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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 16 — Jul. 30, 2012
  • pp: 17684–17694

Nonparaxial and paraxial focusing of azimuthal-variant vector beams

Bing Gu and Yiping Cui  »View Author Affiliations


Optics Express, Vol. 20, Issue 16, pp. 17684-17694 (2012)
http://dx.doi.org/10.1364/OE.20.017684


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Abstract

Based on the vectorial Rayleigh-Sommerfeld formulas under the weak nonparaxial approximation, we investigate the propagation behavior of a lowest-order Laguerre-Gaussian beam with azimuthal-variant states of polarization. We present the analytical expressions for the radial, azimuthal, and longitudinal components of the electric field with an arbitrary integer topological charge m focused by a nonaperturing thin lens. We illustrate the three-dimensional optical intensities, energy flux distributions, beam waists, and focal shifts of the focused azimuthal-variant vector beams under the nonparaxial and paraxial approximations.

© 2012 OSA

OCIS Codes
(260.1960) Physical optics : Diffraction theory
(260.5430) Physical optics : Polarization
(350.5500) Other areas of optics : Propagation

ToC Category:
Physical Optics

History
Original Manuscript: May 9, 2012
Revised Manuscript: July 1, 2012
Manuscript Accepted: July 1, 2012
Published: July 19, 2012

Citation
Bing Gu and Yiping Cui, "Nonparaxial and paraxial focusing of azimuthal-variant vector beams," Opt. Express 20, 17684-17694 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-17684


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References

  1. A. A. Tovar, “Production and propagation of cylindrically polarized Laguerre-Gaussian laser beams,” J. Opt. Soc. Am. A15, 2705–2711 (1998). [CrossRef]
  2. J. S. Ahn, H. W. Kihm, J. E. Kihm, D. S. Kim, and K. G. Lee, “3-dimensional local field polarization vector mapping of a focused radially polarized beam using gold nanoparticle functionalized tips,” Opt. Express17, 2280–2286 (2009). [CrossRef] [PubMed]
  3. A. F. Abouraddy and K. C. Toussaint, “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett.96, 153901 (2006). [CrossRef] [PubMed]
  4. X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105, 253602 (2010). [CrossRef]
  5. V. V. Kotlyar and A. A. Kovalev, “Nonparaxial propagation of a Gaussian optical vortex with initial radial polarization,” J. Opt. Soc. Am. A27, 372–380 (2010). [CrossRef]
  6. X. Jia and Y. Wang “Vectorial structure of far field of cylindrically polarized beams diffracted at a circular aperture,” Opt. Lett.36, 295–297 (2011). [CrossRef] [PubMed]
  7. D. M. Deng, Q. Guo, S. Lan, and X. B. Yang, “Application of the multiscale singular perturbation method to nonparaxial beam propagation in free space,” J. Opt. Soc. Am. A24, 3317–3325 (2007). [CrossRef]
  8. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A253, 358–379 (1959). [CrossRef]
  9. R. Borghi and M. Santarsiero, “Nonparaxial propagation of spirally polarized optical beams,” J. Opt. Soc. Am. A21, 2029–2037 (2004). [CrossRef]
  10. Z. Mei and D. Zhao, “Nonparaxial propagation of controllable dark-hollow beams,” J. Opt. Soc. Am. A25, 537–542 (2008). [CrossRef]
  11. D. Deng and Q. Guo, “Exact nonparaxial propagation of a hollow Gaussian beam,” J. Opt. Soc. Am. B26, 2044–2049 (2009). [CrossRef]
  12. Z. Mei and D. Zhao, “Nonparaxial analysis of vectorial Laguerre-Bessel-Gaussian beams,” Opt. Express15, 11942–11951 (2007). [CrossRef] [PubMed]
  13. G. Zhou, “Nonparaxial propagation of a Lorentz-Gauss beam,” J. Opt. Soc. Am. B26, 141–147 (2009). [CrossRef]
  14. X. Li and Y. Cai, “Nonparaxial propagation of a partially coherent dark hollow beam,” Appl. Phys. B102, 205–213 (2011). [CrossRef]
  15. B. Lü and K. Duan, “Nonparaxial propagation of vectorial Gaussian beams diffracted at a circular aperture,” Opt. Lett.28, 2440–2442 (2003). [CrossRef] [PubMed]
  16. S. Guha and G. D. Gillen, “Description of light propagation through a circular aperture using nonparaxial vector diffraction theory,” Opt. Express13, 1424–1447 (2005). [CrossRef] [PubMed]
  17. X. Jia, Y. Wang, and B. Li, “Nonparaxial analyses of radially polarized beams diffracted at a circular aperture,” Opt. Express18, 7064–7075 (2010). [CrossRef] [PubMed]
  18. K. Duan and B. Lü, “Vectorial nonparaxial propagation equation of elliptical Gaussian beams in the presence of a rectangular aperture,” J. Opt. Soc. Am. A21, 1613–1620 (2004). [CrossRef]
  19. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett.86, 5251–5254 (2001). [CrossRef] [PubMed]
  20. C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrafast pulses,” Phys. Rev. Lett.106, 123901 (2011). [CrossRef] [PubMed]
  21. P. L. Greene and D. G. Hall, “Focal shift in vector beams,” Opt. Express4, 411–419 (1999). [CrossRef] [PubMed]
  22. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express7, 77–87 (2000). [CrossRef] [PubMed]
  23. D. M. Deng, Q. Guo, L. J. Wu, and X. B. Yang, “Propagation of radially polarized elegant light beams,” J. Opt. Soc. Am. B24, 636–643 (2007). [CrossRef]
  24. M. Rashid, O. M. Maragò, and P. H. Jones, “Focusing of high order cylindrical vector beams,” J. Opt. A: Pure Appl. Opt.11, 065204 (2009). [CrossRef]
  25. D. M. Deng, “Nonparaxial propagation of radially polarized light beams,” J. Opt. Soc. Am. B23, 1228–1234 (2006). [CrossRef]
  26. P. P. Banerjee, G. Cook, and D. R. Evans, “A q-parameter approach to analysis of propagation, focusing, and waveguiding of radially polarized Gaussian beams,” J. Opt. Soc. Am. A26, 1366–1374 (2009). [CrossRef]
  27. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91, 233901 (2003). [CrossRef] [PubMed]
  28. V. V. Kotlyar, A. A. Kovalev, and V. A. Soifer, “Lensless focusing of hypergeometric laser beams,” J. Opt.13, 075703 (2011). [CrossRef]
  29. B. Gu, F. Ye, K. Lou, Y. Li, J. Chen, and H. T. Wang, “Vectorial self-diffraction effect in optically Kerr medium,” Opt. Express20, 149–157 (2012). [CrossRef] [PubMed]
  30. A. Ciattoni, B. Crosignani, and P. D. Porto, “Vectorial analytical description of propagation of a highly nonparaxial beam,” Opt. Commun.202, 17–20 (2002). [CrossRef]

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