## Ultrashort pulsed Bessel beams and spatially induced group-velocity dispersion

JOSA A, Vol. 19, Issue 1, pp. 49-53 (2002)

http://dx.doi.org/10.1364/JOSAA.19.000049

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### Abstract

We find a new family of solutions of the nonparaxial wave equation that represents ultrashort pulsed light beam propagation in free space. The spatial and temporal parts of these pulsed beams are separable; the spatial transverse part is described by a Bessel function and remains unchanged during propagation, but the temporal profile can be arbitrary. Therefore the pulsed beam exhibits diffraction-free behavior with no transverse spreading, but the temporal part changes as if in a dispensive medium; the change is dominated by what we call spatially induced group-velocity dispersion. The analytical and numerical investigations show that the even- and odd-order spatially induced dispersions partially compensate for each other so as to give rise to pulse spreading, weakening, asymmetry, and center shift.

© 2002 Optical Society of America

**OCIS Codes**

(010.3310) Atmospheric and oceanic optics : Laser beam transmission

(260.1960) Physical optics : Diffraction theory

(270.5530) Quantum optics : Pulse propagation and temporal solitons

(320.0320) Ultrafast optics : Ultrafast optics

**Citation**

Wei Hu and Hong Guo, "Ultrashort pulsed Bessel beams and spatially induced group-velocity dispersion," J. Opt. Soc. Am. A **19**, 49-53 (2002)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-1-49

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### References

- See, e.g., I. N. Duling III, ed., Compact Sources of Ultrashort Pulses (Cambridge U. Press, New York, 1995).
- M. A. Porras, “Ultrashort pulsed Gaussian light beams,” Phys. Rev. E 58, 1086–1093 (1998).
- M. A. Porras, “Nonsinusoidal few-cycle pulsed light beams in free space,” J. Opt. Soc. Am. B 16, 1468–1474 (1999).
- 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).
- S. Feng, H. G. Winful, and R. W. Hellwarth, “Spatiotemporal evolution of focused single-cycle electromagnetic pulses,” Phys. Rev. E 59, 4630–4649 (1999).
- S. Feng and H. G. Winful, “Spatiotemporal transformation of isodiffracting ultrashort pulses by nondispersive quadratic phase media,” J. Opt. Soc. Am. A 16, 2500–2509 (1999).
- R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2033 (1989).
- A. E. Kaplan, “Diffraction-induced transformation of near-cycles and sub-cycles 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).
- G. P. Agrawal, “Far-field diffraction of pulsed optical beams in dispersive media,” Opt. Commun. 167, 15–22 (1999).
- M. A. Porras, “Propagation of single-cycle pulse light beams in dispersive media,” Phys. Rev. A 60, 5069–5073 (1999).
- T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
- A. T. Friberg, J. Fagerholm, and M. M. Salomaa, “Space-frequency analysis of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997).
- J. Lu and J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free space scalar wave equation and their finite aperture realization,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19–31 (1992).
- J. Lu and J. F. Greenleaf, “Experimental verification of X waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 441–446 (1992).
- M. A. Porras, R. Borghi, and M. Santarsiero, “Few-optical-cycle Bessel–Gauss pulsed beams in free space,” Phys. Rev. E 62, 5729–5737 (2000).
- J. Durnin, J. Miceli, Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
- J. Durnin, “Exact solution for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
- J. Durnin, J. Miceli, Jr., and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13, 79–80 (1988).
- Z. Y. Liu and D. Y. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, 17–21 (1998).
- A. E. Kaplan and P. L. Shkolnikov, “Electromagnetic ‘bubbles’ and shock waves: unipolar, nonoscillating EM solitons,” Phys. Rev. Lett. 75, 2316–2319 (1995).
- See, e.g., M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, Cambridge, UK, 1998).
- See, e.g., G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, 1995).
- E. M. Belenov and A. V. Nazakin, “Transient diffraction and precursorlike effects in vacuum,” J. Opt. Soc. Am. A 11, 168–172 (1994).

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