## Bessel pulse beams and focus wave modes

JOSA A, Vol. 18, Issue 10, pp. 2594-2600 (2001)

http://dx.doi.org/10.1364/JOSAA.18.002594

Acrobat PDF (168 KB)

### Abstract

Free-space propagation of ultrashort pulses is investigated. Space–time couplings are reduced for a particular form of beams that is termed a pulse beam, or a type 3 pulsed beam. General conditions for the formation of pulse beams in the paraxial approximation are presented. The free-space propagation of spatially localized ultrashort laser pulses is investigated. This treatment is based on a particular pulsed form of the well-known Bessel beam, which is termed a Bessel pulse beam. The connections with focus wave modes and X waves are discussed.

© 2001 Optical Society of America

**OCIS Codes**

(140.7090) Lasers and laser optics : Ultrafast lasers

(260.1960) Physical optics : Diffraction theory

(270.5530) Quantum optics : Pulse propagation and temporal solitons

(280.3640) Remote sensing and sensors : Lidar

(320.5550) Ultrafast optics : Pulses

**Citation**

Colin J. R. Sheppard, "Bessel pulse beams and focus wave modes," J. Opt. Soc. Am. A **18**, 2594-2600 (2001)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-10-2594

Sort: Year | Journal | Reset

### References

- D. You and P. H. Bucksbaum, “Propagation of half-cycle far infrared pulses,” J. Opt. Soc. Am. B 14, 1651–1655 (1997).
- S. Feng, H. G. Winful, and R. W. Hellwarth, “Gouy shift and temporal reshaping of focused single-cycle electromagnetic pulses,” Opt. Lett. 23, 385–387 (1998).
- I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun. 53, 364–366 (1985).
- R. W. Ziolkowski and J. B. Judkins, “Propagation characteristics of ultrawide-bandwidth pulsed Gaussian beams,” J. Opt. Soc. Am. A 9, 2021–2030 (1992).
- M. M. Wefers and K. A. Nelson, “Space–time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
- A. E. Kaplan, “Diffraction-induced transformation of near-cycle and sub-cycle pulses,” J. Opt. Soc. Am. B 15, 951–956 (1998).
- G. P. Agrawal, “Spectrum-induced changes in diffraction of pulsed optical beams,” Opt. Commun. 157, 52–56 (1998).
- M. Gu and C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short laser pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
- C. J. R. Sheppard and X. Gan, “Free-space propagation of femto-second light pulses,” Opt. Commun. 133, 1–6 (1997).
- Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Spectral and temporal properties of ultrashort light pulses in the far zone,” Opt. Commun. 123, 5–10 (1996).
- Z. Wang, Z. Xu, and Z. Zhang, “Diffraction integral formulas of the pulsed wave field in the temporal domain,” Opt. Lett. 22, 354–356 (1997).
- Z. L. Horváth and Z. S. Bor, “Focusing of femtosecond pulses having Gaussian spatial distribution,” Opt. Commun. 100, 6–12 (1993).
- A. Federico and O. Martinez, “Distortion of femtosecond pulses due to chromatic aberration in lenses,” Opt. Commun. 91, 104–110 (1992).
- Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space–time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).
- M. A. Porras, “Ultrashort pulsed Gaussian light beams,” Phys. Rev. E 58, 1086–1093 (1998).
- C. F. R. Caron and R. M. Potvliege, “Free-space propagation of ultrashort pulses: space–time couplings in Gaussian pulse beams,” J. Mod. Opt. 45, 1881–1892 (1999).
- A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991).
- R. H. Enns and S. S. Rangnekar, “Variational approach to bistable solitary waves of the first kind in d dimensions,” Phys. Rev. E 48, 3998–4007 (1993).
- D. E. Edmundson and R. H. Enns, “Particle-like nature of colliding three-dimensional optical solitons,” Phys. Rev. A 51, 2491–2498 (1995).
- R. McLeod, K. Wagner, and S. Blair, “(3+1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
- J. N. Brittingham, “Focus wave modes in homogeneous Maxwell’s equations: transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
- J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
- G. B. Airy, “The diffraction of an annular aperture,” Phil. Mag. Ser. 3 18, 1–10 (1841).
- Lord Rayleigh, “On the diffraction of object glasses,” Mon. Not. R. Astron. Soc. 33, 59–63 (1872).
- J. H. McLeod, “Axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592–597 (1954).
- C. J. R. Sheppard and T. Wilson, “Gaussian-beam theory of lenses with annular aperture,” IEE J. Microwaves Opt. Acoust. 2, 105–112 (1978).
- F. Gori, G. Guatteri, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
- C. J. R. Sheppard, “Electromagnetic field in the focal region of wide-angular annular lens and mirror systems,” IEE J. Microwaves Opt. Acoust. 2, 163–166 (1978).
- J. F. Nye and M. Berry, “Dislocations of wave-fronts,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
- J. A. Campbell and S. Soloway, “Generation of a nondiffracting beam with a frequency independent beam width,” J. Acoust. Soc. Am. 88, 2467–2477 (1990).
- Z. Y. Liu and D. Y. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, L17–L21 (1998).
- J. Lu and J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free-space scalar wave equations and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19–31 (1992).
- J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular spectrum representation of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997).
- P. A. Bélanger, “Packetlike solutions of the homogeneous-wave equation,” J. Opt. Soc. Am. A 1, 723–724 (1984).
- A. Sezginer, “A general formulation of focus wave modes,” J. Appl. Phys. 57, 678–683 (1985).
- R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Math. Phys. 26, 861–863 (1985).
- E. Heyman and L. B. Felsen, “Propagating pulsed beam solutions by complex source parameter substitution,” IEEE Trans. Antennas Propag. AP-34, 1062–1065 (1986).
- E. Heyman, B. Z. Steinberg, and L. B. Felsen, “Spectral analysis of focus wave modes,” J. Opt. Soc. Am. A 4, 2081–2091 (1987).
- E. Heyman and B. Z. Steinberg, “Spectral analysis of complex-source pulsed beams,” J. Opt. Soc. Am. A 4, 3–10 (1987).
- E. Heyman and L. B. Felson, “Complex-source pulsed-beam fields,” J. Opt. Soc. Am. A 6, 806–817 (1989).
- E. Heyman, “Focus wave modes: a dilemma with causality,” IEEE Trans. Antennas Propag. 37, 1604–1608 (1989).
- R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2033 (1989).
- I. Besieris and A. M. Shaarawi, “A bidirectional traveling wave representation of exact solutions of the scalar wave equation,” J. Math. Phys. 30, 1254–1269 (1989).
- R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, “Aperture realizations of exact solutions to homogeneous-wave equations,” J. Opt. Soc. Am. A 10, 75–87 (1993).
- A. M. Shaarawi, I. M. Besieris, and R. W. Ziolkowski, “The propagating and evanescent field components of localized wave solutions,” Opt. Commun. 116, 183–192 (1995).
- A. M. Shaarawi, R. W. Ziolkowski, and I. M. Besieris, “On the evanescent fields and the causality of the focus wave modes,” J. Math. Phys. 36, 5565–5587 (1995).
- A. E. Siegman, “Hermite–Gaussian functions of complex arguments as optical-beam eigenfunctions,” J. Opt. Soc. Am. 63, 1093–1094 (1973).
- S. Saghafi and C. J. R. Sheppard, “Near field and far field of elegant Hermite–Gaussian and Laguerre–Gaussian modes,” J. Mod. Opt. 45, 1999–2009 (1998).
- E. H. Linfoot and E. Wolf, “Diffraction images in systems with an annular aperture,” Proc. Phys. Soc. London Sect. B 66, 145–149 (1953).
- A. Yoshida and T. Asakura, “Electromagnetic field in the focal plane of a coherent beam from a wide-angular annular-aperture system,” Optik (Stuttgart) 40, 322–331 (1974).
- P. K. Overfelt, “Bessel–Gauss pulses,” Phys. Rev. A 44, 3941–3947 (1991).
- A. Yoshida and T. Asakura, “Electromagnetic field near the focus of Gaussian beams,” Optik (Stuttgart) 41, 281–291 (1974).
- M. Couture and P.-A. Belanger, “From Gaussian beam to complex-source-point spherical wave,” Phys. Rev. A 24, 355–359 (1981).
- G. P. Agrawal and M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
- C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A 57, 2971–2979 (1998).
- K. Reivelt and P. Saari, “Optical generation of focus wave modes,” J. Opt. Soc. Am. A 17, 1785–1790 (2000).
- C. J. R. Sheppard and S. Saghafi, “Electromagnetic Gausssian beams beyond the paraxial approximation,” J. Opt. Soc. Am. A 16, 1381–1386 (1999).

## 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.

« Previous Article | Next Article »

OSA is a member of CrossRef.