Skip to main content
Log in

A Comparative Analysis of Intensity and Energy Flux in the Focus of the High-Numeric-Aperture Conventional and Spiral Zone Plates

  • Published:
Optics and Spectroscopy Aims and scope Submit manuscript

Abstract

Using simulation by means of the finite difference method in the time domain (FDTD), we demonstrated that focal spots of different shape with respect to both intensity and energy flux form upon tight focusing of a Gaussian linearly polarized beam containing an optical vortex by a Fresnel zone plate and upon focusing of a Gaussian beam by a spiral zone plate. The most significant differences are observed for the topological charge equal three. The energy flux upon focusing of a Gaussian beam by a Fresnel zone plate has a ring distribution, while the distribution of intensity and energy flux upon beam focusing by a spiral zone plate has three local maxima, which corresponds to the spiral-zone-plate order. The petal structure of intensity (and the energy flux) changes to a ring distribution at a certain distance from the focus.

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.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.

Similar content being viewed by others

REFERENCES

  1. Q. Zhan, Adv. Opt. Photonics 1, 1 (2009). https://doi.org/10.1364/aop.1.000001

    Article  ADS  Google Scholar 

  2. E. S. Kozlova, S. S. Stafeev, S. A. Fomchenkov, V. V. Podlipnov, and V. V. Kotlyar, Komp’yuternaya Opt. 45, 165 (2021). https://doi.org/10.18287/2412-6179-co-835

    Article  ADS  Google Scholar 

  3. M. Soskin, S. Boriskina, Y. Chong, M. Dennis, and A. Desyatnikov, J. Opt. 19, 10401 (2017). https://doi.org/10.1088/2040-8986/19/1/010401

    Article  ADS  Google Scholar 

  4. M. J. Padgett, Opt. Express 25, 11265 (2017). https://doi.org/10.1364/OE.25.011265

    Article  ADS  Google Scholar 

  5. Y. Shen, X. Wang, and Z. Xie, Light Sci. Appl. 8, 90 (2019). https://doi.org/10.1038/s41377-019-0194-2

    Article  ADS  Google Scholar 

  6. A. V. Volyar, M. V. Bretsko, Y. E. Akimova, and Y. A. Egorov, Komp’yuternaya Opt. 43, 517 (2019). https://doi.org/10.18287/2412-6179-2019-43-4-517-527

    Article  ADS  Google Scholar 

  7. K. Cheng, G. Lu, and X. Zhong, Opt. Commun. 396, 517 (2017). https://doi.org/10.1016/j.optcom.2017.03.038

    Article  Google Scholar 

  8. V. V. Kotlyar and A. A. Kovalev, Komp’yuternaya Opt. 41, 609 (2017). https://doi.org/10.18287/2412-6179-2017-41-5-609-616

    Article  ADS  Google Scholar 

  9. H. Zhang, X. Li, H. Ma, M. Tang, and Y. Cai, Appl. Sci. 9, 1429 (2019). https://doi.org/10.3390/app9071429

    Article  Google Scholar 

  10. S. N. Khonina, D. A. Savelyev, and N. L. Kazanskiy, Opt. Express 23, 17845 (2015). https://doi.org/10.1364/OE.23.017845

    Article  ADS  Google Scholar 

  11. K. Kitamura, M. Kitazawa, and S. Noda, Opt. Express 27, 1045 (2019). https://doi.org/10.1364/OE.27.001045

    Article  ADS  Google Scholar 

  12. X. Wang, Z. Nie, Y. Liang, J. Wang, T. Li, and B. Jia, Nanophotonics 7, 1533 (2018). https://doi.org/10.1515/nanoph-2018-0072

    Article  Google Scholar 

  13. R. Uren, S. Beecher, C. R. Smith, and W. A. Clarkson, IEEE J. Quantum. Electron. 55, 1700109 (2019). https://doi.org/10.1109/JQE.2019.2931006

  14. H. Zhou, J. Yang, C. Gao, and Sh. Fu, Opt. Mater. Express 9, 2699 (2019). https://doi.org/10.1364/OME.9.002699

    Article  ADS  Google Scholar 

  15. Z. Liu and D. Zhao, Laser Phys. Lett. 16, 056003 (2019). https://doi.org/10.1088/1612-202x/ab0a6b

  16. C. Luo and X. Han, Opt. Commun. 460, 124888 (2020). https://doi.org/10.1016/j.optcom.2019.124888

  17. Ye. Li, L. Yu, and Yi. Zhang, Opt. Express 25, 12203 (2017). https://doi.org/10.1364/oe.25.012203

    Article  ADS  Google Scholar 

  18. J. Yu, Ya. Huang, G. Gbur, F. Wang, and Ya. Cai, J. Quant. Spectrosc. Radiat. Transfer 228, 1 (2019). https://doi.org/10.1016/j.jqsrt.2019.02.021

    Article  ADS  Google Scholar 

  19. M. Á. Olvera-Santamaría, J. García-García, A. Tlapale-Aguilar, J. Silva-Barranco, C. Rickenstorff-Parrao, and A. S. Ostrovsky, Opt. Commun. 467, 125693 (2020). https://doi.org/10.1016/j.optcom.2020.125693

  20. S. S. Stafeev and A. G. Nalimov, Komp’yuternaya Opt. 42, 190 (2018). https://doi.org/10.18287/2412-6179-2018-42-2-190-196

    Article  ADS  Google Scholar 

  21. S. S. Stafeev and V. V. Kotlyar, Komp’yuternaya Opt. 41, 147 (2017). https://doi.org/10.18287/2412-6179-2017-41-2-147-154

    Article  ADS  Google Scholar 

  22. S. N. Khonina, N. L. Kazanskiy, and S. G. Volotovsky, Opt. Mem. Neural Networks 20, 23 (2011). https://doi.org/10.3103/s1060992x11010024

    Article  Google Scholar 

  23. F. Kanev, V. Aksenov, and I. Veretekhin, Proc. SPIE 11560, 115602B (2020). https://doi.org/10.1117/12.2575935

  24. V. V. Kotlyar and A. A. Kovalev, Komp’yuternaya Opt. 44, 510 (2020). https://doi.org/10.18287/2412-6179-co-719

    Article  ADS  Google Scholar 

  25. S. V. Karpeev, V. D. Paranin, and S. N. Khonina, Quantum Electron. 48, 521 (2018). https://doi.org/10.1070/qel16603

    Article  ADS  Google Scholar 

  26. Yi-M. Lu, Zh.-N. Tian, Sh.-N. Yang, J.-G. Hua, X.‑Q. Liu, Ya. Zhao, Q.-D. Chen, Yo.-L. Zhang, and H.-B. Sun, IEEE Photonics Technol. Lett. 31, 979 (2019). https://doi.org/10.1109/lpt.2019.2913712

    Article  ADS  Google Scholar 

  27. E. S. Kozlova, Komp’yuternaya Opt. 42, 977 (2018). https://doi.org/10.18287/2412-6179-2018-42-6-977-984

    Article  ADS  Google Scholar 

  28. Yu. Zhang, X. Yang, and J. Gao, Sci. Rep. 9, 9133 (2019). https://doi.org/10.1038/s41598-019-45727-6

    Article  ADS  Google Scholar 

  29. A. Rubano, F. Cardano, B. Piccirillo, and L. Marrucci, J. Opt. Soc. Am. B 36, D70 (2019). https://doi.org/10.1364/josab.36.000d70

    Article  Google Scholar 

  30. W. Ji, Ch.-H. Lee, P. Chen, W. Hu, Ya. Ming, L. Zhang, Ts.-H. Lin, V. Chigrinov, and Ya.-Q. Lu, Sci. Rep. 6, 25528 (2016). https://doi.org/10.1038/srep25528

    Article  ADS  Google Scholar 

  31. M. Sharma, F. Amirkhan, S. K. Mishra, D. Sengupta, Yo. Messaddeq, F. Blanchard, and B. Ung, in OSA Advanced Photonics Congress (AP) 2020 (IPR, NP, NOMA, Networks, PVLED, PSC, SPPCom, SOF), Washington, D.C., 2020 (Optica Publishing Group, 2020), p. 2020. https://doi.org/10.1364/sof.2020.som3h.7

  32. V. V. Kotlyar and A. G. Nalimov, Komp’yuternaya Opt. 41, 645 (2017). https://doi.org/10.18287/2412-6179-2017-41-5-645-654

    Article  ADS  Google Scholar 

  33. M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, Sci. Adv. 3, 1700552 (2017). https://doi.org/10.1126/sciadv.1700552

  34. Yu. Zhu, H. Tan, N. Zhou, L. Chen, J. Wang, and X. Cai, Opt. Lett. 45, 1607 (2020). https://doi.org/10.1364/ol.385878

    Article  ADS  Google Scholar 

  35. F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, Sci. Rep. 6, 21738 (2016). https://doi.org/10.1038/srep21738

    Article  ADS  Google Scholar 

  36. M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, Proc. SPIE 8590, 85900 (2013). https://doi.org/10.1117/12.2001671

    Article  ADS  Google Scholar 

  37. R. A. B. Suarez, L. A. Ambrosio, A. A. R. Neves, M. Zamboni-Rached, and M. R. R. Gesualdi, Opt. Lett. 45, 2514 (2020). https://doi.org/10.1364/ol.390909

    Article  ADS  Google Scholar 

  38. A. -I. Bunea and J. Glückstad, Laser Photonics Rev. 13, 1800227 (2019). https://doi.org/10.1002/lpor.201800227

  39. S. Yu, F. Pang, H. Liu, X. Li, J. Yang, and T. Wang, Appl. Phys. Lett. 111, 91107 (2017). https://doi.org/10.1063/1.4989651

    Article  Google Scholar 

  40. V. V. Kotlyar, S. S. Stafeev, and A. G. Nalimov, Reverse Flow of Light Energy in Focus (Fizmatlit, Moscow, 2021).

    Google Scholar 

  41. V. V. Kotlyar, A. A. Kovalev, and A. P. Porfirev, Appl. Opt. 56, 4095 (2017). https://doi.org/10.1364/ao.56.004095

    Article  ADS  Google Scholar 

  42. V. V. Kotlyar, S. S. Stafeev, and A. G. Nalimov, Phys. Rev. A 99, 33840 (2019). https://doi.org/10.1103/physreva.99.033840

    Article  ADS  Google Scholar 

  43. V. V. Kotlyar, S. S. Stafeev, A. G. Nalimov, S. Schulz, and L. O’Faolain, Opt. Laser Technol. 119, 105649 (2019). https://doi.org/10.1016/j.optlastec.2019.105649

  44. S. A. Degtyarev, A. P. Porfirev, and S. N. Khonina, Appl. Opt. 55, B44 (2016). https://doi.org/10.1364/ao.55.000b44

    Article  Google Scholar 

  45. V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, O. Yu. Moiseev, and V. A. Soifer, J. Opt. Soc. Am. A 24, 1955 (2007). https://doi.org/10.1364/josaa.24.001955

    Article  ADS  Google Scholar 

  46. V. V. Kotlyar, S. S. Stafeev, and A. G. Nalimov, Sharp Focusing of Laser Light (CRC Press, 2020). https://doi.org/10.1201/9780429346071

    Book  Google Scholar 

Download references

Funding

Research presented in Sections 3 and 4 was supported by the Russian Foundation for Basic Research (project 22-12-00137). Research presented in Sections 1, 2, and 5 was carried out within the framework of the State Assignment of the National Research Center “Kurchatov Institute.”

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. S. Kozlova.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kozlova, E.S., Savel’eva, A.A. & Kotlyar, V.V. A Comparative Analysis of Intensity and Energy Flux in the Focus of the High-Numeric-Aperture Conventional and Spiral Zone Plates. Opt. Spectrosc. 131, 1209–1217 (2023). https://doi.org/10.1134/S0030400X24700139

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0030400X24700139

Keywords:

Navigation