OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 7 — Jul. 1, 2014
  • pp: 1395–1400

Generation of hollow beam with radially polarized vortex beam and complex amplitude filter

Jie Lin, Ran Chen, Haichao Yu, Peng Jin, Yuan Ma, and Michael Cada  »View Author Affiliations

JOSA A, Vol. 31, Issue 7, pp. 1395-1400 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (715 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The generation of hollow beams with a long focal depth from a radially polarized Bessel–Gaussian beam with a second-order vortex phase and an amplitude filter is theoretically investigated by Richards–Wolf’s integral. The null intensity on the optical axis is achieved by introducing the second-order vortex. The long focal depth is a result of the amplitude filtering based on the cosine function and Euler transformation. Numerical results indicate that the focal depth of a hollow beam is improved from 0.96λ to 2.28λ with a slight increase of the transverse size for the simplest amplitude filter design. The intensity distribution twist phenomenon of the x- and y-polarized components around the optical axis due to the introducing of the vortex phase is also discussed. It is believed that the proposed scheme can be used to achieve particle acceleration and optical trapping.

© 2014 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(140.3300) Lasers and laser optics : Laser beam shaping
(260.5430) Physical optics : Polarization
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Diffraction and Gratings

Original Manuscript: March 18, 2014
Revised Manuscript: April 28, 2014
Manuscript Accepted: April 29, 2014
Published: June 9, 2014

Jie Lin, Ran Chen, Haichao Yu, Peng Jin, Yuan Ma, and Michael Cada, "Generation of hollow beam with radially polarized vortex beam and complex amplitude filter," J. Opt. Soc. Am. A 31, 1395-1400 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express 7, 77–87 (2000). [CrossRef]
  2. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003). [CrossRef]
  3. H. Wang, L. Shi, B. Lùkyhanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008). [CrossRef]
  4. X. P. Li, Y. Y. Cao, and M. Gu, “Superresolution-focal-volume induced 3.0 Tbytes/disk capacity by focusing a radially polarized beam,” Opt. Lett. 36, 2510–2512 (2011). [CrossRef]
  5. H. Wang, C. J. R. Sheppard, K. Ravi, S. T. Ho, and G. Vienne, “Fighting against diffraction: apodization and near field diffraction structures,” Laser Photon. Rev. 6, 354–392 (2012). [CrossRef]
  6. T. Grosjean and I. Gauthier, “Longitudinally polarized electric and magnetic optical nano-needles of ultra high lengths,” Opt. Commun. 294, 333–337 (2013). [CrossRef]
  7. Y. Zha, J. Wei, H. Wang, and F. Gan, “Creation of an ultra-long depth of focus super-resolution longitudinally polarized beam with a ternary optical element,” J. Opt. 15, 075703 (2013). [CrossRef]
  8. T. Liu, J. Tan, J. Liu, and J. Lin, “Creation of subwavelength light needle, equidistant multi-focus, and uniform light tunnel,” J. Mod. Opt. 60, 378–381 (2013). [CrossRef]
  9. X. Xie, H. Sun, L. Yang, S. Wang, and J. Zhou, “Effect of polarization purity of cylindrical vector beam on tightly focused spot,” J. Opt. Soc. Am. A 30, 1937–1940 (2013). [CrossRef]
  10. G.-Y. Chen, F. Song, and H.-T. Wang, “Sharper focal spot generated by 4π tight focusing of higher-order Laguerre–Gaussian radially polarized beam,” Opt. Lett. 38, 3937–3940 (2013). [CrossRef]
  11. J. Lin, K. Yin, Y. Li, and J. Tan, “Achievement of longitudinally polarized focusing with long focal depth by amplitude modulation,” Opt. Lett. 36, 1185–1188 (2011). [CrossRef]
  12. Q. Tan, K. Cheng, Z. Zhou, and G. Jin, “Diffractive superresolution elements for radially polarized light,” J. Opt. Soc. Am. 27, 1355–1360 (2010). [CrossRef]
  13. H. Guo, X. Weng, M. Jiang, Y. Zhao, G. Sui, Q. Hu, Y. Wang, and S. Zhuang, “Tight focusing of a higher-order radially polarized beam transmitting through multi-zone binary phase pupil filters,” Opt. Express 21, 5363–5372 (2013). [CrossRef]
  14. K. Huang, P. Shi, X.-L. Kang, X. Zhang, and Y.-P. Li, “Design of DOE for generating a needle of a strong longitudinally polarized field,” Opt. Lett. 35, 965–967 (2010). [CrossRef]
  15. G. H. Yuan, S. B. Wei, and X.-C. Yuan, “Nondiffracting transversally polarized beam,” Opt. Lett. 36, 3479–3481 (2011). [CrossRef]
  16. S. N. Khonina, “Simple phase optical elements for narrowing of a focal spot in high-numerical-aperture conditions,” Opt. Eng. 52, 091711 (2013). [CrossRef]
  17. S. G. Reddy, A. Kumar, S. Prabhakar, and R. P. Singh, “Experimental generation of ring-shaped beams with random sources,” Opt. Lett. 38, 4441–4444 (2013). [CrossRef]
  18. S. N. Khonina, S. V. Alferov, and S. V. Karpeev, “Strengthening the longitudinal component of the sharply focused electric field by means of higher-order laser beams,” Opt. Lett. 38, 3223–3226 (2013). [CrossRef]
  19. J. Wang, Q. Liu, Y. Liu, W. Chen, and Q. Zhan, “Discrete complex amplitude filter for ultra long optical tube,” Proc. SPIE 8097, 809722 (2011). [CrossRef]
  20. J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269–4274 (2013). [CrossRef]
  21. Y. Song, D. Milam, and W. T. Hill, “Long, narrow all-light atom guide,” Opt. Lett. 24, 1805–1807 (1999). [CrossRef]
  22. D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11, 2747–2752 (2003). [CrossRef]
  23. Z. Wang, Y. Dong, and Q. Lin, “Atomic trapping and guiding by quasi-dark hollow beams,” J. Opt. A 7, 147–153 (2005). [CrossRef]
  24. Z. Liu, H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, “Generation of hollow Gaussian beams by spatial filtering,” Opt. Lett. 32, 2076–2078 (2007). [CrossRef]
  25. A. Calatayud, V. Ferrando, L. Remón, W. D. Furlan, and J. A. Monsoriu, “Twin axial vortices generated by Fibonacci lenses,” Opt. Express 21, 10234–10239 (2013). [CrossRef]
  26. A. Ortiz-Ambriz, S. Lopez-Aguayo, Y. V. Kartashov, V. A. Vysloukh, D. Petrov, H. Garcia-Gracia, J. C. Gutiérrez-Vega, and L. Torner, “Generation of arbitrary complex quasi-non-diffracting optical patterns,” Opt. Express 21, 22221–22231 (2013). [CrossRef]
  27. Q. Zhan, “Properties of circularly polarized vortex beams,” Opt. Lett. 31, 867–869 (2006). [CrossRef]
  28. S. N. Khonina, N. L. Kazanskiy, and S. G. Volotovsky, “Vortex phase transmission function as a factor to reduce the focal spot of high-aperture focusing system,” J. Mod. Opt. 58, 748–760 (2011). [CrossRef]
  29. L. Rao, J. Pu, Z. Chen, and P. Yei, “Focus shaping of cylindrically polarized vortex beams by a high numerical-aperture lens,” Opt. Laser Technol. 41, 241–246 (2009). [CrossRef]
  30. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358–379 (1959). [CrossRef]
  31. S. N. Khonina and S. G. Volotovsky, “Controlling the contribution of the electric field components to the focus of a high-aperture lens using binary phase structures,” J. Opt. Soc. Am. A 27, 2188–2197 (2010). [CrossRef]
  32. S. F. Pereira and A. S. van de Nes, “Superresolution by means of polarisation, phase and amplitude pupil masks,” Opt. Commun. 234, 119–124 (2004). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited