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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 12 — Dec. 1, 2004
  • pp: 2455–2463

Chirped optical X-shaped pulses in material media

Michel Zamboni-Rached, Hugo E. Hernández-Figueroa, and Erasmo Recami  »View Author Affiliations

JOSA A, Vol. 21, Issue 12, pp. 2455-2463 (2004)

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We analyze the properties of chirped optical X-shaped pulses propagating in material media without boundaries. We show that such (“superluminal”) pulses may recover their transverse and longitudinal shapes after some propagation distance, whereas the ordinary chirped Gaussian pulses can recover their longitudinal width only (since Gaussian pulses suffer a progressive transverse spreading during their propagation). We therefore propose the use of chirped optical X-type pulses to overcome the problems of both dispersion and diffraction during pulse propagation.

© 2004 Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(060.4080) Fiber optics and optical communications : Modulation
(070.1060) Fourier optics and signal processing : Acousto-optical signal processing
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(220.0220) Optical design and fabrication : Optical design and fabrication
(230.0230) Optical devices : Optical devices
(260.2030) Physical optics : Dispersion
(320.5540) Ultrafast optics : Pulse shaping
(320.5550) Ultrafast optics : Pulses
(350.0350) Other areas of optics : Other areas of optics

Original Manuscript: May 21, 2004
Revised Manuscript: July 30, 2004
Manuscript Accepted: July 30, 2004
Published: December 1, 2004

Michel Zamboni-Rached, Hugo E. Hernández-Figueroa, and Erasmo Recami, "Chirped optical X-shaped pulses in material media," J. Opt. Soc. Am. A 21, 2455-2463 (2004)

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  17. The chirped Gaussian pulse can recover its longitudinal width, but with a diminished intensity, owing to progressive transverse spreading.
  18. This problem could be overcome, in principle, by using a lens. But it would not be a good solution, because a different lens would be necessary (besides a different chirp parameter C) for each different value of ZT1=T0.
  19. I. S. Gradshteyn, I. M. Ryzhik, Integrals, Series and Products, 4th ed. (Academic, New York, 1965).
  20. Obviously, in the case of finite apertures, one must take into account the finite field depth of the X-shaped pulses. We shall see this in Section 4.
  21. Again, if we consider finite-aperture generation, one must take into account the finite field depth of the X-shaped pulses, as we shall see in Section 4.
  22. We call spot size the transverse width, which for Gaussian pulses is the transverse distance from the pulse center to the position at which the intensity decreases by a factor 1/eand, in the case of the considered X-shaped pulses, the transverse distance from the pulse center to where the first zero of the intensity occurs.
  23. Remembering that (Vg)X=(Vg)Gauss/cos θand (β2)X= cos θ(β2)Gauss.
  24. One can easily verify that in this case the distance Ldispcoincides with zdiff=3πw02/λ0,which is the distance where a Gaussian pulsedoubles its transverse width.

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