Skip to main content
SpringerLink
Log in

Interference analysis of radially polarized laser beams generated by ring optical elements with vortical phases at sharp focusing

  • Published:
Optical Memory and Neural Networks Aims and scope Submit manuscript

Abstract

We performed theoretical analysis of sharp focusing of radially polarized beams when there are annular apertures at vortex phase elements in the focusing system. We obtained analytical expressions for the field in the focal region in case of one and two annular apertures. We also present asymptotic expressions for the focal field near the optical axis and at a distance from it. We showed that for one narrow annular aperture with a vortex phase the focal distribution is proportional to a superposition of Bessel functions of different orders. In this case, the focal field is an axially symmetric and does not depend on the longitudinal coordinate. When two narrow annular apertures are used an interference pattern of two vector Bessel-type beams is generated in the focal region. In the case of equal vortex phases in both rings, the field in the focal region remains an axisymmetric one, but a periodic dependence on the longitudinal coordinate appears. If in each of the rings there are vortex phases of different orders, we obtain an interference pattern of more intricate type leading to formation of spiral beams.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dienerowitz, M., Mazilu, M., and Dholakia, K., Optical manipulation of nanoparticles: a review, J. Nanophotonics, 2008, vol. 2, p. 021875.

    Article  Google Scholar 

  2. Martínez-Corral, M. and Saavedra, G., The resolution challenge in 3D optical microscopy, Progress Optics, 2009, vol. 53, pp. 1–67.

    Article  Google Scholar 

  3. Walker, E., Dvornikov, A., Coblentz, K., Esener, S., and Rentzepis, P., Toward terabyte two-photon 3D disk, Opt. Express, 2007, vol. 15, pp. 12264–12276.

    Article  Google Scholar 

  4. Khonina, S.N. and Ustinov, A.V., Formation of light balls on the basis of interference of oncoming fine-focused beams with different polarizations, Herald of Samara State Univ., 2013, vol. 2, no. 40, pp. 208–224.

    Google Scholar 

  5. Dorn, R., Quabis, S., and Leuchs, G., Sharper focus for a radially polarized light beam, Phys. Rev. Lett., 2003, vol. 91, p. 233901.

    Article  MATH  Google Scholar 

  6. Davidson, N. and Bokor, N., High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens, Opt. Lett., 2004, vol. 29, pp. 1318–1320.

    Article  MATH  Google Scholar 

  7. Kalosha, V.P. and Golub, I., Toward the subdiffraction focusing limit of optical superresolution, Opt. Lett., 2007, vol. 32, pp. 3540–3542.

    Article  Google Scholar 

  8. Kozawa, Y. and Sato, S., Sharper focal spot formed by higher-order radially polarized laser beams, J. Opt. Soc. Am., Ser. A, 2007, vol. 24, p. 1793.

    Article  Google Scholar 

  9. Khonina, S.N. and Ustinov, A.V., Sharper focal spot for a radially polarized beam using ring aperture with phase jump, J. Eng., 2013, ID 512971.

    Google Scholar 

  10. Khonina, S.N. and Volotovsky, S.G., Investigation of axicon application in high-aperture focusing system, Computer Optics, 2010, vol. 34, no. 1, pp. 35–51.

    Google Scholar 

  11. Khonina, S.N. and Pelevina, E.A., Reduction of the focal spot size in high-aperture focusing systems at inserting of aberrations, Opt. Mem. Neural Networks (Inform. Opt.), 2011, vol. 20, no. 3, pp. 155–167.

    Article  MATH  Google Scholar 

  12. Khonina, S.N., Simple phase optical elements for narrowing of a focal spot in high-numerical-aperture conditions, Opt. Eng., 2013, vol. 52, no. 9, p. 091711.

    Article  Google Scholar 

  13. Hell, S. and Stelzer, E.H.K., Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation, Opt. Commun., 1992, vol. 93, pp. 277–282.

    Article  Google Scholar 

  14. Bokor, N. and Davidson, N., Toward a spherical spot distribution with 4p focusing of radially polarized light, Opt. Lett., 2004, vol. 29, no. 17, pp. 1968–1970.

    Article  Google Scholar 

  15. Sandeau, N. and Giovannini, H., Arrangement of a 4Pi microscope for reducing the confocal detection volume with two-photon excitation, Opt. Commun., 2006, vol. 264, pp. 123–129.

    Article  Google Scholar 

  16. Bokor, N. and Davidson, N., A three dimensional dark focal spot uniformly surrounded by light, Opt. Commun., 2007, vol. 279, pp. 229–234.

    Article  Google Scholar 

  17. Chen, Z. and Zhao, D., 4pi focusing of spatially modulated radially polarized vortex beams, Opt. Lett., 2012, vol. 37, no. 8, pp. 1286–1288.

    Article  Google Scholar 

  18. Khonina, S.N., Ustinov, A.V., and Volotovsky, S.G., Shaping of spherical light intensity based on the interference of tightly focused beams with different polarizations, Opt. Laser Technol., 2014, vol. 60, pp. 99–106.

    Article  Google Scholar 

  19. Khonina, S.N. and Fidirko, N.S., Research of interference of sharp-focused oncoming beams with different polarizations, Proceedings of the Samara Scientific Center RAS, 2014, vol. 16, no. 4, pp. 27–33.

    Google Scholar 

  20. Chen, W. and Zhan, Q., Three-dimensional focus shaping with cylindrical vector beams, Opt. Commun., 2006, vol. 265, pp. 411–417.

    Article  Google Scholar 

  21. Jabbour, T.G. and Kuebler, S.M., Vector diffraction analysis of high numerical aperture focused beams modified by two- and three-zone annular multi-phase plates, Opt. Express, 2006, vol. 14, no. 3, pp. 1033–1043.

    Article  Google Scholar 

  22. Gao, X., Wang, J., Gu, H., and Xu, W., Focusing properties of concentric piecewise cylindrical vector beam, Optik, 2007, vol. 118, pp. 257–265.

    Article  Google Scholar 

  23. Khonina, S.N. and Volotovsky, S.G., Controlling the contribution of the electric field components to the focus of a high-aperture lens using binary phase structures, J. Opt. Soc. Am., Ser. A, 2010, vol. 27, no. 10, pp. 2188–2197.

    Article  Google Scholar 

  24. Khonina, S.N., Kazanskiy, N.L., and Volotovsky, S.G., Vortex phase transmission function as a factor to reduce the focal spot of high-aperture focusing system, J. Mod. Opt., 2011, vol. 58, no. 9, pp. 748–760.

    Article  MATH  Google Scholar 

  25. Khonina, S.N., Kazanskiy, N.L., and Volotovsky, S.G., Influence of vortex transmission phase function on intensity distribution in the focal area of high-aperture focusing system, Opt. Mem. Neural Networks (Inform. Opt.), 2011, no. 20, no. 1, pp. 23–42.

    Google Scholar 

  26. Zhan, Q., Cylindrical vector beams: from mathematical concepts to applications, Adv. Opt. Photon., 2009, vol. 1, p. 1457.

    Article  Google Scholar 

  27. Khonina, S.N. and Ustinov, A.V., Thin light tube formation by tightly focused azimuthally polarized light beams, ISRN Optics, Hindawi Publishing Corporation, 2013, Article ID 185495, 6 p.

    Google Scholar 

  28. Bouchal, Z. and Olivík, M., Non-diffractive vector Bessel beams, J. Mod. Opt., 1995, vol. 42, no. 8, pp. 1555–1566.

    Article  MATH  Google Scholar 

  29. Dudley, A., Li, Y., Mhlanga, T., Escuti, M., and Forbes, A., Generating and measuring nondiffracting vector Bessel beams, Opt. Lett., 2013, vol. 38, no. 17, pp. 3429–3432.

    Article  Google Scholar 

  30. Kotlyar, V.V., Soifer, V.A., and Khonina, S.N., An algorithm for the generation of laser beams with longitudinal periodicity: rotating images, J. Mod. Opt., 1997, vol. 44, no. 7, pp. 1409–1416.

    Article  Google Scholar 

  31. Paakkonen, P., Lautanen, J., Honkanen, M., Kuittinen, M., Turunen, J., Khonina, S.N., Kotlyar, V.V., Soifer, V.A., and Friberg, A.T., Rotating optical fields: experimental demonstration with diffractive optics, J. Mod. Opt., 1998, vol. 45, no. 11, pp. 2355–2369.

    Article  Google Scholar 

  32. Porfirev, A.P. and Skidanov, R.V., A simple method of the formation nondiffracting hollow optical beams with intensity distribution in form of a regular polygon contour, Computer Optics, 2014, vol. 38, no. 2, pp. 243–248.

    Google Scholar 

  33. Fidirko, N.S. and Khonina, S.N., Formation of three-dimensional intensity distributions by diffraction of laser radiation on annular apertures at sharp focusing, Proceedings of the Samara Scientific Center RAS, 2014, vol. 16, no. 6, pp. 19–25.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Image Processing Systems Institute, Russian Academy of Sciences, Samara, Russia

    S. N. Khonina & A. V. Ustinov

  2. Samara State Aerospace University, Samara, Russia

    S. N. Khonina & A. V. Ustinov

Authors
  1. S. N. Khonina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Ustinov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. N. Khonina.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khonina, S.N., Ustinov, A.V. Interference analysis of radially polarized laser beams generated by ring optical elements with vortical phases at sharp focusing. Opt. Mem. Neural Networks 24, 130–144 (2015). https://doi.org/10.3103/S1060992X15020071

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1060992X15020071

Keywords

Search

Navigation