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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 6 — Mar. 24, 2014
  • pp: 6899–6904

Quantitative description of the self-healing ability of a beam

Xiuxiang Chu and Wei Wen  »View Author Affiliations

Optics Express, Vol. 22, Issue 6, pp. 6899-6904 (2014)

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Quantitative description of the self-healing ability of a beam is very important for studying or comparing the self-healing ability of different beams. As describing the similarity by using the angle of two infinite-dimensional complex vectors in Hilbert space, the angle of two intensity profiles is proposed to quantitatively describe the self-healing ability of different beams. As a special case, quantitative description of the self-healing ability of a Bessel-Gaussian beam is studied. Results show that the angle of two intensity profiles can be used to describe the self-healing ability of arbitrary beams as the reconstruction distance for quantitatively describing the self-healing ability of Bessel beam. It offers a new method for studying or comparing the self-healing ability of different beams.

© 2014 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Physical Optics

Original Manuscript: February 26, 2014
Revised Manuscript: March 11, 2014
Manuscript Accepted: March 11, 2014
Published: March 17, 2014

Xiuxiang Chu and Wei Wen, "Quantitative description of the self-healing ability of a beam," Opt. Express 22, 6899-6904 (2014)

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  1. H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, eds., Localized Waves: Theory and. Applications (John Wiley, 2008).
  2. V. Garcés-Chávez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85(18), 4001–4003 (2004). [CrossRef]
  3. X. Tsampoula, V. Garcés-Chávez, M. Comrie, D. J. Stevenson, B. Agate, C. T. A. Brown, F. Gunn-Moore, K. Dholakia, “Femtosecond cellular transfection using a nondiffracting light beam,” Appl. Phys. Lett. 91(5), 053902 (2007). [CrossRef]
  4. M. Boguslawski, P. Rose, C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 061111 (2011). [CrossRef]
  5. A. Chong, W. H. Renninger, D. N. Christodoulides, F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010). [CrossRef]
  6. M. V. Berry, N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979). [CrossRef]
  7. S. Vyas, Y. Kozawa, S. Sato, “Self-healing of tightly focused scalar and vector Bessel-Gauss beams at the focal plane,” J. Opt. Soc. Am. A 28(5), 837–843 (2011). [CrossRef] [PubMed]
  8. J. D. Ring, J. Lindberg, A. Mourka, M. Mazilu, K. Dholakia, M. R. Dennis, “Auto-focusing and self-healing of Pearcey beams,” Opt. Express 20(17), 18955–18966 (2012). [CrossRef] [PubMed]
  9. R. Cao, Y. Hua, C. Min, S. Zhu, X. C. Yuan, “Self-healing optical pillar array,” Opt. Lett. 37(17), 3540–3542 (2012). [CrossRef] [PubMed]
  10. M. Anguiano-Morales, A. Martínez, M. D. Iturbe-Castillo, S. Chávez-Cerda, N. Alcalá-Ochoa, “Self-healing property of a caustic optical beam,” Appl. Opt. 46(34), 8284–8290 (2007). [CrossRef] [PubMed]
  11. P. Vaity, R. P. Singh, “Self-healing property of optical ring lattice,” Opt. Lett. 36(15), 2994–2996 (2011). [CrossRef] [PubMed]
  12. J. Broky, G. A. Siviloglou, A. Dogariu, D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008). [CrossRef] [PubMed]
  13. I. A. Litvin, M. G. Mclaren, A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009). [CrossRef]
  14. M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46(7), 078001 (2007). [CrossRef]
  15. E. Greenfield, M. Segev, W. Walasik, O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011). [CrossRef] [PubMed]
  16. Y. Kaganovsky, E. Heyman, “Wave analysis of Airy beams,” Opt. Express 18(8), 8440–8452 (2010). [CrossRef] [PubMed]
  17. R. Martínez-Herrero, I. Juvells, A. Carnicer, “On the physical realizability of highly focused electromagnetic field distributions,” Opt. Lett. 38(12), 2065–2067 (2013). [CrossRef] [PubMed]
  18. J. James, Mathematics Dictionary Mathematics Dictionary, 5th ed. (Springer, 1992).

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