Abstract

The existence and properties of propagative nondispersive and nondiffracting localized envelope waves in dispersive transparent media, with either normal or anomalous group-velocity dispersion, showing subluminal group velocities and strong spatial localization are pointed out. Nonparaxial effects may lead to group-velocity reduction of several orders of magnitude. Numerical simulations are given for wave propagation in sapphire.

© 2004 Optical Society of America

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References

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  1. R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, Proc. IEEE 79, 1371 (1991).
    [CrossRef]
  2. J. Y. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
    [CrossRef]
  3. H. Sonajalg, M. Ratsep, and P. Saari, Opt. Lett. 22, 310 (1997).
    [CrossRef]
  4. P. Saari and M. Ratsep, Phys. Rev. Lett. 79, 4135 (1997).
    [CrossRef]
  5. E. Recami, Physica A 252, 586 (1998) and references therein.
    [CrossRef]
  6. H. Sonajalg and P. Saari, Opt. Lett. 21, 1162 (1996).
    [CrossRef]
  7. M. A. Porras, Opt. Lett. 26, 1364 (2001).
    [CrossRef]
  8. S. Orlov, A. Piskarskas, and A. Stabinis, Opt. Lett. 27, 2167 (2002).
    [CrossRef]
  9. M. A. Porras, S. Trillo, C. Conti, and P. Di Trapani, Opt. Lett. 28, 1090 (2003).
    [CrossRef] [PubMed]
  10. C. Conti, S. Trillo, P. Di Trapani, O. Jedrkiewicz, G. Valiulis, and J. Trull, Phys. Rev. Lett. 90, 170406 (2003).
    [CrossRef]
  11. C. Conti and S. Trillo, Opt. Lett. 28, 1251 (2003).
    [CrossRef] [PubMed]
  12. J. Salo and M. M. Salomaa, Acoust. Res. Lett. Online 2, 31 (2001), http://ojps.aip.org/ARLO/ .
    [CrossRef]
  13. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 2 (Gordon and Breach, New York, 1986); see Eq. (2.12.21.6).
  14. I. H. Malitson, J. Opt. Soc. Am. 52, 1377 (1962).

2003 (3)

2002 (1)

2001 (2)

M. A. Porras, Opt. Lett. 26, 1364 (2001).
[CrossRef]

J. Salo and M. M. Salomaa, Acoust. Res. Lett. Online 2, 31 (2001), http://ojps.aip.org/ARLO/ .
[CrossRef]

1998 (1)

E. Recami, Physica A 252, 586 (1998) and references therein.
[CrossRef]

1997 (2)

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

P. Saari and M. Ratsep, Phys. Rev. Lett. 79, 4135 (1997).
[CrossRef]

1996 (1)

1992 (1)

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

1991 (1)

R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, Proc. IEEE 79, 1371 (1991).
[CrossRef]

1962 (1)

Besieris, I. M.

R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, Proc. IEEE 79, 1371 (1991).
[CrossRef]

Brychkov, Yu. A.

A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 2 (Gordon and Breach, New York, 1986); see Eq. (2.12.21.6).

Conti, C.

Di Trapani, P.

C. Conti, S. Trillo, P. Di Trapani, O. Jedrkiewicz, G. Valiulis, and J. Trull, Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef]

M. A. Porras, S. Trillo, C. Conti, and P. Di Trapani, Opt. Lett. 28, 1090 (2003).
[CrossRef] [PubMed]

Greenleaf, J. F.

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

Jedrkiewicz, O.

C. Conti, S. Trillo, P. Di Trapani, O. Jedrkiewicz, G. Valiulis, and J. Trull, Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef]

Lu, J. Y.

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

Malitson, I. H.

Marichev, O. I.

A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 2 (Gordon and Breach, New York, 1986); see Eq. (2.12.21.6).

Orlov, S.

Piskarskas, A.

Porras, M. A.

Prudnikov, A. P.

A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 2 (Gordon and Breach, New York, 1986); see Eq. (2.12.21.6).

Ratsep, M.

P. Saari and M. Ratsep, Phys. Rev. Lett. 79, 4135 (1997).
[CrossRef]

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

Recami, E.

E. Recami, Physica A 252, 586 (1998) and references therein.
[CrossRef]

Saari, P.

Salo, J.

J. Salo and M. M. Salomaa, Acoust. Res. Lett. Online 2, 31 (2001), http://ojps.aip.org/ARLO/ .
[CrossRef]

Salomaa, M. M.

J. Salo and M. M. Salomaa, Acoust. Res. Lett. Online 2, 31 (2001), http://ojps.aip.org/ARLO/ .
[CrossRef]

Shaarawi, A. M.

R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, Proc. IEEE 79, 1371 (1991).
[CrossRef]

Sonajalg, H.

Stabinis, A.

Trillo, S.

Trull, J.

C. Conti, S. Trillo, P. Di Trapani, O. Jedrkiewicz, G. Valiulis, and J. Trull, Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef]

Valiulis, G.

C. Conti, S. Trillo, P. Di Trapani, O. Jedrkiewicz, G. Valiulis, and J. Trull, Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, Proc. IEEE 79, 1371 (1991).
[CrossRef]

Acoust. Res. Lett. Online (1)

J. Salo and M. M. Salomaa, Acoust. Res. Lett. Online 2, 31 (2001), http://ojps.aip.org/ARLO/ .
[CrossRef]

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

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

J. Opt. Soc. Am. (1)

Opt. Lett. (6)

Phys. Rev. Lett. (2)

C. Conti, S. Trillo, P. Di Trapani, O. Jedrkiewicz, G. Valiulis, and J. Trull, Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef]

P. Saari and M. Ratsep, Phys. Rev. Lett. 79, 4135 (1997).
[CrossRef]

Physica A (1)

E. Recami, Physica A 252, 586 (1998) and references therein.
[CrossRef]

Proc. IEEE (1)

R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, Proc. IEEE 79, 1371 (1991).
[CrossRef]

Other (1)

A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 2 (Gordon and Breach, New York, 1986); see Eq. (2.12.21.6).

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Figures (3)

Fig. 1
Fig. 1

(a) Space–time plot of envelope modulus ψr,τ (in arbitrary units) for a localized nondispersive and nondiffracting wave in the anomalous dispersion region (λ0=1550 nm, f=1.00001); transverse beam size and pulse duration are, respectively, w0=198 µm and τ0=95 fs [see Eqs. (8)]. (b) Behavior of normalized transverse wave vector k/k0 versus wavelength (solid curve); the dashed curve is the corresponding behavior as given by the approximate Eq. (4). (c) Radial behavior of wave intensity ψr,02 at time τ=0 (solid curve) and the corresponding approximate curve as given by Eq. (7) (dashed curve, almost overlapping the solid curve).

Fig. 2
Fig. 2

Same as Fig. 1 but in the normal dispersion region (λ0=780 nm, f=1.4). The transverse beam size and pulse duration are now w0=633 nm and τ0=3.6 fs, respectively.

Fig. 3
Fig. 3

(a) Space–time plot of envelope modulus ψr,τ (in arbitrary units) for a strongly localized nonparaxial subluminal wave (λ0=780 nm in vacuum, f=105). (b) Longitudinal profile of the on-axis electric field Er=0,z,t at different times [t=0 (solid curve), t=2π/ω0/6=0.433 fs (dashed curve), and t=2π/ω0/3=0.867 fs (dotted curve)], showing the pulsating behavior of the envelope.

Equations (9)

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Er,z,t=0dωSωJ0krexpiωt-kzz+c.c.,
ψr,τ=dΩSω0+ΩJ0kΩrexpiΩτ,
kΩ=k2ω0+Ω-kz0+kz0Ω21/2.
kΩ=A+BΩ-CΩ21/2,
2ψ+C2ψτ2-iBψτ+Aψ=0,
ψr,τ=-A/CA/CdΩSω0+Ω×J0A-CΩ2rexpiΩτ.
ψr,τ=sinAr2+Aτ2/C1/2r2+τ2/C1/2.
w0=2πk0ff2-11/2, τ0=2πfk0k0f2-1-k0k0/k02f2-11/2.
Er,z,t=2sink0r2+z-vgt21/2r2+z-vgt21/2×cosk0fz-vft.

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