Abstract

The process of optical frequency doubling in the undepleted regime can lead to the generation of an X-wave envelope with group velocity locked to the pump beam. Its parameters and its angular spectrum are directly related to the zeroth- and first-order dispersive features of the nonlinear process. This constitutes a novel mechanism for spatiotemporal localization of light.

© 2003 Optical Society of America

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References

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  1. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  2. E. Recami, Physica A 252, 586 (1998).
    [CrossRef]
  3. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  4. R. W. Ziolkowski, D. K. Lewis, and B. D. Cook, Phys. Rev. Lett. 62, 147 (1989).
    [CrossRef] [PubMed]
  5. H. Sonajalg, M. Ratsep, and P. Saari, Opt. Lett. 22, 310 (1997).
    [CrossRef]
  6. P. Saari and K. Reivelt, Phys. Rev. Lett. 79, 4135 (1997).
    [CrossRef]
  7. D. Mugnai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000).
    [CrossRef] [PubMed]
  8. R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, J. Opt. Soc. Am. A 10, 75 (1993).
    [CrossRef]
  9. A. M. Shaarawi, J. Opt. Soc. Am. A 14, 1804 (1997).
    [CrossRef]
  10. P. R. Stepanishen and J. Sun, J. Acoust. Soc. Am. 102, 3308 (1997).
    [CrossRef]
  11. P. R. Stepanishen, J. Acoust. Soc. Am. 104, 1742 (1998).
    [CrossRef]
  12. H. Sonajalg and P. Saari, Opt. Lett. 21, 1162 (1996).
    [CrossRef]
  13. M. A. Porras, Opt. Lett. 26, 1364 (2001).
    [CrossRef]
  14. M. Zamboni-Rached, E. Recami, and F. Fontana, Phys. Rev. E 64, 0666031 (2001).
    [CrossRef]
  15. P. Saari, March 19, 2001, arXiv.org e-Print archive, preprint physics/0103054, http://arxiv.org.
  16. C. Conti, S. Trillo, P. D. Trapani, O. Jedrkiewicz, G. Valiulis, and J. Trull, Phys. Rev. Lett. 90, 170406 (2003).
    [CrossRef]
  17. C. Conti, “X-wave mediated instability of plane waves in Kerr media,” Phys. Rev. E (to be published).
  18. S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, Opt. Lett. 27, 1451 (2002).
    [CrossRef]
  19. P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. (to be published).
  20. T. Levi-Civita, Caratteristiche dei Sistemi Differenziali e Propagazione Ondosa (Zanichelli, Bologna, Italy, 1931).
  21. J. T. Lunardi, Phys. Lett. A 291, 66 (2001).
    [CrossRef]
  22. W. A. Rodrigues, D. S. Thober, and A. L. Xavier, Phys. Lett. A 284, 217 (2001).
    [CrossRef]
  23. J. Salo and M. M. Salomaa, Acoust. Res. Lett. Online 2, 31 (2001).
    [CrossRef]
  24. E. C. de Oliveira and W. A. Rodrigues, Phys. Lett. A 291, 367 (2001).
    [CrossRef]
  25. M. Zamboni-Rached, E. Recami, and H. E. Harnandez-Figueroa, October 2, 2002, arXiv.org e-Print archive, preprint physics/0109062, http://arxiv.org.
  26. K. Reivelt and P. Saari, J. Opt. Soc. Am. A 17, 1785 (2000).
    [CrossRef]
  27. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).
  28. J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
    [CrossRef]

2003 (1)

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

2002 (1)

2001 (6)

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

J. T. Lunardi, Phys. Lett. A 291, 66 (2001).
[CrossRef]

W. A. Rodrigues, D. S. Thober, and A. L. Xavier, Phys. Lett. A 284, 217 (2001).
[CrossRef]

J. Salo and M. M. Salomaa, Acoust. Res. Lett. Online 2, 31 (2001).
[CrossRef]

E. C. de Oliveira and W. A. Rodrigues, Phys. Lett. A 291, 367 (2001).
[CrossRef]

M. Zamboni-Rached, E. Recami, and F. Fontana, Phys. Rev. E 64, 0666031 (2001).
[CrossRef]

2000 (3)

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
[CrossRef]

D. Mugnai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000).
[CrossRef] [PubMed]

K. Reivelt and P. Saari, J. Opt. Soc. Am. A 17, 1785 (2000).
[CrossRef]

1998 (2)

P. R. Stepanishen, J. Acoust. Soc. Am. 104, 1742 (1998).
[CrossRef]

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

1997 (4)

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

P. R. Stepanishen and J. Sun, J. Acoust. Soc. Am. 102, 3308 (1997).
[CrossRef]

A. M. Shaarawi, J. Opt. Soc. Am. A 14, 1804 (1997).
[CrossRef]

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

1996 (1)

1993 (1)

R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, J. Opt. Soc. Am. A 10, 75 (1993).
[CrossRef]

1989 (1)

R. W. Ziolkowski, D. K. Lewis, and B. D. Cook, Phys. Rev. Lett. 62, 147 (1989).
[CrossRef] [PubMed]

1987 (1)

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

Bellanca, G.

Besieris, I. M.

R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, J. Opt. Soc. Am. A 10, 75 (1993).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Conti, C.

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

S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, Opt. Lett. 27, 1451 (2002).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. (to be published).

C. Conti, “X-wave mediated instability of plane waves in Kerr media,” Phys. Rev. E (to be published).

Cook, B. D.

R. W. Ziolkowski, D. K. Lewis, and B. D. Cook, Phys. Rev. Lett. 62, 147 (1989).
[CrossRef] [PubMed]

de Oliveira, E. C.

E. C. de Oliveira and W. A. Rodrigues, Phys. Lett. A 291, 367 (2001).
[CrossRef]

Di Trapani, P.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. (to be published).

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]

Fagerholm, J.

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
[CrossRef]

Fontana, F.

M. Zamboni-Rached, E. Recami, and F. Fontana, Phys. Rev. E 64, 0666031 (2001).
[CrossRef]

Friberg, A. T.

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
[CrossRef]

Harnandez-Figueroa, H. E.

M. Zamboni-Rached, E. Recami, and H. E. Harnandez-Figueroa, October 2, 2002, arXiv.org e-Print archive, preprint physics/0109062, http://arxiv.org.

Jedrkiewicz, O.

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

S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, Opt. Lett. 27, 1451 (2002).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. (to be published).

Levi-Civita, T.

T. Levi-Civita, Caratteristiche dei Sistemi Differenziali e Propagazione Ondosa (Zanichelli, Bologna, Italy, 1931).

Lewis, D. K.

R. W. Ziolkowski, D. K. Lewis, and B. D. Cook, Phys. Rev. Lett. 62, 147 (1989).
[CrossRef] [PubMed]

Lunardi, J. T.

J. T. Lunardi, Phys. Lett. A 291, 66 (2001).
[CrossRef]

Miceli, J. J.

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

Mugnai, D.

D. Mugnai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000).
[CrossRef] [PubMed]

Piskarskas, A.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. (to be published).

Porras, M. A.

Ranfagni, A.

D. Mugnai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000).
[CrossRef] [PubMed]

Ratsep, M.

Recami, E.

M. Zamboni-Rached, E. Recami, and F. Fontana, Phys. Rev. E 64, 0666031 (2001).
[CrossRef]

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

M. Zamboni-Rached, E. Recami, and H. E. Harnandez-Figueroa, October 2, 2002, arXiv.org e-Print archive, preprint physics/0109062, http://arxiv.org.

Reivelt, K.

K. Reivelt and P. Saari, J. Opt. Soc. Am. A 17, 1785 (2000).
[CrossRef]

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

Rodrigues, W. A.

E. C. de Oliveira and W. A. Rodrigues, Phys. Lett. A 291, 367 (2001).
[CrossRef]

W. A. Rodrigues, D. S. Thober, and A. L. Xavier, Phys. Lett. A 284, 217 (2001).
[CrossRef]

Ruggeri, R.

D. Mugnai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000).
[CrossRef] [PubMed]

Saari, P.

K. Reivelt and P. Saari, J. Opt. Soc. Am. A 17, 1785 (2000).
[CrossRef]

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

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

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

P. Saari, March 19, 2001, arXiv.org e-Print archive, preprint physics/0103054, http://arxiv.org.

Salo, J.

J. Salo and M. M. Salomaa, Acoust. Res. Lett. Online 2, 31 (2001).
[CrossRef]

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
[CrossRef]

Salomaa, M. M.

J. Salo and M. M. Salomaa, Acoust. Res. Lett. Online 2, 31 (2001).
[CrossRef]

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
[CrossRef]

Shaarawi, A. M.

A. M. Shaarawi, J. Opt. Soc. Am. A 14, 1804 (1997).
[CrossRef]

R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, J. Opt. Soc. Am. A 10, 75 (1993).
[CrossRef]

Sonajalg, H.

Stepanishen, P. R.

P. R. Stepanishen, J. Acoust. Soc. Am. 104, 1742 (1998).
[CrossRef]

P. R. Stepanishen and J. Sun, J. Acoust. Soc. Am. 102, 3308 (1997).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Sun, J.

P. R. Stepanishen and J. Sun, J. Acoust. Soc. Am. 102, 3308 (1997).
[CrossRef]

Thober, D. S.

W. A. Rodrigues, D. S. Thober, and A. L. Xavier, Phys. Lett. A 284, 217 (2001).
[CrossRef]

Trapani, P. D.

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

S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, Opt. Lett. 27, 1451 (2002).
[CrossRef]

Trillo, S.

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

S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, Opt. Lett. 27, 1451 (2002).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. (to be published).

Trull, J.

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

S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, Opt. Lett. 27, 1451 (2002).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. (to be published).

Valiulis, G.

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

S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, Opt. Lett. 27, 1451 (2002).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. (to be published).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Xavier, A. L.

W. A. Rodrigues, D. S. Thober, and A. L. Xavier, Phys. Lett. A 284, 217 (2001).
[CrossRef]

Zamboni-Rached, M.

M. Zamboni-Rached, E. Recami, and F. Fontana, Phys. Rev. E 64, 0666031 (2001).
[CrossRef]

M. Zamboni-Rached, E. Recami, and H. E. Harnandez-Figueroa, October 2, 2002, arXiv.org e-Print archive, preprint physics/0109062, http://arxiv.org.

Ziolkowski, R. W.

R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, J. Opt. Soc. Am. A 10, 75 (1993).
[CrossRef]

R. W. Ziolkowski, D. K. Lewis, and B. D. Cook, Phys. Rev. Lett. 62, 147 (1989).
[CrossRef] [PubMed]

Acoust. Res. Lett. Online (1)

J. Salo and M. M. Salomaa, Acoust. Res. Lett. Online 2, 31 (2001).
[CrossRef]

J. Acoust. Soc. Am. (2)

P. R. Stepanishen and J. Sun, J. Acoust. Soc. Am. 102, 3308 (1997).
[CrossRef]

P. R. Stepanishen, J. Acoust. Soc. Am. 104, 1742 (1998).
[CrossRef]

J. Opt. Soc. Am. A (1)

R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, J. Opt. Soc. Am. A 10, 75 (1993).
[CrossRef]

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

Opt. Lett. (4)

Phys. Lett. A (3)

E. C. de Oliveira and W. A. Rodrigues, Phys. Lett. A 291, 367 (2001).
[CrossRef]

J. T. Lunardi, Phys. Lett. A 291, 66 (2001).
[CrossRef]

W. A. Rodrigues, D. S. Thober, and A. L. Xavier, Phys. Lett. A 284, 217 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

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

Phys. Rev. E (3)

C. Conti, “X-wave mediated instability of plane waves in Kerr media,” Phys. Rev. E (to be published).

M. Zamboni-Rached, E. Recami, and F. Fontana, Phys. Rev. E 64, 0666031 (2001).
[CrossRef]

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
[CrossRef]

Phys. Rev. Lett. (5)

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

R. W. Ziolkowski, D. K. Lewis, and B. D. Cook, Phys. Rev. Lett. 62, 147 (1989).
[CrossRef] [PubMed]

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

D. Mugnai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000).
[CrossRef] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. (to be published).

Physica A (1)

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

Other (5)

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

T. Levi-Civita, Caratteristiche dei Sistemi Differenziali e Propagazione Ondosa (Zanichelli, Bologna, Italy, 1931).

P. Saari, March 19, 2001, arXiv.org e-Print archive, preprint physics/0103054, http://arxiv.org.

M. Zamboni-Rached, E. Recami, and H. E. Harnandez-Figueroa, October 2, 2002, arXiv.org e-Print archive, preprint physics/0109062, http://arxiv.org.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).

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Figures (1)

Fig. 1
Fig. 1

Orientation (and support) of a generated SH X wave for (top) β1>β2 and (bottom) β1<β2.

Equations (9)

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

Er,z,t=0SωJ0κrexpikzz-ωtdω,
kzω=α+βXω.
iaz+iβ2at+12k22a+χA2exp-iΔkz=-iϵa,
aˆ=χψ×expiβ1Ω-Δkz-expiβ2Ω-κ2/2k2+iϵzβ1-β2Ω-Δk+κ2/2k2-iϵ,
ar,t,z=1β1-β2exp-iΔkt-β2zβ1-β2×0XκJ0κrexpiκ22k2t-β1zβ1-β2κdκ
E=e2 exp-ik2-βXω2-αt-β2zβX-β2×0XκJ0κrexpiκ22k2t-βXzβX-β2κdκ,
βX=β1;    α=k2-βXω2-Δk=2k1-β1ω2.
Ω=Δkβ1-β2-k22β1-β2θ2,
E=χ2k2EF2z22πtFexp-k2wF2β1-β222tF×exp-ξ1+erfσξ,

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