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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 28, Iss. 6 — Jun. 1, 2011
  • pp: 1243–1255

Airy pulsed beams

Yan Kaganovsky and Ehud Heyman  »View Author Affiliations

JOSA A, Vol. 28, Issue 6, pp. 1243-1255 (2011)

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The Airy beam (AiB) has attracted a lot of attention recently because of its intriguing features; the most distinctive ones are the propagation along curved trajectories in free space and the weak diffraction. We have previously shown that the AiB is, in fact, a caustic of the rays that radiate from the tail of the Airy function aperture distribution. Here we derive a class of ultra wideband Airy pulsed beams (AiPBs), which are the extension of the AiB into the time domain. We introduce a frequency scaling of the initial aperture field that renders the ray skeleton of the field, including the caustic, frequency independent, thus ensuring that all the frequency components propagate along the same curved trajectory and that the AiPB does not disperse. The resulting AiPB preserves the intriguing features of the time-harmonic AiB discussed above. An exact closed-form solution for the AiPB is derived using the spectral theory of transients. We also derive wavefront approximations for the field in the time window around the pulse arrival, which are valid uniformly in the vicinity of the caustic. These approximations are based on the so-called uniform geometrical optics, which is extended here to the time domain.

© 2011 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(080.2720) Geometric optics : Mathematical methods (general)
(260.0260) Physical optics : Physical optics
(260.1960) Physical optics : Diffraction theory

ToC Category:
Physical Optics

Original Manuscript: January 24, 2011
Manuscript Accepted: April 2, 2011
Published: May 25, 2011

Yan Kaganovsky and Ehud Heyman, "Airy pulsed beams," J. Opt. Soc. Am. A 28, 1243-1255 (2011)

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  1. G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007). [CrossRef]
  2. G. Siviloglou and D. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007). [CrossRef] [PubMed]
  3. M. Bandres and J. Gutiérrez-Vega, “Airy–Gauss beams and their transformation by paraxial optical systems,” Opt. Express 15, 16719–16728 (2007). [CrossRef] [PubMed]
  4. G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33, 207–209 (2008). [CrossRef] [PubMed]
  5. J. Broky, G. Siviloglou, A. Dogariu, and D. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008). [CrossRef] [PubMed]
  6. Y. Kaganovsky and E. Heyman, “Wave analysis of Airy beams,” Opt. Express 18, 8440–8452 (2010). [Note that, in Eq. (16), the factor 2π1/2e−iπ/4ω1/6 is missing due to a typo; see Eq. .] [CrossRef] [PubMed]
  7. D. Ludwig, “Wave propagation near a smooth caustic,” Bull. Am. Math. Soc. 71, 776–779 (1965). [CrossRef]
  8. Yu. A. Kravtsov, “A modification of the geometrical optics method,” Radiophys. Quantum Electron. 7, 664–673 (1964).
  9. P. Saari, “Laterally accelerating Airy pulses,” Opt. Express 16, 10303–10308 (2008). [CrossRef] [PubMed]
  10. E. Heyman and L. B. Felsen, “Weakly dispersive spectral theory of transients (STT), part I: formulation and interpretation,” IEEE Trans. Antennas Propag. 35, 80–86 (1987). [CrossRef]
  11. E. Heyman and L. B. Felsen, “Weakly dispersive spectral theory of transients (STT), part II: evaluation of the spectral integral,” IEEE Trans. Antennas Propag. 35, 574–580 (1987). [CrossRef]
  12. E. Heyman, “Weakly dispersive spectral theory of transients (STT), part III: applications,” IEEE Trans. Antennas Propag. 35, 1258–1266 (1987). [CrossRef]
  13. E. Heyman and L. B. Felsen, “Propagating pulsed beam solution by complex source parameter substitution,” IEEE Trans. Antennas Propag. 34, 1062–1065 (1986). [CrossRef]
  14. E. Heyman and L. B. Felsen, “Gaussian beam and pulsed beam dynamics: complex source and spectrum formulations within and beyond paraxial asymptotics,” J. Opt. Soc. Am. A 18, 1588–1610 (2001). [CrossRef]
  15. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 10th ed. (Dover, 1972).
  16. E. Heyman, and L. B. Felsen, “Real and complex spectra—a generalization of WKBJ seismograms,” Geophys. J. R. Astron. Soc. 91, 1087–1126 (1987). [CrossRef]

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