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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 7 — Mar. 29, 2010
  • pp: 7108–7120

Gouy phase shift in nondiffracting Bessel beams

Paolo Martelli, Matteo Tacca, Alberto Gatto, Giorgio Moneta, and Mario Martinelli  »View Author Affiliations

Optics Express, Vol. 18, Issue 7, pp. 7108-7120 (2010)

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The results of a theoretical and experimental investigation of the Gouy effect in Bessel beams are presented. We point out that the peculiar feature of the Bessel beams of being nondiffracting is related to the accumulation of an extra axial phase shift (i.e., the Gouy phase shift) linearly dependent on the propagation distance. The constant spatial rate of variation of the Gouy phase shift is independent of the order of the Bessel beam, while it is a growing function of the transverse component of the angular spectrum wave-vectors, originated by the transverse confinement of the beam. A free-space Mach-Zehnder interferometer has been set-up for measuring the transverse intensity distribution of the interference between holographically-produced finite-aperture Bessel beams of order from zero up to three and a reference Gaussian beam, at a wavelength of 633 nm. The interference patterns have been registered for different propagation distances and show a spatial periodicity, in agreement with the expected period due to the linear increase of the Gouy phase shift of the realized Bessel beams.

© 2010 OSA

OCIS Codes
(260.1960) Physical optics : Diffraction theory
(350.5030) Other areas of optics : Phase

ToC Category:
Physical Optics

Original Manuscript: December 16, 2009
Manuscript Accepted: February 9, 2010
Published: March 23, 2010

Paolo Martelli, Matteo Tacca, Alberto Gatto, Giorgio Moneta, and Mario Martinelli, "Gouy phase shift in nondiffracting Bessel beams," Opt. Express 18, 7108-7120 (2010)

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  1. L. G. Gouy, “Sur une proprieté nouvelle des ondes lumineuses,” Acad. Sci., Paris, C. R. 110, 1251–1253 (1890).
  2. A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986).
  3. M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. Lond. A Math. Phys. Sci. 392(1802), 45–57 (1984). [CrossRef]
  4. R. Simon and N. Mukunda, “Bargmann invariant and the geometry of the Güoy effect,” Phys. Rev. Lett. 70(7), 880–883 (1993). [CrossRef] [PubMed]
  5. D. Subbarao, “Topological phase in Gaussian beam optics,” Opt. Lett. 20(21), 2162–2164 (1995). [CrossRef] [PubMed]
  6. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5(10), 1550–1567 (1966). [CrossRef] [PubMed]
  7. B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, Inc., 1991).
  8. T. Ackermann, W. Grosse-Nobis, and G. L. Lippi, “The Gouy phase shift, the average phase lag of Fourier components of Hermite-Gaussian modes and their application to resonance conditions in optical cavities,” Opt. Commun. 189(1-3), 5–14 (2001). [CrossRef]
  9. J. H. Chow, G. de Vine, M. B. Gray, and D. E. McClelland, “Measurement of gouy phase evolution by use of spatial mode interference,” Opt. Lett. 29(20), 2339–2341 (2004). [CrossRef] [PubMed]
  10. J. Hamazaki, Y. Mineta, K. Oka, and R. Morita, “Direct observation of Gouy phase shift in a propagating optical vortex,” Opt. Express 14(18), 8382–8392 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-18-8382 . [CrossRef] [PubMed]
  11. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987). [CrossRef]
  12. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987). [CrossRef] [PubMed]
  13. A. Vasara, J. Turunen, and A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6(11), 1748–1754 (1989). [CrossRef] [PubMed]
  14. A. J. Cox and D. C. Dibble, “Nondiffracting beam from a spatially filtered Fabry-Perot resonator,” J. Opt. Soc. Am. A 9(2), 282–286 (1992). [CrossRef]
  15. J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000). [CrossRef]
  16. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001). [CrossRef]
  17. S. A. Tatarkova, W. Sibbett, and K. Dholakia, “Brownian particle in an optical potential of the washboard type,” Phys. Rev. Lett. 91(3), 038101 (2003). [CrossRef] [PubMed]
  18. V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003). [CrossRef] [PubMed]
  19. G. B. Arfken, and H. J. Weber, Mathematical Methods for Physicists (Harcourt/Academic Press, 5th Ed., 2001).
  20. N. N. Lebedev, Special Functions and their Applications (Dover Publications, Inc., New York, 1972).
  21. S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett. 26(8), 485–487 (2001). [CrossRef]
  22. G. Indebetouw, “Nondiffracting optical fields: some remarks on their analysis and synthesis,” J. Opt. Soc. Am. A 6(1), 150–152 (1989). [CrossRef]
  23. M. A. Porras, C. J. Zapata-Rodríguez, and I. Gonzalo, “Gouy wave modes: undistorted pulse focalization in a dispersive medium,” Opt. Lett. 32(22), 3287–3289 (2007). [CrossRef] [PubMed]
  24. J. A. Davis, E. Carcole, and D. M. Cottrell, “Intensity and phase measurements of nondiffracting beams generated with a magneto-optic spatial light modulator,” Appl. Opt. 35(4), 593–598 (1996). [CrossRef] [PubMed]
  25. C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124(1-2), 121–130 (1996). [CrossRef]
  26. W.-H. Lee, "Computer-generated holograms," in Progress in Optics XVI, E. Wolf, ed., (North-Holland, Amsterdam, 1978).

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