OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 6 — Jun. 1, 2008
  • pp: 1307–1318

Effect of primary spherical aberration on high-numerical-aperture focusing of a Laguerre–Gaussian beam

Rakesh Kumar Singh, P. Senthilkumaran, and Kehar Singh  »View Author Affiliations

JOSA A, Vol. 25, Issue 6, pp. 1307-1318 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (1591 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Effect of primary spherical aberration on the tight focusing of linearly and circularly polarized Laguerre–Gaussian (LG) beams is studied by using the vectorial Debye integral. Results are presented for the intensity distribution and square of the polarization components. In the case of the linearly polarized LG beam with unit and double topological charge, the presence of aberration reduces the residual intensity at the focal point and spreads the sidelobes. If the beam is circularly polarized, the aberration results in an increase in the size of the dark core along with a reduction in the intensity at the periphery of the bright ring. The effect of aberration is also discussed in the context of the fluorescent spot size in the focal plane of a stimulated-emission-depletion microscope.

© 2008 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(170.2520) Medical optics and biotechnology : Fluorescence microscopy
(260.5430) Physical optics : Polarization
(080.4865) Geometric optics : Optical vortices

ToC Category:
Lasers and Laser Optics

Original Manuscript: January 17, 2008
Manuscript Accepted: March 14, 2008
Published: May 14, 2008

Virtual Issues
Vol. 3, Iss. 7 Virtual Journal for Biomedical Optics

Rakesh Kumar Singh, P. Senthilkumaran, and Kehar Singh, "Effect of primary spherical aberration on high-numerical-aperture focusing of a Laguerre-Gaussian beam," J. Opt. Soc. Am. A 25, 1307-1318 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. London, Ser. A 253, 349-357 (1959). [CrossRef]
  2. 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. A 253, 358-379 (1959). [CrossRef]
  3. A. Yoshida and T. Asakura, “Electromagnetic field near the focus of Gaussian beams,” Optik (Stuttgart) 41, 281-292 (1974).
  4. A. Yoshida and T. Asakura, “Electromagnetic field in the focal plane of a coherent beam from a wide-angular annular-aperture system,” Optik (Stuttgart) 40, 322-331 (1974).
  5. C. J. R. Sheppard and H. J. Matthews, “Imaging in a high aperture optical systems,” J. Opt. Soc. Am. A 4, 1354-1360 (1987). [CrossRef]
  6. R. Kant, “An analytical solution of vector diffraction for focusing optical systems,” J. Mod. Opt. 40, 337-347 (1993). [CrossRef]
  7. C. J. R. Sheppard, “High aperture beams,” J. Opt. Soc. Am. A 18, 1579-1587 (2001). [CrossRef]
  8. J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81, 1576-1578 (2002). [CrossRef]
  9. L. E. Helseth, “Smallest focal hole,” Opt. Commun. 257, 1-8 (2006). [CrossRef]
  10. N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485-2492 (1996). [CrossRef]
  11. K. T. Gahagan and G. A. Swartzlander, Jr., “Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap,” J. Opt. Soc. Am. B 16, 533-537 (1999). [CrossRef]
  12. G. D. M. Jeffries, J. S. Edgar, Y. Zhao, J. P. Shelby, C. Fong, and D. T. Chiu, “Using polarization-shaped optical vortex traps for single-cell nanosurgery,” Nano Lett. 7, 415-420 (2007). [CrossRef] [PubMed]
  13. Y. Iketaki, T. Watanabe, M. Sakai, S.-I. Ishiuchi, M. Fujii, and T. Watanabe, “Theoretical investigation of the point-spread function given by super-resolving fluorescence microscopy using two-color fluorescence dip spectroscopy,” Opt. Eng. (Bellingham) 44, 033602-033602/9 (2005). [CrossRef]
  14. P. Torok and P. R. T. Munro, “The use of Gauss-Laguerre vector beams in STED microscopy,” Opt. Express 12, 3605-3617 (2004). [CrossRef] [PubMed]
  15. N. Bokor, Y. Iketaki, T. Watanabe, and M. Fujii, “Investigation of polarization effects for high numerical-aperture first order Laguerre-Gaussian beams by 2D scanning with a single fluorescent microbead,” Opt. Express 13, 10440-10447 (2005). [CrossRef] [PubMed]
  16. K. I. Willig, J. Keller, M. Bossi, and S. W. Hell, “STED microscopy resolves nanoparticle assemblies,” New J. Phys. 8, 106/1-8 (2006). [CrossRef]
  17. N. Bokor, Y. Iketaki, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272, 263-268 (2007). [CrossRef]
  18. A. E. Siegman, Lasers (Oxford U. Press, 1986).
  19. H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312-1329 (1966). [CrossRef]
  20. L.Allen, S.M.Barnett, and M.J.Padgett, eds., Optical Angular Momentum (Bristol: Institute of Physics, 2003). [CrossRef]
  21. Y. Iketaki, T. Watanabe, N. Bokor, and M. Fujii, “Investigation of the center intensity of first- and second-order Laguerre-Gaussian beams with linear and circular polarization,” Opt. Lett. 32, 2357-2359 (2007). [CrossRef] [PubMed]
  22. Y. Roichman, A. Waldron, E. Gardel, and D. G. Grier, “Optical traps with geometrical aberrations,” Appl. Opt. 45, 3425-3429 (2006). [CrossRef] [PubMed]
  23. Y. Unno, T. Ebihara, and M. D. Levenson, “Impact of mask errors and lens aberrations on the image formation of a vortex mask,” J. Microlithogr., Microfabr., Microsyst. 4, 023006-023017 (2005). [CrossRef]
  24. T. D. Visser and S. H. Wiersma, “Spherical aberration and the electromagnetic field in high-aperture systems,” J. Opt. Soc. Am. A 8, 1404-1410 (1991). [CrossRef]
  25. R. Kant, “An analytical solution of vector diffraction for focusing optical systems with Seidel aberrations. I. Spherical aberration, curvature of field, and distortion,” J. Mod. Opt. 40, 2293-2310 (1993). [CrossRef]
  26. D. P. Biss and T. G. Brown, “Primary aberrations in focused radially polarized vortex beams,” Opt. Express 12, 384-393 (2004). [CrossRef] [PubMed]
  27. R. K. Singh, P. Senthilkumaran, and K. Singh, “Focusing of vortex carrying beam with Gaussian background by a lens in the presence of spherical aberration and defocusing,” Opt. Lasers Eng. 45, 773-782 (2007). [CrossRef]
  28. S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81, 597-600 (2005). [CrossRef]
  29. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780-782 (1994). [CrossRef] [PubMed]
  30. T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe's diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066613 (2001). [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