Article  CAS  ADS  Google Scholar 

  34. E. E. Elsayed, and B. B. Yousif, Opt. Commun. 475, 126219 (2020).

    Article  CAS  Google Scholar 

  35. B. B. Yousif, and E. E. Elsayed, IEEE Access 7, 84401 (2019).

    Article  Google Scholar 

  36. H. Chang, X. Yin, X. Cui, X. Z. Chen, Y. Z. Su, J. X. Ma, Y. J. Wang, L. Zhang, and X. Xin, Appl. Opt. 58, 6085 (2019).

    Article  PubMed  ADS  Google Scholar 

  37. M. I. Dedo, Z. Wang, K. Guo, Y. Sun, F. Shen, H. Zhou, J. Gao, R. Sun, Z. Ding, and Z. Guo, Appl. Sci. 9, 2269 (2019).

    Article  CAS  Google Scholar 

  38. C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, Appl. Phys. Lett. 101, 261104 (2012).

    Article  ADS  Google Scholar 

  39. M. Dong, X. Y. Lu, C. Zhao, Y. Cai, and Y. Yang, Opt. Express 26, 33035 (2018).

    Article  CAS  PubMed  ADS  Google Scholar 

  40. Y. Yang, M. Mazilu, and K. Dholakia, Opt. Lett. 37, 4949 (2012).

    Article  PubMed  ADS  Google Scholar 

  41. B. Perez-Garcia, A. Yepiz, R. I. Hernandez-Aranda, A. Forbes, and G. A. Swartzlander, Opt. Lett. 41, 3471 (2016).

    Article  CAS  PubMed  ADS  Google Scholar 

  42. P. Ma, X. Liu, Q. Zhang, Q. Chen, J. Zeng, Y. Cai, Q. Zhan, and C. Liang, Opt. Lett. 47, 6037 (2022).

    Article  PubMed  ADS  Google Scholar 

  43. R. Liu, F. Wang, D. Chen, Y. Wang, Y. Zhou, H. Gao, P. Zhang, and F. Li, Appl. Phys. Lett. 108, 051107 (2016).

    Article  ADS  Google Scholar 

  44. Z. Zhang, Z. Liu, X. Liu, G. Gbur, C. Liang, Y. Cai, and J. Zeng, Appl. Phys. Lett. 122, 011101 (2023).

    Article  CAS  ADS  Google Scholar 

  45. X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, Appl. Phys. Lett. 110, 181104 (2017).

    Article  ADS  Google Scholar 

  46. X. Xiao, and D. G. Voelz, Opt. Eng. 51, 026001 (2012).

    Article  ADS  Google Scholar 

  47. J. Yu, X. Zhu, F. Wang, D. Wei, G. Gbur, and Y. Cai, Opt. Lett. 44, 4371 (2019).

    Article  CAS  PubMed  ADS  Google Scholar 

  48. B. B. Mandelbrot, The Fractal Geometry of Nature (New York: WH Freeman, 1982).

    Google Scholar 

  49. J. Uozumi, H. Kimura, and T. Asakura, J. Mod. Opt. 37, 1011 (1990).

    Article  ADS  Google Scholar 

  50. H. Zhang, H. Wang, X. Lu, X. Zhao, B. J. Hoenders, C. Zhao, and Y. Cai, Opt. Express 30, 29923 (2022).

    Article  PubMed  Google Scholar 

  51. H. Zhang, X. Lu, Z. Wang, A. P. Konijnenberg, H. Wang, C. Zhao, and Y. Cai, Front. Phys. 9, 781688 (2021).

    Article  Google Scholar 

  52. A. Forbes, A. Dudley, and M. McLaren, Adv. Opt. Photon. 8, 200 (2016).

    Article  Google Scholar 

  53. M. V. Berry, and W. Liu, J. Phys. A-Math. Theor. 55, 374001 (2022).

    Article  Google Scholar 

  54. J. Zeng, X. Liu, C. Zhao, F. Wang, G. Gbur, and Y. Cai, Opt. Express 27, 25342 (2019).

    Article  PubMed  ADS  Google Scholar 

  55. H. Wang, Z. Zhan, F. Hu, Y. Meng, Z. Liu, X. Fu, and Q. Liu, PhotoniX 4, 9 (2023).

    Article  Google Scholar 

  56. V. P. Aksenov, V. V. Kolosov, G. A. Filimonov, and C. E. Pogutsa, J. Opt. 18, 054013 (2016).

    Article  ADS  Google Scholar 

  57. V. P. Aksenov, and C. E. Pogutsa, Quantum Electron. 38, 343 (2008).

    Article  CAS  ADS  Google Scholar 

  58. S. Y. Huang, G. L. Zhang, Q. Wang, M. Wang, C. Tu, Y. Li, and H. T. Wang, Optica 8, 1231 (2021).

    Article  ADS  Google Scholar 

  59. J. Chen, C. Wan, and Q. Zhan, Adv. Photon. 3, 064001 (2021).

    CAS  ADS  Google Scholar 

  60. L. Zhou, T. Zhou, F. Wang, X. Li, R. Chen, Y. Zhou, and G. Zhou, Opt. Laser Tech. 143, 107334 (2021).

    Article  Google Scholar 

  61. R. Zeng, Q. Zhao, Y. Shen, Y. Liu, and Y. Yang, Appl. Phys. Lett. 119, 171105 (2021).

    Article  CAS  ADS  Google Scholar 

  62. D. Peng, Z. Huang, Y. Liu, Y. Chen, F. Wang, S. A. Ponomarenko, and Y. Cai, PhotoniX 2, 6 (2021).

    Article  PubMed  PubMed Central  Google Scholar 

  63. X. Lu, Y. Shao, C. Zhao, S. Konijnenberg, X. Zhu, Y. Tang, Y. Cai, and H. P. Urbach, Adv. Photon. 1, 1 (2019).

    Article  CAS  Google Scholar 

  64. X. Lu, C. Zhao, Y. Shao, J. Zeng, S. Konijnenberg, X. Zhu, S. Popov, H. P. Urbach, and Y. Cai, Appl. Phys. Lett. 114, 201106 (2019).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Xingyuan Lu, Qiwen Zhan, Yangjian Cai or Chengliang Zhao.

Ethics declarations

Conflict of interest The authors declare that they have no conflict of interest.

Additional information

This work was supported by the National Key Research and Development Program of China (Grant Nos. 2022YFA1404800, and 2019YFA0705000), the National Natural Science Foundation of China (Grant Nos. 12174280, 12204340, 12192254, 11974218, 92250304, and 92050202), the China Postdoctoral Science Foundation (Grant No. 2022M722325), the Priority Academic Program Development of Jiangsu Higher Education Institutions, Key Lab of Modern Optical Technologies of Jiangsu Province (Grant No. KJS2138).

Supporting Information

The supporting information is available online at http://phys.scichina.com and https://link.springer.com. The supporting materials are published as submitted, without typesetting or editing. The responsibility for scientific accuracy and content remains entirely with the authors.

Supporting Information

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, H., Zhu, J., Lu, X. et al. Single-shot phase retrieval for randomly fluctuated and obstructed vortex beams. Sci. China Phys. Mech. Astron. 67, 244211 (2024). https://doi.org/10.1007/s11433-023-2290-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-023-2290-8

Keywords

Navigation