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ISSN: 1023-5086


ISSN: 1023-5086

Scientific and technical

Opticheskii Zhurnal

A full-text English translation of the journal is published by Optica Publishing Group under the title “Journal of Optical Technology”

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DOI: 10.17586/1023-5086-2023-90-05-19-28

УДК: 535.42

Influence of 3D the helical microstructure shape deviations on the properties of the generated vortex beam in the near diffraction zone

For Russian citation (Opticheskii Zhurnal):
Хорин П.А., Хонина С.Н. Влияние отклонений 3D формы спиральной микроструктуры на свойства формируемого вихревого пучка в ближней зоне дифракции // Оптический журнал. 2023. Т. 90. № 5. С. 19–28.     Khorin P.A., Khonina S.N. Influence of 3D the helical microstructure shape deviations on the properties of the generated vortex beam in the near diffraction zone [in Russian] // Opticheskii Zhurnal. 2023. V. 90. № 5. P. 19–28.
For citation (Journal of Optical Technology):
Pavel A. Khorin and Svetlana N. Khonina, "Influence of 3D helical microstructure shape deviations on the properties of a vortex beam generated in the near diffraction zone," Journal of Optical Technology. 90(5), 236-241 (2023)

Subject of study. The effect of various deviations of the helical microstructure shape and position associated with manufacturing and alignment errors on the properties of the formed vortex beam in the near diffraction zone (at a distance of about a dozen wavelengths) has been studied. Aim of study is determination of the shape deviations different types influence and the spiral microstructure position on the formed vortex beam properties. Method. Numerical simulation is carried out using the finite-difference time-domain method of both linear and nonlinear spiral phase plate. It allows us to take into account the real features of the 3D structure of the element under study, related to reflection and refraction on a complex surface. The height of the microrelief, the radius of the illuminating beam, and its displacement vary in a number of numerical experiments. Main results. As a result of the research, it was shown that 3D shape deviations of the helical microstructure, for example, the nonlinearity of the relief, leads to a distortion of the vortex dependence of the phase and breaks the annular intensity of the formed beam. However, in this case, the overall stability of the singular beam structure is preserved, which is completely destroyed at the misalignment of the illuminating beam and the optical element. A change in the height of the microrelief leads to a change in both the topological charge and the shape of the beam. As for the influence of the aperture radius of the input Gaussian beam, by changing the aperture radius, it is possible to scale the formed vortex beams. Misalignment in the optical system leads to the loss of the annular structure of the vortex beam and its invariant properties. Practical significance. The obtained results can be useful in applying of adjustable optical elements, as well as microstructures formed in photosensitive media. The main reasons for the distortion of the formed beam structure are both technological inaccuracies during etching, including the height mismatch and changes in the structure of the zones of the diffractive optical element, and alignment errors of the optical system, including the misalignment of the illuminating beam and the optical element. It should be noted that the characteristics of the 3D the optical elements structure most noticeably affect the diffraction pattern in the near zone.


generalized spiral phase plate, vortex beams, near diffraction zone, microstructure, diffractive optical element

OCIS codes: 050.1970, 260.1960

  1. Coullet P., Gil, L., Rocca, F. Optical vortices // Opt. Commun. 1989. V. 73. P. 403–408.­019­0194­2
  2. Khonina S.N., Kotlyar V.V., Shinkaryev M.V., et al. The phase rotor filter // J. Mod. Opt. 1992. V. 39. № 5. P. 1147–1154.
  3. Davis J.A., McNamara D.E., Cottrell D.M., et al. Image processing with the radial Hilbert transform: Theory and experiments // Opt. Lett. 2000. V. 25. P. 99–101.
  4. Shen Y., Wang X., Xie Z., et al. Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities // Light Sci. Appl. 2019. V. 8. P. 90.­019­0194­2
  5. Порфирьев А.П., Кучмижак А.А., Гурбатов С.О. и др. Фазовые сингулярности и оптические вихри в фотонике // УФН. 2022. Т. 192. № 8. С. 841–866. Porfirev A.P., Kuchmizhak A.A., Gurbatov S.O., et al. Phase singularities and optical vortices in photonics // Phys. Usp. 2022. V. 192. № 8. P. 841–866.
  6. Oemrawsingh S.S.R., Van Houwelingen J.A.W., Eliel E.R., et al. Production and characterization of spiral phase plates for optical wavelengths // Appl. Opt. 2004. V. 43. P. 688–694.
  7. Wang J., Cao A., Zhang M., et al. Study of characteristics of vortex beam produced by fabricated spiral phase plates // IEEE Photon. J. 2016. V. 8. № 2. P. 1.
  8. Sugioka K. and Cheng Ya. Femtosecond laser three­dimensional micro and nanofabrication // 2014. Appl. Phys. Rev. V. 1. P. 041303.
  9. Yu Y.J., Noh H., Hong M.H., et al. Focusing characteristics of optical fiber axicon microlens for near­field spectroscopy: dependence of tip apex angle // Opt. Commun. 2006. V. 267. № 1. P. 264–270.
  10. Žukauskas A., Malinauskas M., Brasselet E. Monolithic generators of pseudo­nondiffracting optical vortex beams at the microscale // Appl. Phys. Lett. 2013. V. 103. № 18. P. 181122.
  11. Sanchez­Padilla B., Žukauskas A., Aleksanyan A., et al. Wrinkled axicons: shaping light from cusps // Opt. Exp. 2016. V. 24. № 21. P. 24075–24082.
  12. Khonina S.N., Degtyarev S.A., Savelyev D.A., et al. Focused, evanescent, hollow, and collimated beams formed by microaxicons with different conical angles // Opt. Exp. 2017. V. 25. № 16. P. 19052–19064.
  13. Gorelick S., Paganin D.M., Marco A. Axilenses: Refractive micro­optical elements with arbitrary exponential profiles // Appl. Photon. 2020. V. 5. P. 106110.
  14. Banerji S., Cooke J., and Sensale­Rodriguez B. Impact of fabrication errors and refractive index on multilevel diffractive lens performance // Sci. Rep. 2020. V. 10. P. 14608.­020­71480­2
  15. Хонина С.Н., Савельев Д.А., Серафимович П.Г. и др. Дифракция на бинарных микроаксиконах в ближней зоне // Оптический журнал. 2012. Т. 79. № 10. С. 22–29. Khonina S.N., Savelyev D.A., Serafimovich P.G., et al. Diffraction at binary microaxicons in the near field // J. Opt. Technol. 2012. V. 79. № 10. P. 626–631.
  16. Degtyarev S.A., Porfirev A.P., and Khonina S.N. Photonic nanohelix generated by a binary spiral axicon // Appl. Opt. 2016. V. 55. № 12. P. B44–B48.
  17. Khonina S.N., Krasnov S.V., Ustinov A.V., et al. Refractive twisted microaxicons // Opt. Lett. 2020.V. 45. № 6. P. 1334–1337.
  18. Berry M.V. Optical vortices evolving from helicoidal integer and fractional phase steps // J. Opt. A: Pure Appl. Opt. 2004. V. 6. P. 259–268.­4258/6/2/018
  19. Leach J., Yao E., and Padgett M.J. Observation of the vortex structure of a non­integer vortex beam // New J. Phys. 2004. V. 6. P. 71.­2630/6/1/071
  20. Khonina S.N., Podlipnov V.V., Karpeev S.V., et al. Spectral control of the orbital angular momentum of a laser beam based on 3D properties of spiral phase plates fabricated for an infrared wavelength // Opt. Exp. 2020. V. 28. № 12. P. 18407–18417.
  21. Korolkov V.P., Nasyrov R.K., Shimansky R.V. Zone­boundary optimization for direct laser writing of continuous­relief diffractive optical elements // Appl. Opt. 2006. V. 45. № 1. P. 53–62.
  22. Korolkov V.P., Nasyrov R.K., Sametov A.R., et al. Optimization of half­tone technology for diffractive microlens fabrication // Proc. SPIE. 2011. V. 7957. P. 795710.
  23. Скиданов Р.В., Хонина С.Н., Морозов А.А. Оптическое вращение микрочастиц в гипергеометрических пучках, сформированных дифракционными оптическими элементами с многоуровневым микрорельефом // Оптический журнал. 2013. Т. 80. № 10. С. 3–8. Skidanov R.V., Khonina S.N., Morozov A.A. Optical rotation of microparticles in hypergeometric beams formed by diffraction optical elements with multilevel microrelief // J. Opt. Technol. 2013. V. 80. № 10. P. 585–589.
  24. Poleshchuk A.G., Korolkov V.P., Veiko V.P., et al. Laser technologies in micro­optics. Part 2. Fabrication of elements with a three­dimensional profile // Optoelectron. Instrument. Proc. 2018. V. 54. № 2. P. 113–126.
  25. Beijersbergen M.W., Coerwinkel R.P.C., Kristensen M., et al. Helical­wavefront laser beams produced with a spiral phaseplate // Opt. Commun. 1994. V. 112. P. 321–327.­4018(94)90638­6
  26. Sueda K., Miyaji G., Miyanaga N., et al. Laguerre­Gaussian beam generated with a multilevel spiral phase plate for high intensity laser pulses // Opt. Exp. 2004. V. 12. № 15. P. 3548–3553.
  27. Watanabe T., Fujii M., Watanabe Y., et al. Generation of a doughnut­shaped beam using a spiral phase plate // Rev. Sci. Instrum. 2004. V. 75. № 12. P. 5131–5135.
  28. Li P., Liu S., Peng T., et al. Spiral autofocusing Airy beams carrying power­exponent­phase vortices // Opt. Exp. 2014. V. 22. P. 7598–7606.
  29. Lao G., Zhang Z., and Zhao D. Propagation of the power­exponent phase vortex beam in paraxial ABCD system // Opt. Exp. 2016. V. 24. P. 18082–18094.
  30. Khonina S.N., Ustinov A.V., Logachev V.I., et al. Properties of vortex light fields generated by generalized spiral phase plates // Phys. Rev. A. 2020. V. 101. P. 043829.
  31. Ustinov A.V., Khonina S.N., Khorin P.A., et al. Control of the intensity distribution along the light spiral generated by a generalized spiral phase plate // JOSA B. 2021. V. 38. № 2. P. 420–427.
  32. Khorin P.A., Porfirev A.P. Modeling diffraction of a polarized light by three­dimensional nonlinear spiral phase in the near zone // Proc. SPIE. 2021. V. 11846. P. 118460O.
  33. Khorin P.A., Ustinov A.V. Simulation of the action of a three­dimensional nonlinear spiral phase plate in the near diffraction zone // J. Phys. Conf. Ser. 2020. V. 1695. P. 012165.­6596/1695/1/012165
  34. Rozas D., Law C.T., and Swartzlander G.A. Propagation dynamics of optical vortices // JOSA B. 1997. V. 14. P. 3054–3065.
  35. Khonina S.N., Porfirev A.P., Ustinov A.V. Diffraction patterns with mth order symmetry generated by sectional spiral phase plates // J. Opt. 2015. V. 17. P. 125607­8pp.­8978/17/12/125607
  36. Zhao X., Zhang J., Pang X., et al. Properties of a strongly focused Gaussian beam with an off­axis vortex // Opt. Commun. 2017. V. 389. P. 275–282.
  37. Khonina S.N., Ustinov A.V. Focusing of shifted vortex beams of arbitrary order with different polarization // Opt. Commun. 2018. V. 426. P. 359–365.
  38. Rotschild C., Zommer S., Moed S., et al. Adjustable spiral phase plate // Appl. Opt. 2004. V. 43. P. 2397–2399.
  39. Ojeda­Castaneda J., Ledesma S., and Gómez­Sarabia C.M. Tunable apodizers and tunable focalizers using helical pairs // Photon. Lett. Pol. 2013. V. 5. P. 20–22.
  40. Grewe A. and Sinzinger S. Efficient quantization of tunable helix phase plates // Opt. Lett. 2016. V. 41. P. 4755–4758.
  41. Priimagi A., Shevchenko A. Azopolymer­based micro­ and nanopatterning for photonic applications // J. Polym. Sci. B. Polym. Phys. 2014. V. 52. P. 163–182.
  42. Syubaev S., Zhizhchenko A., Vitrik O., et al. Chirality of laser­printed plasmonic nanoneedles tunable by tailoring spiralshape pulses // Appl. Surf. Sci. 2019. V. 470. P. 526–534.
  43. Porfirev A.P., Khonina S.N., Ivliev N.A., et al. Writing and reading with the longitudinal component of light using carbazole­containing azopolymer thin films // Sci. Rep. 2022. V. 12. P. 3477 (12 pp).­022­07440­9
  44. Bian S., Williams J.M., Kim D.Y., et al. Photoinduced surface deformations on azobenzene polymer films // J. Appl. Phys. 1999. V. 86. № 8. P. 4498–4508.
  45. Poplipnov V.V., Ivliev N.A., Khonina S.N., et al. Investigation of photoinduced formation of microstructures on the surface of carbaseole­containing azopolymer depending on the power density of incident beams // Comput. Opt. 2018. V. 42 № 5. P. 779–785.­6179­2018­42­5­779­785
  46. Porfirev A.P., Khonina S.N., Khorin P.A., et al. Polarization­sensitive direct laser patterning of azopolymer thin films with vortex beams // Opt. Lett. 2022. V. 47. № 19. P. 5080–5083.