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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 4 — Apr. 1, 1998
  • pp: 884–899

Airy pattern reorganization and subwavelength structure in a focus

G. P. Karman, M. W. Beijersbergen, A. van Duijl, D. Bouwmeester, and J. P. Woerdman  »View Author Affiliations


JOSA A, Vol. 15, Issue 4, pp. 884-899 (1998)
http://dx.doi.org/10.1364/JOSAA.15.000884


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Abstract

An early result of optical focusing theory is the Lommel field, resulting from a uniformly illuminated lens; the dark rings in the focal plane, the Airy rings, have been recognized as phase singularities. On the other hand, it is well known that Gaussian illumination leads to a Gaussian beam in the focal region without phase singularities. We report a theoretical and experimental study of the transition between the two cases. Theoretically, we studied this transition both within and outside the paraxial limit by means of diffraction theory. We show that in the gradual transition from uniform toward Gaussian illumination, the Airy rings reorganize themselves by means of a creation/annihilation process of the singularities. The most pronounced effect is the occurrence of extra dark rings (phase singularities) in front of and behind the focal plane. We demonstrate theoretically that one can bring these rings arbitrarily close together, thus leading to structures on a scale arbitrarily smaller than 1 wavelength, although at low intensities. Experimentally, we have studied the consequences of the reorganization process in the paraxial limit at optical wavelengths. To this end, we developed a technique to measure the three-dimensional intensity (3D) distribution of a focal field. We applied this technique in the study of truncated Gaussian beams; the experimentally obtained 3D intensity distributions confirm the existence and the reorganization of extra dark rings outside the focal plane.

© 1998 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(220.2560) Optical design and fabrication : Propagating methods

History
Original Manuscript: July 21, 1997
Revised Manuscript: October 15, 1997
Manuscript Accepted: October 20, 1997
Published: April 1, 1998

Citation
G. P. Karman, M. W. Beijersbergen, A. van Duijl, D. Bouwmeester, and J. P. Woerdman, "Airy pattern reorganization and subwavelength structure in a focus," J. Opt. Soc. Am. A 15, 884-899 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-4-884


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References

  1. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1986).
  2. A. Boivin, J. Dow, E. Wolf, “Energy flow in the neighborhood of the focus of a coherent beam,” J. Opt. Soc. Am. 57, 1171–1175 (1967). [CrossRef]
  3. I. V. Basistiy, M. S. Soskin, M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995). [CrossRef]
  4. J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974). [CrossRef]
  5. M. Berry, “Singularities in waves and rays,” in Physics of Defects, R. Balian, M. Kléman, J.-P. Poirier, eds. (North-Holland, Amsterdam, 1981).
  6. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  7. J. J. Stamnes, Waves in Focal Regions (Institute of Physics, Bristol, UK, 1986).
  8. M. W. Beijersbergen, “Phase singularities in optical beams,” Ph.D. thesis (Leiden University, The Netherlands, 1996).
  9. G. P. Karman, A. van Duijl, M. W. Beijersbergen, J. P. Woerdman, “Creation and annihilation of phase singularities in a focal field,” Opt. Lett. 22, 1503–1505 (1997). [CrossRef]
  10. G. P. Karman, A. van Duijl, M. W. Beijersbergen, J. P. Woerdman, “Measurement of the 3D intensity distribution in the neighbourhood of a paraxial focus,” Appl. Opt. 36, 8091–8095 (1997). [CrossRef]
  11. E. Wolf, Y. Li, “Conditions for the validity of the Debye integral representation of focused fields,” Opt. Commun. 39, 205–210 (1981). [CrossRef]
  12. E. Collett, E. Wolf, “Symmetry properties of focused fields,” Opt. Lett. 5, 264–266 (1980). [CrossRef] [PubMed]
  13. I. Freund, N. Shvartsman, “Wave-field phase singularities: the sign-principle,” Phys. Rev. A 50, 5164–5172 (1994). [CrossRef] [PubMed]
  14. P. Jacquinot, B. Roizen-Dossier, “Apodization,” in Progress in Optics III, E. Wolf, ed. (North-Holland, Amsterdam, 1964).
  15. J. F. Nye, J. V. Hajnal, J. H. Hannay, “Phase saddles and dislocations in two-dimensional waves such as the tides,” Proc. R. Soc. London, Ser. A 417, 7–20 (1988). [CrossRef]
  16. I. Freund, “Saddles, singularities, and extreme in random phase fields,” Phys. Rev. E 52, 2348–2360 (1995). [CrossRef]
  17. M. V. Berry, “Evanescent and real waves in quantum billiards and Gaussian beams,” J. Phys. A 27, L391 (1994). [CrossRef]
  18. T. D. Visser, S. H. Wiersma, “Spherical aberration and the electromagnetic field in high-aperture systems,” J. Opt. Soc. Am. A 8, 1404–1410 (1991). [CrossRef]
  19. T. D. Visser, S. H. Wiersma, “Diffraction of converging electromagnetic waves,” J. Opt. Soc. Am. A 9, 2034–2047 (1992). [CrossRef]
  20. W. L. Erikson, S. Singh, “Polarization properties of Maxwell–Gaussian laser beams,” Phys. Rev. E 49, 5778–5786 (1994). [CrossRef]
  21. J. F. Nye, “Polarization effects in the diffraction of electromagnetic waves: the role of disclinations,” Proc. R. Soc. London, Ser. A 387, 105–132 (1983). [CrossRef]
  22. M. V. Berry, “Faster than Fourier,” in Quantum Coherence and Reality, J. S. Anandan, J. L. Safko, eds. (World Scientific, Singapore, 1994), pp. 55–65.
  23. W. P. Ambrose, P. M. Goodwin, J. C. Martin, R. A. Keller, “Single molecule detection and photochemistry on a surface using near-field optical excitation,” Phys. Rev. Lett. 72, 160–163 (1994). [CrossRef] [PubMed]
  24. Y. Li, E. Wolf, “Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers,” J. Opt. Soc. Am. A 1, 801–808 (1984). [CrossRef]
  25. J. J. Stamnes, B. Spjelkavik, “Focusing at small angular apertures in the Debye and Kirchhoff approximations,” Opt. Commun. 40, 81–85 (1981). [CrossRef]
  26. M. Totzeck, H. J. Tiziani, “Phase singularities in 2D diffraction fields and interference microscopy,” Opt. Commun. 138, 365–382 (1997). [CrossRef]

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