Abstract

We examine the effects of tightly focusing a radially polarized beam with uniform, Gaussian, or Bessel–Gauss pupil functions. The resulting FWHM is smallest for the case of a uniform amplitude profile, while the Bessel–Gauss beam results in the largest FWHM. The uniform amplitude profile also results in an axial field component that increases fastest with increasing NA. The ratio of the axial component to the transverse component is also the greatest for the uniform pupil function. On the other hand, the Bessel–Gauss beam benefits the most from the use of an annulus.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
    [CrossRef]
  2. B. Sick, B. Hecht, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
    [CrossRef] [PubMed]
  3. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001).
    [CrossRef] [PubMed]
  4. K. Yoshiki, M. Hashimoto, and T. Araki, Opt. Lett. 32, 1680 (2007).
    [CrossRef] [PubMed]
  5. D. P. Biss and T. G. Brown, Opt. Lett. 28, 923 (2003).
    [CrossRef] [PubMed]
  6. E. Y. S. Yew and C. J. R. Sheppard, Opt. Commun. 275, 453 (2007).
    [CrossRef]
  7. D. P. Biss, K. S. Youngworth, and T. G. Brown, Appl. Opt. 45, 470 (2006).
    [CrossRef] [PubMed]
  8. S. C. Tidwell, D. H. Ford, and W. D. Kimura, Appl. Opt. 29, 2234 (1990).
    [CrossRef] [PubMed]
  9. K. Youngworth and T. Brown, Opt. Express 7, 77 (2000).
    [CrossRef] [PubMed]
  10. R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  11. J. A. Davis, D. E. McNamara, D. M. Cottrell, and T. Sonehara, Appl. Opt. 39, 1549 (2000).
    [CrossRef]
  12. M. Stalder and M. Schadt, Opt. Lett. 21, 1948 (1996).
    [CrossRef] [PubMed]
  13. D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
    [CrossRef]
  14. B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
    [CrossRef]
  15. D. G. Hall, Opt. Lett. 21, 9 (1996).
    [CrossRef] [PubMed]
  16. P. L. Greene and D. G. Hall, J. Opt. Soc. Am. A 13, 962 (1996).
    [CrossRef]
  17. A. van de Nes, P. Munro, S. Pereira, J. Braat, and P. Török, Opt. Express 12, 967 (2004).
    [CrossRef] [PubMed]

2007 (2)

K. Yoshiki, M. Hashimoto, and T. Araki, Opt. Lett. 32, 1680 (2007).
[CrossRef] [PubMed]

E. Y. S. Yew and C. J. R. Sheppard, Opt. Commun. 275, 453 (2007).
[CrossRef]

2006 (1)

2004 (1)

2003 (2)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

D. P. Biss and T. G. Brown, Opt. Lett. 28, 923 (2003).
[CrossRef] [PubMed]

2001 (1)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

2000 (4)

K. Youngworth and T. Brown, Opt. Express 7, 77 (2000).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

B. Sick, B. Hecht, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
[CrossRef] [PubMed]

J. A. Davis, D. E. McNamara, D. M. Cottrell, and T. Sonehara, Appl. Opt. 39, 1549 (2000).
[CrossRef]

1996 (3)

1990 (1)

1972 (1)

D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

E. Y. S. Yew and C. J. R. Sheppard, Opt. Commun. 275, 453 (2007).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. Lett. (3)

B. Sick, B. Hecht, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
[CrossRef] [PubMed]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A (1)

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

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 (4)

Fig. 1
Fig. 1

Schematic of a plane polarized beam with a Gaussian (left inset) profile passing through a mode-converter to result in a radially polarized beam, or a with a BG (right inset) profile. Plot, a Gaussian and BG beam sharing the same 1 e 2 value.

Fig. 2
Fig. 2

Ratios of the peak axial and transverse components for uniform, Gaussian, and BG illumination. Uniform illumination results in the greatest ratio ( 3.3 × ) . The Gaussian ( 2 × ) and BG ( 1.75 × ) beams are comparable.

Fig. 3
Fig. 3

Normalized intensity profile of the total intensity in the focal plane. Uniform illumination gives the smallest spot size in terms of FWHM (normalized to λ), while the BG beam gives the broadest.

Fig. 4
Fig. 4

Spot size as measured with the FWHM (normalized to λ) for the three types of beam with an increasing annulus. The BG beam gains the most from the presence of an annulus, but the uniform beam still has the smallest spot size. The resolution for circularly polarized light with a uniform or Gaussian pupil function does not increase greatly with an annulus.

Equations (4)

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

E ρ ( ρ , z ) = A α 1 α 2 P ( θ ) cos 1 2 θ sin 2 θ J 1 ( k ρ sin θ ) exp [ 2 i k z sin θ ] d θ ,
E z ( ρ , z ) = 2 i A α 1 α 2 P ( θ ) cos 1 2 θ sin 2 θ J 0 ( k ρ sin θ ) exp [ 2 i k z sin θ ] d θ ,
P ( θ ) = J 1 ( 2 β 1 sin θ sin α 2 ) exp [ ( β 2 sin θ sin α 2 ) 2 ] .
P ( θ ) = exp [ ( β 3 sin θ sin α 2 ) 2 ] .

Metrics