OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 11 — Nov. 1, 2012
  • pp: 2439–2443

Focusing of higher-order radially polarized Laguerre–Gaussian beam

Yuichi Kozawa and Shunichi Sato  »View Author Affiliations

JOSA A, Vol. 29, Issue 11, pp. 2439-2443 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (340 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We consider the formation of a small focal spot, which has been reported in [J. Opt. Soc. Am. A 24, 1793 (2007)], by separating a higher-order radially polarized Laguerre–Gaussian beam into two parts: a Bessel-like multi-ring part and an annular part. The latter forms a dominant small spot of longitudinal electric field component near the focus, while the former mainly contributes to a weak annular pattern of radial component.

© 2012 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(140.3300) Lasers and laser optics : Laser beam shaping
(260.3160) Physical optics : Interference
(260.5430) Physical optics : Polarization

ToC Category:
Physical Optics

Original Manuscript: August 22, 2012
Revised Manuscript: October 1, 2012
Manuscript Accepted: October 4, 2012
Published: October 22, 2012

Yuichi Kozawa and Shunichi Sato, "Focusing of higher-order radially polarized Laguerre–Gaussian beam," J. Opt. Soc. Am. A 29, 2439-2443 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. Quabis, R. Dorn, M. Everler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000). [CrossRef]
  2. C. J. R. Sheppard, and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43, 4322–4327 (2004). [CrossRef]
  3. T. Grosjean and D. Courjon, “Smallest focal spots,” Opt. Commun. 272, 314–319 (2007). [CrossRef]
  4. G. M. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16, 4567–4581 (2008). [CrossRef]
  5. K. Kitamura, K. Sakai, and S. Noda, “Sub-wavelength focal spot with long depth of focus generated by radially polarized, narrow-width annular beam,” Opt. Express 18, 4518–4525 (2010). [CrossRef]
  6. H. Dehez, A. April, and M. Piché, “Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent,” Opt. Express 20, 14891–14905 (2012). [CrossRef]
  7. J. W. Strutt, “On the diffraction of object-glasses,” Mon. Not. R. Astron. Soc. 33, 59–63 (1872).
  8. L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun. 191, 161–172 (2001). [CrossRef]
  9. C. C. Sun and C. K. Liu, “Ultrasmall focusing spot with a long depth of focus based on polarization and phase modulation,” Opt. Lett. 28, 99–101 (2003). [CrossRef]
  10. H. Wang, L. Shi, B. Lukyanchuk, 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]
  11. Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24, 1793–1798 (2007). [CrossRef]
  12. Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 19, 15947–15954 (2011). [CrossRef]
  13. A. A. Tovar, “Production and propagation of cylindrically polarized Laguerre–Gaussian laser beams,” J. Opt. Soc. Am. A 15, 2705–2711 (1998). [CrossRef]
  14. Y. Kozawa and S. Sato, “Demonstration and selection of a single-transverse higher-order-mode beam with radial polarization,” J. Opt. Soc. Am. A 27, 399–403 (2010). [CrossRef]
  15. A. Ito, Y. Kozawa, and S. Sato, “Generation of hollow scalar and vector beams using a spot-defect mirror,” J. Opt. Soc. Am. A 27, 2072–2077 (2010). [CrossRef]
  16. M. A. Porras, R. Borghi, and M. Santarsiero, “Relationship between elegant Laguerre–Gauss and Bessel–Gauss beams,” J. Opt. Soc. Am. A 18, 177–184 (2001). [CrossRef]
  17. M. Alfaro, J. J. Moreno-Balcázar, and M. L. Rezola, “Laguerre–Sobolev orthogonal polynomials: asymptotics for coherent pairs of type II,” J. Approx. Theory 122, 79–96 (2003). [CrossRef]
  18. A. Flores-Pérez, J. Hernández-Hernández, R. Jáuregui, and K. Volke-Sepúlveda, “Experimental generation and analysis of first-order TE and TM Bessel modes in free space,” Opt. Lett. 31, 1732–1734 (2006). [CrossRef]
  19. R. Horák, Z. Bouchal, and J. Bajer, “Nondiffracting stationary electromagnetic field,” Opt. Commun. 133, 315–327 (1997). [CrossRef]
  20. 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]
  21. B. Lü, W. Huang, and B. Zhang, “Fraunhofer diffraction of a Bessel beam focused by an aperture lens,” Opt. Commun. 119, 6–12 (1995). [CrossRef]
  22. A. Erdélyi, ed., Tables of Integral Transforms (McGraw-Hill, 1954), Vol. 1.
  23. S. Vyas, Y. Kozawa, and S. Sato, “Self-healing of tightly focused scalar and vector Bessel–Gauss beams at the focal plane,” J. Opt. Soc. Am. A 28, 837–843 (2011). [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.


Fig. 1. Fig. 2. Fig. 3.
Fig. 4.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited