OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 20 — Sep. 28, 2009
  • pp: 18148–18164

Spatiotemporal bessel beams: theory and experiments

Michaël Dallaire, Nathalie McCarthy, and Michel Piché  »View Author Affiliations

Optics Express, Vol. 17, Issue 20, pp. 18148-18164 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (9053 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We describe a family of dispersion-free and diffraction-free optical beams consisting in two-dimensional wave packets with a spatiotemporal Bessel (STB) profile propagating in media with anomalous dispersion. We also describe quasi-invariant optical beams with a spatiotemporal Bessel-Gauss (STBG) profile; these wave packets have finite dimensions and energy, conditions to be representative of physical beams. The paper provides a detailed account of the properties of STB and STBG beams, including their spatially resolved frequency spectrum, their far-field behaviour and a comparison of the propagation of STBG beams with that of Gaussian wave packets. An experimental setup based on a folded pulse shaper has allowed to generate STBG beams using the ultrashort pulses from a Ti:sapphire laser. The analysis of the spatially resolved frequency spectrum and of the spatial and temporal profiles obtained experimentally shows good agreement with theory.

© 2009 OSA

OCIS Codes
(320.5540) Ultrafast optics : Pulse shaping
(320.5550) Ultrafast optics : Pulses
(320.7090) Ultrafast optics : Ultrafast lasers

ToC Category:
Ultrafast Optics

Original Manuscript: July 9, 2009
Manuscript Accepted: September 15, 2009
Published: September 24, 2009

Michaël Dallaire, Nathalie McCarthy, and Michel Piché, "Spatiotemporal bessel beams:
theory and experiments," Opt. Express 17, 18148-18164 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23(3), 142–144 (1973). [CrossRef]
  2. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980). [CrossRef]
  3. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987). [CrossRef]
  4. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987). [CrossRef] [PubMed]
  5. F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987). [CrossRef]
  6. M. A. Porras, R. Borghi, and M. Santarsiero, “Few-optical-cycle bessel-gauss pulsed beams in free space,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(44 Pt B), 5729–5737 (2000). [CrossRef] [PubMed]
  7. B. Lü and Z. Liu, “Propagation properties of ultrashort pulsed Bessel beams in dispersive media,” J. Opt. Soc. Am. A 20(3), 582–587 (2003). [CrossRef]
  8. C. A. Dartora, K. Z. Nóbrega, H. E. Hernández-Figueroa, and E. Recami, “Properties of localized pulses through the analysis of temporal modulation effects in Bessel beams and the convolution theorem,” Opt. Commun. 229(1-6), 99–107 (2004). [CrossRef]
  9. M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersive broadening of light with Bessel-Gauss beams,” Opt. Commun. 206(4-6), 235–241 (2002). [CrossRef]
  10. H. Sõnajalg, M. Rätsep, and P. Saari, “Demonstration of the Bessel-X pulse propagating with strong lateral and longitudinal localization in a dispersive medium,” Opt. Lett. 22(5), 310–312 (1997). [CrossRef] [PubMed]
  11. M. A. Porras and I. Gonzalo, “Control of temporal characteristics of Bessel-X pulses in dispersive media,” Opt. Commun. 217(1-6), 257–264 (2003). [CrossRef]
  12. D. N. Christodoulides, N. K. Efremidis, P. Di Trapani, and B. A. Malomed, “Bessel X waves in two- and three-dimensional bidispersive optical systems,” Opt. Lett. 29(13), 1446–1448 (2004). [CrossRef] [PubMed]
  13. D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Three-dimensional arrays of optical bottle beams,” Opt. Commun. 225(4-6), 215–222 (2003). [CrossRef]
  14. A. G. Sedukhin, “Periodically focused propagation-invariant beams with sharp central peak,” Opt. Commun. 228(4-6), 231–247 (2003). [CrossRef]
  15. C. Paterson and R. Smith, “Helicon waves: propagation-invariant waves in a rotating coordinate system,” Opt. Commun. 124(1-2), 131–140 (1996). [CrossRef]
  16. S. Longhi, “Localized subluminal envelope pulses in dispersive media,” Opt. Lett. 29(2), 147–149 (2004). [CrossRef] [PubMed]
  17. M. A. Porras and P. Di Trapani, “Localized and stationary light wave modes in dispersive media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 066606 (2004). [CrossRef] [PubMed]
  18. M. Dallaire, M. Piché, and N. McCarthy, “Spatiotemporal Bessel Beams,” Proc. SPIE 6796, 67963O (2007). [CrossRef]
  19. S. Malaguti, G. Bellanca, and S. Trillo, “Two-dimensional envelope localized waves in the anomalous dispersion regime,” Opt. Lett. 33(10), 1117–1119 (2008). [CrossRef] [PubMed]
  20. A. E. Siegman, Lasers, (University Science Books, Mill Valley, California, 1986). See p. 277, Eq. (32).
  21. P. M. Morse, and L. Feshbach, Methods of Theoretical Physics, (McGraw-Hill, New York, 1953).
  22. G. Arfken, Mathematical Methods for Physicists, third edition. (Academic Press, New York, 1985). See p.797.
  23. I. S. Gradshteyn, and I. M. Ryzhik, Tables of Integrals, Series, and Products, fourth edition,( Academic Press, New York, 1980).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Supplementary Material

» Media 1: MPG (414 KB)     
» Media 2: MPG (474 KB)     
» Media 3: MPG (1513 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited