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Control of the formation and detection of on-axis and off-axis diffraction orders with two-level phase quantization of a vortex lens
O.A. Dyukareva 1, A.V. Ustinov 2, S.N. Khonina 1,2

1 Samara National Research University,
443086, Samara, Russia, Moskovskoye Shosse 34;
2 Image Processing Systems Institute, NRC "Kurchatov Institute",
443001, Samara, Russia, Molodogvardeyskaya 151

 PDF, 2356 kB

DOI: 10.18287/2412-6179-CO-1527

Pages: 36-43.

Full text of article: Russian language.

Abstract:
The paper investigates the performance of a tilted vortex phase lens, quantized at a given level and allowing the generation of specified local maxima both on the optical axis and off it. A possibility of detecting individual diffraction orders and their combination is demonstrated. A combination of quantized optical elements is considered, which makes it possible to generate local maxima in both the longitudinal and transverse planes.

Keywords:
vortex lens, phase quantization, local foci, vortex beams detection.

Citation:
Dyukareva OA, Ustinov AV, Khonina SN. Control of the formation and detection of on-axis and off-axis diffraction orders with two-level phase quantization of a vortex lens. Computer Optics 2025; 49(1): 36-43. DOI: 10.18287/2412-6179-CO-1527.

Acknowledgements:
This work was funded within the Development Program of Samara National Research University and under a government project of the National Research Center "Kurchatov Institute".

References:
  1. Du J, Wang J. High-dimensional structured light coding/decoding for freespace optical communications free of obstructions. Opt Lett 2015; 40(21): 4827-4857. DOI: 10.1364/OL.40.004827.
  2. He C, Shen Y, Forbes A. Towards higher-dimensional structured light. Light Sci Appl 2022; 11: 205. DOI: 10.1038/s41377-022-00897-3.
  3. Goossens JW, Yousefi MI, Jaouën Y, Hafermann H. Polarization-division multiplexing based on the nonlinear Fourier transform. Opt Express 2017; 25; 26437–26452. DOI: 10.1364/OE.25.026437
  4. Man Z, Min C, Zhang Y, Shen Z, Yuan X-C. Arbitrary vector beams with selective polarization states patterned by tailored polarizing films. Laser Phys 2013; 23(10): 105001. DOI: 10.1088/1054-660X/23/10/105001.
  5. Khonina SN, Ustinov AV, Porfirev AP. Vector Lissajous laser beams. Opt Lett 2020; 45(15): 4112-4115. DOI: 10.1364/OL.398209.
  6. Khonina SN, Ustinov AV, Fomchenkov SA, Porfirev AP. Formation of hybrid higher-order cylindrical vector beams using binary multi-sector phase plates. Sci Rep 2018; 8: 14320. DOI: 10.1038/s41598-018-32469-0.
  7. Dorrah AH, Rubin NA, Tamagnone M, Zaidi A, Capasso F. Structuring total angular momentum of light along the propagation direction with polarization-controlled meta-optics. Nat Commun 2021; 12: 6249. DOI: 10.1038/s41467-021-26253-4.
  8. Li A, Singh S, Sievenpiper D. Metasurfaces and their applications. Nanophotonics 2018; 7(6): 989-1011. DOI: 10.1515/nanoph-2017-0120.
  9. Yoon G, Tanaka T, Zentgraf T, Rho J. Recent progress on metasurfaces: applications and fabrication. J Phys D: Appl Phys 2021; 54(38): 383002. DOI: 10.1088/1361-6463/ac0faa.
  10. Khonina SN, Butt MA, Kazanskiy NL. A review on reconfigurable metalenses revolutionizing flat optics. Adv Opt Mater 2023; 12(14): 2302794. DOI: 10.1002/adom.202302794.
  11. Kani J, Iwatsuki K, Imai T. Optical multiplexing technologies for access-area applications. IEEE J Sel Top Quantum Electron 2006; 12(4): 661-668. DOI: 10.1109/JSTQE.2006.876170.
  12. Kotlyar VV, Kovalev AA, Skidanov RV, Khonina SN, Turunen J. Generating hypergeometric laser beams with a diffractive optical element. Appl Opt 2008; 47(32): 6124-6133. DOI: 10.1364/AO.47.006124.
  13. Wang Z, Zhang N, Yuan X-C. High-volume optical vortex multiplexing and de-multiplexing for free-space optical communication. Opt Express 2011; 19(2): 482-492. DOI: 10.1364/OE.19.000482.
  14. Sun CL, Yu Y, Chen GY, Zhang XL. Integrated switchable mode exchange for reconfigurable mode-multiplexing optical networks. Opt Lett 2016; 41(14): 3257-3260. DOI: 10.1364/OL.41.003257.
  15. Fazea Y, Mezhuyev V. Selective mode excitation techniques for mode-division multiplexing: a critical review. Opt Fiber Technol 2018; 45: 280-288. DOI: 10.1016/j.yofte.2018.08.004.
  16. Su YK, He Y, Chen HS, Li XY, Li GF. Perspective on mode-division multiplexing. Appl Phys Lett 2021; 118(20): 200502. DOI: 10.1063/5.0046071.
  17. Wang X, Yan D, Chen Y, Qi T, Gao W. Parallel multiplexing optical spatial differentiation based on a superposed complex amplitude filter, Optics and Lasers in Engineering, 2025; 184(1): 108669. DOI: 10.1016/j.optlaseng.2024.108669.
  18. Borghi R, Cincotti G, Santarsiero M. Diffractive variable beam splitter: optimal design. J Opt Soc Am A 2000; 17(1): 63-67. DOI: 10.1364/JOSAA.17.000063.
  19. Lei T, Zhang M, Li Y, Jia P, Liu GN, Xu X, Li Z, Min C, Lin J, Yu C, Niu H. Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings. Light Sci Appl 2015; 4: e257. DOI: 10.1038/lsa.2015.30.
  20. Khorin PA, Mamaeva MP, Kapitonov YV, Khonina SN. Polarization-Mode Transformation of the Light Field during Diffraction on Amplitude Binary Gratings, Photonics 2024; 11: 848. DOI: 10.3390/photonics11090848.
  21. Rastani K, Marrakchi A, Habiby SF, Hubbard WM, Gilchrist H, and Nahory RE. Binary phase Fresnel lenses for generation of two-dimensional beam arrays, Appl Opt 1991; 30: 1347–1354. DOI: 10.1364/AO.30.001347
  22. Faklis D, Morris GM. Spectral properties of multi-order diffractive lenses. Appl Opt 1995; 34(14): 2462-2468. DOI: 10.1364/AO.34.002462.
  23. Khonina SN, Ustinov AV, Skidanov RV, Porfirev AP. Local foci of a parabolic binary diffraction lens. Appl Opt 2015; 54(18): 5680-5685. DOI: 10.1364/AO.54.005680.
  24. Motogaito A, Iguchi Y, Kato S, Hiramatsu K. Fabrication and characterization of a binary diffractive lens for controlling focal distribution. Appl Opt 2020; 59(3): 742-747. DOI: 10.1364/AO.381139.
  25. Janicijevic L, Topuzoski S. Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings. J Opt Soc Am A 2008; 25(11): 2659-2669. DOI: 10.1364/JOSAA.25.002659.
  26. Topuzoski S. Generation of optical vortices with curved fork-shaped holograms. Opt Quant Electron 2016; 48(2): 138. DOI: 10.1007/s11082-016-0405-5.
  27. Saad F, El Halba EM, Belafhal A. Generation of generalized spiraling Bessel beams of arbitrary order by curved fork-shaped holograms. Opt Quant Electron 2016; 48: 454. DOI: 10.1007/s11082-016-0723-7.
  28. Khonina SN, Ustinov AV, Kirilenko MS, Kuchmizhak AA, Porfirev AP. Application of binary curved fork grating for the generation and detection of optical vortices outside the focal plane. J Opt Soc Am B 2020; 37(6): 1714-1721. DOI: 10.1364/JOSAB.388431.
  29. Degtyarev SA, Porfirev AP, Khonina SN, Karpeev SV. Demonstration of vortical beams spectral stability formed in non-zero diffraction orders. J Phys Conf Ser 2016; 735: 012023. DOI: 10.1088/1742-6596/735/1/012023.
  30. Berezny AE, Karpeev SV, Uspleniev GV. Computer-generated holographic optical elements produced by photolithography. Opt Lasers Eng 1991; 15(5): 331-340. DOI: 10.1016/0143-8166(91)90020-T.
  31. Sohn J-S, et al. Design and fabrication of diffractive optical elements by use of gray-scale photolithography. Appl Opt 2005; 44(4): 506-511. DOI: 10.1364/AO.44.000506.
  32. Aguiam DE, et al. Fabrication and optical characterization of large aperture diffractive lenses using greyscale lithography. Micro Nano Eng 2022; 14(5): 100111. DOI: 10.1016/j.mne.2022.100111.
  33. Anh NNH, Rhee H-G, Ghim Y-S. Novel fabrication and designs for hybrid optical elements with wider angle field of view by using integrated direct laser lithographic system. Opt Lasers Eng 2023; 170: 107774. DOI: 10.1016/j.optlaseng.2023.107774.
  34. Khonina SN, Ustinov AV, Porfirev AP. Diatom optical element: a quantized version of the generalized spiral lens. Opt Lett 2022; 47(16): 3988-3991. DOI: 10.1364/OL.469113.
  35. Zhou X, Song Q, Yang X, Cai W. Generating phase-only diffractive optical elements using adaptive constraints in the Fourier domain. Opt Commun 2023; 535: 129360. DOI: 10.1016/j.optcom.2023.129360.
  36. Khorin PA, Khonina SN. Influence of 3D helical microstructure shape deviations on the properties of a vortex beam generated in the near diffraction zone. J Opt Technol 2023; 90(5): 236-241. DOI: 10.1364/JOT.90.000236.
  37. Hsu W-F, Lin C-H. Optimal quantization method for uneven-phase diffractive optical elements by use of a modified iterative Fourier-transform algorithm. Appl Opt 2005; 44(27): 5802-5808. DOI: 10.1364/AO.44.005802.
  38. Liu X, Lv G, Ding S, Wang Z, Wang S, Feng Q. Regional iterative optimization algorithm to reduce error caused by DOE binarization. Appl Opt 2019; 58(26): 7227-7232. DOI: 10.1364/AO.58.007227.
  39. Khonina SN, Ustinov AV. Binary multi-order diffraction optical elements with variable fill factor for the formation and detection of optical vortices of arbitrary order. Appl Opt 2019; 58(30): 8227-8236. DOI: 10.1364/AO.58.008227.
  40. Khonina SN, Ustinov AV. Spatially-spectral analysis of binary diffractive optical elements coded using the complex-conjugated addition. Izvestia of the Samara Scientific Center of the Russian Academy of Sciences 2014; 6: 10-17.
  41. Ferstl M, Hermerschmidt A, Dias D, Steingrüber R. Theoretical and experimental properties of a binary linear beam-splitting element with a large fan angle. J Mod Opt 2004; 51(14): 2125–2139. DOI: 10.1080/09500340408232518
  42. Hermerschmidt A, Krüger S, and Wernicke G. Binary diffractive beam splitters with arbitrary diffraction angles. Opt Lett 2007; 32: 448-450. DOI: 10.1364/OL.32.000448
  43. Barlev O, Golub MA. Multifunctional binary diffractive optical elements for structured light projectors. Opt Express 2018; 26(16): 21092-21107. DOI: 10.1364/OE.26.021092.
  44. Meshalkin AYu, Podlipnov VV, Ustinov AV, Achimova EA. Analysis of diffraction efficiency of phase gratings in dependence of duty cycle and depth. J Phys Conf Ser 2019; 1368: 022047. DOI: 10.1088/1742-6596/1368/2/022047.
  45. Xu C, Pang H, Cao A, Deng Q. Alternative design of binary phase diffractive optical element with non-π phase difference. Appl Sci 2021; 11(3): 1116. DOI: 10.3390/app11031116.
  46. Gretzki P, Gillner A. Programmable diffractive optic for multi-beam processing: applications and limitations. Proc. SPIE 2017; 10347: 103470V. DOI: 10.1117/12.2274448
  47. Huang K, et al. Planar diffractive lenses: Fundamentals, functionalities, and applications. Adv Mater 2018; 30(26): 1704556. DOI: 10.1002/adma.201704556.
  48. Wang F, Zhang Z, Wang R, Zeng X, Yang X, Lv S, Zhang F, Xue D, Yan J, and Zhang X. Distortion measurement of optical system using phase diffractive beam splitter. Opt Express 2019; 27: 29803-29816 DOI: 10.1364/OE.27.029803.

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