Abstract

We report on, in this letter, a phenomenon that the central zero-intensity point of a doughnut beam, caused by phase singularity, disappears in the focus, when such a beam is focused by a high numerical-aperture objective in free space. In addition, the focal shape of the doughnut beam of a given topological charge exhibits the increased ring intensity in the direction orthogonal to the incident polarization state and an elongation in the polarization direction. These phenomena are caused by the effect of depolarization, associated with a high numerical-aperture objective, and become pronounced by the use of a central obstruction in the objective aperture.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. A. Ashkin, �??Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,�?? Biophys. J. 61, 569-581 (1992).
    [CrossRef] [PubMed]
  2. A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, �??Single-molecule biomechanics with optical methods,�?? Science 283, 1689-1695 (1999).
    [CrossRef] [PubMed]
  3. K. T. Gahagan and G. A. Swartzlander Jr., �??Optical vortex trapping of particles,�?? Opt. Lett. 21, 827-829 (1996).
    [CrossRef] [PubMed]
  4. M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, K. Dholakia, �??Creation and manipulation of three-dimensional optically trapped structures,�?? Science, 296, 1101-1103 (2002).
    [CrossRef]
  5. L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, �??Controlled rotation of optically trapped microscopic particles,�?? Science 292, 912-914 (2001).
    [CrossRef] [PubMed]
  6. M. Dyba and S. W. Hell, �??Focal spots of size λ/23 open up far-field florescence microscopy at 33 nm axial resolution,�?? Phys. Rev. Lett. 88, 163901-1-4 (2002).
    [CrossRef] [PubMed]
  7. D. McGloin, V. Garcés-Chávez, and K. Dholakia, �??Interfering Bessel beams for optical micromanipulation,�?? Opt. Lett. 28, 657-659 (2003).
    [CrossRef] [PubMed]
  8. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, �??Hellical-wavefront laser beam produced with a spiral phase plate,�?? Opt. Commun. 112, 321-327 (1994).
    [CrossRef]
  9. D. Ganic, X. Gan, and M. Gu, �??Generation of doughnut laser beams by use of a liquid-crystal cell with a conversion efficiency near 100%,�?? Opt. Lett. 27, 1351-1353 (2002).
    [CrossRef]
  10. Y. Shin, K. Kim, J. A. Kim, H. R. Noh, W. Jhe, K. Oh, and U. C. Pack, �??Diffraction-limited dark laser spot produced by a hollow optical fiber,�?? Opt. Lett. 26, 119-121 (2001).
    [CrossRef]
  11. N. R. Heckenberg, R. G. Mcduff, C. P. Smith, and A. G. White, �??Generation of optical phase singularities by computer-generated holograms,�?? Opt. Lett. 17, 221-223 (1992).
    [CrossRef] [PubMed]
  12. M. Gu, Advanced Optical Imaging Theory (Springer, Heidelberg, 2000).
  13. B. Richards, and E. Wolf, �??Electromagnetic diffraction in optical systems, II. Structure of the image in an aplanatic system,�?? Proc. Royal Soc. A. 253 (1959) 358-379.
    [CrossRef]
  14. 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]
  15. H. C. Kim, and Y. H. Lee, �??Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation,�?? Opt. Commun. 169, 9-16 (1999).
    [CrossRef]
  16. A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, �??The structure of a nonparaxial Gaussian beam near the focus: II. Optical vortices,�?? Opt. Spectrosc. 90, 93-100 (2001).
    [CrossRef]

Appl. Phys. Lett. (1)

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]

Biophys. J. (1)

A. Ashkin, �??Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,�?? Biophys. J. 61, 569-581 (1992).
[CrossRef] [PubMed]

Opt. Commun. (2)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, �??Hellical-wavefront laser beam produced with a spiral phase plate,�?? Opt. Commun. 112, 321-327 (1994).
[CrossRef]

H. C. Kim, and Y. H. Lee, �??Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation,�?? Opt. Commun. 169, 9-16 (1999).
[CrossRef]

Opt. Lett. (5)

Opt. Spectrosc. (1)

A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, �??The structure of a nonparaxial Gaussian beam near the focus: II. Optical vortices,�?? Opt. Spectrosc. 90, 93-100 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

M. Dyba and S. W. Hell, �??Focal spots of size λ/23 open up far-field florescence microscopy at 33 nm axial resolution,�?? Phys. Rev. Lett. 88, 163901-1-4 (2002).
[CrossRef] [PubMed]

Proc. Royal Soc. A. (1)

B. Richards, and E. Wolf, �??Electromagnetic diffraction in optical systems, II. Structure of the image in an aplanatic system,�?? Proc. Royal Soc. A. 253 (1959) 358-379.
[CrossRef]

Science (3)

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, K. Dholakia, �??Creation and manipulation of three-dimensional optically trapped structures,�?? Science, 296, 1101-1103 (2002).
[CrossRef]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, �??Controlled rotation of optically trapped microscopic particles,�?? Science 292, 912-914 (2001).
[CrossRef] [PubMed]

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, �??Single-molecule biomechanics with optical methods,�?? Science 283, 1689-1695 (1999).
[CrossRef] [PubMed]

Other (1)

M. Gu, Advanced Optical Imaging Theory (Springer, Heidelberg, 2000).

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.

Calculated intensity distribution in the focal region of a doughnut beam focused by an objective with NA=1 ((a)–(c)) and NA=0.2 ((d)–(f)): (a) and (d) Topological charge 1; (b) and (e) Topological charge 2; (c) and (f) Topological charge 3.

Fig. 2.
Fig. 2.

Contour plots of the intensity distribution in the focal region of an objective with NA=1, illuminated by a doughnut beam of topological charge 1. (a) |Ex |2; (b) |Ey |2; (c)|Ez |2; (d) |E| 2.

Fig. 3.
Fig. 3.

Contour plots of the intensity distribution in the focal region of an objective with NA=1, illuminated by a doughnut beam of topological charge 2. (a) |Ex |2; (b) |Ey |2; (c) |Ez |2; (d) |E| 2.

Fig. 4.
Fig. 4.

Contour plots of the intensity distribution in the focal region of an objective with NA=1, illuminated by a doughnut beam of topological charge 3. (a) |Ex |2; (b) |Ey |2; (c) |Ez |2; (d) |E| 2.

Fig. 5.
Fig. 5.

Dependence of the peak ratio of |Ez |2/ |Ex |2 on the numerical aperture (a) and on the obstruction radius ε (b).

Equations (3)

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

E ( r 2 , ψ , z 2 ) = i λ Ω cos θ exp ( in φ ) exp [ i k r 2 sin θ cos ( φ ψ ) ] exp ( i k z 2 cos θ )
{ [ cos θ + sin 2 φ ( 1 cos θ ) ] i + cos φ sin φ ( cos θ 1 ) j + cos φ sin θ k }
sin θd θd φ

Metrics