Abstract

The focal intensity distribution of strongly focused (NA=0.9) first-order Laguerre-Gaussian doughnut beams is investigated experimentally for three different polarizations: linear, and left-handed circular and right-handed circular. The investigations are done by 2-dimensional scanning the focal plane with of a 100nm diameter fluorescent microbead, and measuring the fluorescence signal. The results are shown to be in excellent agreement with theoretical predictions, and demonstrate the superiority of one of the circular polarizations to achieve a sharp dark central spot.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, "Novel optical trap of atoms with a doughnut beam," Phys. Rev. Lett. 78, 4714 (1997).
    [CrossRef]
  2. J. Yin and Y. Zhu, "LP01-mode output beam from a micro-sized hollow optical fiber: a simple theoretical model and its applications in atom optics," J. Appl. Phys. 85, 2473 (1999).
    [CrossRef]
  3. S. W. Hell and J. Wichmann, "Breaking the diffraction resolution limit by stimulated emission: stimulated-emission- depletion fluorescence microscopy," Opt. Lett. 19, 780 (1994).
    [CrossRef] [PubMed]
  4. V. Westphal, J. Seeger, T. Salditt, and S. W. Hell, "Stimulated emission depletion microscopy on lithographic nanostructures," J. Phys. B 38, S695 (2005).
    [CrossRef]
  5. T. Watanabe, Y. Iketaki, T. Omatsu, K. Yamamoto, M. Sakai, and M. Fujii, "Two-point-separation in super-resolution fluorescence microscope based on up-conversion fluorescence depletion technique," Opt. Express 11, 3271 (2003).
    [CrossRef] [PubMed]
  6. Y. Iketaki, T. Watanabe, M. Sakai, Sh. 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. 44, 033602 (2005).
    [CrossRef]
  7. L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912 (2001).
    [CrossRef] [PubMed]
  8. 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 (2003).
    [CrossRef] [PubMed]
  9. P. Török and P. R. T. Munro, "The use of Gauss-Laguerre vector beams in STED microscopy," Opt. Express 12, 3605 (200).
    [CrossRef]
  10. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. Royal Soc. A 253, 358 (1959).
    [CrossRef]
  11. N. Davidson and N. Bokor, "High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens," Opt. Lett. 29, 1318 (2004).
    [CrossRef] [PubMed]
  12. N. Bokor and N. Davidson, "Toward a spherical spot distribution with 4π focusing of radially polarized light," Opt. Lett. 29, 1968 (2004).
    [CrossRef] [PubMed]
  13. R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  14. R. Oron, J. L. Guedalia, N. Davidson, A. A. Friesem, and E. Hasman, "Anomaly in a high-numericalaperture diffractive focusing lens," Opt. Lett. 25, 439 (2000).
    [CrossRef]
  15. Y. Iketaki, Y. Horikawa, Sh. Mochimaru, K. Nagai, M. Atsumi, H. Kamijou, and M. Shibuya, "Evaluation of the optical characteristics of the Schwarzschild x-ray objective," Opt. Lett. 19, 1804 (1994).
    [CrossRef] [PubMed]
  16. T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131 (2004).
    [CrossRef]
  17. M. P. Rimmer, and J. C. Wyant, "Evaluation of large aberrations using a lateral-shear interferometer having variable shear," Appl. Opt. 14, 142 (1975).
    [PubMed]

Appl. Opt.

J. Appl. Phys.

J. Yin and Y. Zhu, "LP01-mode output beam from a micro-sized hollow optical fiber: a simple theoretical model and its applications in atom optics," J. Appl. Phys. 85, 2473 (1999).
[CrossRef]

J. Phys. B

V. Westphal, J. Seeger, T. Salditt, and S. W. Hell, "Stimulated emission depletion microscopy on lithographic nanostructures," J. Phys. B 38, S695 (2005).
[CrossRef]

Opt. Eng.

Y. Iketaki, T. Watanabe, M. Sakai, Sh. 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. 44, 033602 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, "Novel optical trap of atoms with a doughnut beam," Phys. Rev. Lett. 78, 4714 (1997).
[CrossRef]

Proc. Royal Soc. A

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. Royal Soc. A 253, 358 (1959).
[CrossRef]

Rev. Sci. Instrum.

T. Watanabe, M. Fujii, Y. Watanabe, N. Toyama, and Y. Iketaki, "Generation of a doughnut-shaped beam using a spiral phase plate," Rev. Sci. Instrum. 75, 5131 (2004).
[CrossRef]

Science

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912 (2001).
[CrossRef] [PubMed]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Experimental setup for measuring the intensity distribution of high-NA first-order Laguerre Gaussian doughnut beams in the focal plane. The helical phase is added to the beam by a spiral phase plate (SPP), and the proper polarization state is created with a quarter-wave-plate (QWP). After reflection from a beam splitter (BS) the beam is focused by a high-NA microscope objective (MO) onto a 100nm diameter fluorescent microbead (FMB) placed on a 2D scanning stage (SS). The dye molecules in the microbead are excited to a fluorescent state by the incoming light (continuous arrows). The reflected fluorescence signal (dashed arrows) passes through a focusing lens (L), a holographic notch filter (HNF) and is detected by a photomultiplier tube (PMT). The aberrations of the illuminating pump beam are measured separately, using a movable mirror (MM) and a Shack-Hartmann sensor (SH).

Fig. 2.
Fig. 2.

Schematic representation of the local electric field vectors (shown with arrow-heads) for first-order Laguerre-Gaussian beams having (a) linear, (b) left-handed circular (LC), and (c) right-handed circular (RC) polarizations. At the top of the Fig., the corresponding orientation of the fast axis (FA) of the QWP is shown for the three cases. The original polarization of the laser is along x.

Fig. 3.
Fig. 3.

Calculated intensity contour maps in the focal plane, and corresponding calculated intensity cross sections along the x and y axis (red and blue curves, respectively), for the (a) linear, (b) LC, and (c) RC polarization case, predicting very large polarization dependence of the intensity distribution. Only the LC polarization case is expected to yield zero intensity in the geometrical focus.

Fig. 4.
Fig. 4.

Measured intensity contour maps in the focal plane, and corresponding intensity cross sections along the x and y axis (red and blue curves, respectively, obtained by averaging the central 5 rows/columns of the corresponding intensity contour maps), for the (a) linear, (b) LC, and (c) RC polarization. The drastically different behaviour of the three polarizations is clearly demonstrated. Also apparent are the excellent properties of the LC polarized beam in achieving a very tightly focused spot with a dark center.

Fig. 5.
Fig. 5.

Calculated intensity contour maps in the focal plane for the (a) linear, (b) LC, and (c) RC polarization case. The numerical calculations include the measured wavefront aberrations of the beams before focusing, the measured aberration of the MO, and convolution with a 120nm diameter circular step function (approximating the combined effect of the finite fluorescent bead size, and the finite pixel size of the measured data). Comparison with Fig. 3 (ideal case) shows that the tilted, asymmetrical nature of the measured intensity distributions and the slight increase in their spot size (see Fig. 4) are satisfactorily accounted for with the refined calculations.

Tables (1)

Tables Icon

Table 1. Numerical values of the central intensity relative to the maximum intensity (in %), of the intensity profiles of Figs. 3 and 4

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

E r 2 ψ z 2 = i λ Ω A 1 ( θ , φ ) A 2 ( θ ) A 3 ( θ , φ ) exp ( itφ ) exp [ ik r 2 sin θ cos ( φ ψ ) ]
exp ( ik z 2 cos θ ) a ( θ , φ ) sin θ ,

Metrics