Abstract

The diffraction of pulsed beams of light is formulated as an anomalously dispersive phenomenon. In a dispersive material, the effects of material group-velocity dispersion and diffraction on pulsed beam propagation can mutually cancel if the transverse profile of the pulse is suitably chosen.

© 2001 Optical Society of America

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References

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  1. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  2. R. W. Ziolkowski, Phys. Rev. A 39, 2005 (1989).
    [CrossRef] [PubMed]
  3. M. A. Porras, F. Salazar-Bloise, and L. Vazquez, Phys. Rev. Lett. 85, 2104 (2000).
    [CrossRef] [PubMed]
  4. See, for example, G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).
  5. S. Szatmári, P. Simon, and M. Feuerhake, Opt. Lett. 21, 1156 (1996).
    [CrossRef]
  6. P. Saari, in Ultrafast Processes in Spectroscopy, O. Svelto, S. De Silvestri, and G. Dernardo, eds. (Plenum, New York, 1997), p. 151.
  7. H. Sônajalg and P. Saari, Opt. Lett. 21, 1162 (1996).
    [CrossRef]
  8. H. Sônajalg, M. Ratsep, and P. Saari, Opt. Lett. 22, 310 (1997).
    [CrossRef]
  9. P. Saari and H. Sônajalg, Laser Phys. 7, 32 (1997).
  10. J. Rosen, B. Salik, and A. Yariv, Opt. Lett. 20, 423 (1995).
    [CrossRef] [PubMed]
  11. Z. Liu and D. Fan, J. Mod. Opt. 45, 17 (1998).
    [CrossRef]
  12. J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
    [CrossRef]
  13. E. M. Belenov and A. V. Nazarkin, J. Opt. Soc. Am. A 11, 168 (1994).
    [CrossRef]
  14. M. A. Porras, R. Borghi, and M. Santarsiero, J. Opt. Soc. Am. A 18, 177 (2001).
    [CrossRef]

2001 (1)

2000 (1)

M. A. Porras, F. Salazar-Bloise, and L. Vazquez, Phys. Rev. Lett. 85, 2104 (2000).
[CrossRef] [PubMed]

1998 (1)

Z. Liu and D. Fan, J. Mod. Opt. 45, 17 (1998).
[CrossRef]

1997 (2)

P. Saari and H. Sônajalg, Laser Phys. 7, 32 (1997).

H. Sônajalg, M. Ratsep, and P. Saari, Opt. Lett. 22, 310 (1997).
[CrossRef]

1996 (2)

1995 (1)

1994 (1)

1992 (1)

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
[CrossRef]

1989 (1)

R. W. Ziolkowski, Phys. Rev. A 39, 2005 (1989).
[CrossRef] [PubMed]

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Agrawal, G. P.

See, for example, G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).

Belenov, E. M.

Borghi, R.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Fan, D.

Z. Liu and D. Fan, J. Mod. Opt. 45, 17 (1998).
[CrossRef]

Feuerhake, M.

Greenleaf, J. F.

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
[CrossRef]

Liu, Z.

Z. Liu and D. Fan, J. Mod. Opt. 45, 17 (1998).
[CrossRef]

Lu, J.

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Nazarkin, A. V.

Porras, M. A.

M. A. Porras, R. Borghi, and M. Santarsiero, J. Opt. Soc. Am. A 18, 177 (2001).
[CrossRef]

M. A. Porras, F. Salazar-Bloise, and L. Vazquez, Phys. Rev. Lett. 85, 2104 (2000).
[CrossRef] [PubMed]

Ratsep, M.

Rosen, J.

Saari, P.

H. Sônajalg, M. Ratsep, and P. Saari, Opt. Lett. 22, 310 (1997).
[CrossRef]

P. Saari and H. Sônajalg, Laser Phys. 7, 32 (1997).

H. Sônajalg and P. Saari, Opt. Lett. 21, 1162 (1996).
[CrossRef]

P. Saari, in Ultrafast Processes in Spectroscopy, O. Svelto, S. De Silvestri, and G. Dernardo, eds. (Plenum, New York, 1997), p. 151.

Salazar-Bloise, F.

M. A. Porras, F. Salazar-Bloise, and L. Vazquez, Phys. Rev. Lett. 85, 2104 (2000).
[CrossRef] [PubMed]

Salik, B.

Santarsiero, M.

Simon, P.

Sônajalg, H.

Szatmári, S.

Vazquez, L.

M. A. Porras, F. Salazar-Bloise, and L. Vazquez, Phys. Rev. Lett. 85, 2104 (2000).
[CrossRef] [PubMed]

Yariv, A.

Ziolkowski, R. W.

R. W. Ziolkowski, Phys. Rev. A 39, 2005 (1989).
[CrossRef] [PubMed]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
[CrossRef]

J. Mod. Opt. (1)

Z. Liu and D. Fan, J. Mod. Opt. 45, 17 (1998).
[CrossRef]

J. Opt. Soc. Am. A (2)

Laser Phys. (1)

P. Saari and H. Sônajalg, Laser Phys. 7, 32 (1997).

Opt. Lett. (4)

Phys. Rev. A (1)

R. W. Ziolkowski, Phys. Rev. A 39, 2005 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

M. A. Porras, F. Salazar-Bloise, and L. Vazquez, Phys. Rev. Lett. 85, 2104 (2000).
[CrossRef] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Other (2)

See, for example, G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).

P. Saari, in Ultrafast Processes in Spectroscopy, O. Svelto, S. De Silvestri, and G. Dernardo, eds. (Plenum, New York, 1997), p. 151.

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Figures (3)

Fig. 1
Fig. 1

(a) Illustration of diffraction-induced angular dispersion and anomalous dispersion in the free-space group velocity vgω=c1-ck/ω21/2<c. Two frequencies ω2>ω1 with the same transversal projection k of the wave vector propagate at different angles θ2<θ1 and then at different effective longitudinal group velocities vg,2>vg,1. (b) Cancellation of material GVD dispersion with diffraction-induced GVD. Provided that the material dispersion is normal, i.e., that 1/kω2<1/kω1 for two close frequencies ω2>ω1, one can find a particular value K of k for which the effective group velocities become equal.

Fig. 2
Fig. 2

Propagation of the pulsed Bessel disturbance J0Kxexp-t2/b2exp-ω0t fused silica (solid curves) and in vacuum (filled circles) and of the pulsed plane wave exp-t2/b2exp-iω0t in fused silica (open circles). The numerical values of the parameters are b=12 fs, K=839.42 mm-1, and ω0=1.9 fs-1. At this frequency the material constants are k0=9193 mm-1, k0=4881 mm-1 fs, and k0=21.78 mm-1 fs2. (a), (b), and (c) show the on-axis temporal pulse forms at z=0, z=zD=3.3 mm, and z=4zD=13.2 mm, respectively.

Fig. 3
Fig. 3

(a) Illustration of the superposition scheme of a free-space Bessel-X wave and its superluminal group velocity vg=c/cosθ>c. All monochromatic Bessel beams have the same cone angle θ, and hence the transverse component k of the wave vector is proportional to the frequency. (b) In a material medium, GVD cancellation is achieved by suitable distortion of the cone angle of the monochromatic Bessel beam components.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

kzω=k2ω-k21/2
Ekz,t=g^k2π-dωA^ω-ω0×exp-iωt+ikzωz,
Ex,z,t=12π2-dkexpik·xEkz,t.
Ekz,t=g^kexp-iω0t+ikz,0z×12π-dωA^ω-ω0expi2kz,0ω-ω02z×exp-iω-ω0t-kz,0z,
kz,0=k03k0-k2k02+k0k0/kz,03.
k2=K2k03k0k02+k0k0.
Ekz,t=g^kexp-iω0t+ikz,0zAt-kz,0z,
Ex,z,t=J0KxAt-kz,0zexp-iω0t+ikz,0z

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