Abstract

We provide a quantum description of X waves by considering two different kinds of quantum states of the electromagnetic field whose field amplitude expectation value coincides with a propagation-invariant solution of the Maxwell equation. The difference between the two states is of pure quantum mechanical origin since they are internally entangled and disentangled and can be generated by different linear or nonlinear processes.

© 2007 Optical Society of America

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  1. E. Recami, M. Zamboni-Rached, and H. E. Hernandez-Figueroa, Localized Waves (Wiley-Interscience, 2007).
  2. J. Lu and J. F. Greenleaf, "Nondiffracting X waves--exact solutions to free-space scalar wave equation and their finite aperture realizations," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19-31 (1992).
    [Crossref] [PubMed]
  3. R. W. Ziolkowski, D. K. Lewis, and B. D. Cook, "Evidence of localized wave transmission," Phys. Rev. Lett. 62, 147-150 (1989).
    [Crossref] [PubMed]
  4. A. Ciattoni, C. Conti, and P. Di Porto, "Vector electromagnetic X waves," Phys. Rev. E 69, 036608 (2004).
    [Crossref]
  5. H. Sonajalg and P. Saari, "Suppression of temporal spread of ultrashort pulses in dispersive media by Bessel beam generators," Opt. Lett. 21, 1162-1164 (1996).
    [Crossref] [PubMed]
  6. A. Ciattoni and P. Di Porto, "Electromagnetic nondiffracting pulses in lossless isotropic plasmalike media," Phys. Rev. E 70, 035601(R) (2004).
    [Crossref]
  7. L. Bergé, K. Germaschewski, R. Grauer, and J. J. Rasmussen, "Hyperbolic shock waves of the optical self-focusing with normal group-velocity dispersion," Phys. Rev. Lett. 89, 153902 (2002).
    [Crossref] [PubMed]
  8. S. Orlov, A. Piskarskas, and A. Stabinis, "Focus wave modes in optical parametric generators," Opt. Lett. 27, 2103-2105 (2002).
    [Crossref]
  9. C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
    [Crossref] [PubMed]
  10. K. Staliunas and M. Tlidi, "Hyperbolic transverse patterns in nonlinear optical resonators," Phys. Rev. Lett. 94, 133902 (2005).
    [Crossref] [PubMed]
  11. C. Conti and S. Trillo, "Nonspreading wave packets in three dimensions formed by an ultracold Bose gas in an optical lattice," Phys. Rev. Lett. 92, 120404 (2004).
    [Crossref] [PubMed]
  12. S. Longhi, "Spatial-temporal Gauss-Laguerre waves in dispersive media," Phys. Rev. E 68, 066612 (2004).
    [Crossref]
  13. O. Manela, M. Segev, and D. N. Christodoulides, "Nondiffracting beams in periodic media," Opt. Lett. 30, 2611-2613 (2005).
    [Crossref] [PubMed]
  14. Y. Lahini, E. Frumker, Y. Silberberg, S. Droulias, K. Hizanidis, R. Morandotti, and D. N. Christodoulides, "Discrete X-wave formation in nonlinear waveguide arrays," Phys. Rev. Lett. 98, 023901 (2007).
    [Crossref] [PubMed]
  15. P. Saari and K. Reivelt, "Evidence of X-shaped propagation-invariant localized light waves," Phys. Rev. Lett. 79, 4135-4138 (1997).
    [Crossref]
  16. O. Jedrkiewicz, A. Picozzi, M. Clerici, D. Faccio, and P. D. Trapani, "Emergence of X-shaped spatiotemporal coherence in optical waves," Phys. Rev. Lett. 97, 243903 (2006).
    [Crossref]
  17. A. Picozzi and M. Haelterman, "Hidden coherence along space-time trajectories in parametric wave mixing," Phys. Rev. Lett. 88, 083901 (2002).
    [Crossref] [PubMed]
  18. P. Saari, M. Menert, and H. Valtna, "Photon localization barrier can be overcome," Opt. Commun. 246, 445-450 (2005).
    [Crossref]
  19. C. Conti, arXiv:quant-ph/0309069v3 (2003).
  20. C. Conti, arXiv.org:quant-ph/0409130 (2004).
  21. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  22. R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford U. Press, 2000).
  23. R. Butkus, S. Orlov, A. Piskarskas, V. Smilgevicius, and A. Stabinis, "Phase matching of optical X-waves in nonlinear crystals," Opt. Commun. 244, 411-421 (2005).
    [Crossref]
  24. S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, "Colored conical emission by means of second-harmonic generation," Opt. Lett. 27, 1451-1453 (2002).
    [Crossref]
  25. C. Conti and S. Trillo, "X waves generated at the second harmonic," Opt. Lett. 28, 1251-1253 (2003).
    [Crossref] [PubMed]
  26. S. Longhi, "Parametric amplification of spatiotemporal localized envelope waves," Phys. Rev. E 69, 016606 (2004).
    [Crossref]
  27. B. Yurke, "Wideband photon counting and homodyne detection," Phys. Rev. A 32, 311-323 (1985).
    [Crossref] [PubMed]
  28. B. Yurke and D. Stoler, "Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion," Phys. Rev. Lett. 57, 13-16 (1986).
    [Crossref] [PubMed]
  29. B. C. Sanders, "Entangled coherent states," Phys. Rev. A 45, 6811-6815 (1992).
    [Crossref] [PubMed]

2007 (2)

E. Recami, M. Zamboni-Rached, and H. E. Hernandez-Figueroa, Localized Waves (Wiley-Interscience, 2007).

Y. Lahini, E. Frumker, Y. Silberberg, S. Droulias, K. Hizanidis, R. Morandotti, and D. N. Christodoulides, "Discrete X-wave formation in nonlinear waveguide arrays," Phys. Rev. Lett. 98, 023901 (2007).
[Crossref] [PubMed]

2006 (1)

O. Jedrkiewicz, A. Picozzi, M. Clerici, D. Faccio, and P. D. Trapani, "Emergence of X-shaped spatiotemporal coherence in optical waves," Phys. Rev. Lett. 97, 243903 (2006).
[Crossref]

2005 (4)

P. Saari, M. Menert, and H. Valtna, "Photon localization barrier can be overcome," Opt. Commun. 246, 445-450 (2005).
[Crossref]

O. Manela, M. Segev, and D. N. Christodoulides, "Nondiffracting beams in periodic media," Opt. Lett. 30, 2611-2613 (2005).
[Crossref] [PubMed]

K. Staliunas and M. Tlidi, "Hyperbolic transverse patterns in nonlinear optical resonators," Phys. Rev. Lett. 94, 133902 (2005).
[Crossref] [PubMed]

R. Butkus, S. Orlov, A. Piskarskas, V. Smilgevicius, and A. Stabinis, "Phase matching of optical X-waves in nonlinear crystals," Opt. Commun. 244, 411-421 (2005).
[Crossref]

2004 (6)

C. Conti, arXiv.org:quant-ph/0409130 (2004).

S. Longhi, "Parametric amplification of spatiotemporal localized envelope waves," Phys. Rev. E 69, 016606 (2004).
[Crossref]

C. Conti and S. Trillo, "Nonspreading wave packets in three dimensions formed by an ultracold Bose gas in an optical lattice," Phys. Rev. Lett. 92, 120404 (2004).
[Crossref] [PubMed]

S. Longhi, "Spatial-temporal Gauss-Laguerre waves in dispersive media," Phys. Rev. E 68, 066612 (2004).
[Crossref]

A. Ciattoni and P. Di Porto, "Electromagnetic nondiffracting pulses in lossless isotropic plasmalike media," Phys. Rev. E 70, 035601(R) (2004).
[Crossref]

A. Ciattoni, C. Conti, and P. Di Porto, "Vector electromagnetic X waves," Phys. Rev. E 69, 036608 (2004).
[Crossref]

2003 (3)

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

C. Conti, arXiv:quant-ph/0309069v3 (2003).

C. Conti and S. Trillo, "X waves generated at the second harmonic," Opt. Lett. 28, 1251-1253 (2003).
[Crossref] [PubMed]

2002 (4)

S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, "Colored conical emission by means of second-harmonic generation," Opt. Lett. 27, 1451-1453 (2002).
[Crossref]

A. Picozzi and M. Haelterman, "Hidden coherence along space-time trajectories in parametric wave mixing," Phys. Rev. Lett. 88, 083901 (2002).
[Crossref] [PubMed]

L. Bergé, K. Germaschewski, R. Grauer, and J. J. Rasmussen, "Hyperbolic shock waves of the optical self-focusing with normal group-velocity dispersion," Phys. Rev. Lett. 89, 153902 (2002).
[Crossref] [PubMed]

S. Orlov, A. Piskarskas, and A. Stabinis, "Focus wave modes in optical parametric generators," Opt. Lett. 27, 2103-2105 (2002).
[Crossref]

2000 (1)

R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford U. Press, 2000).

1997 (1)

P. Saari and K. Reivelt, "Evidence of X-shaped propagation-invariant localized light waves," Phys. Rev. Lett. 79, 4135-4138 (1997).
[Crossref]

1996 (1)

1995 (1)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

1992 (2)

B. C. Sanders, "Entangled coherent states," Phys. Rev. A 45, 6811-6815 (1992).
[Crossref] [PubMed]

J. Lu and J. F. Greenleaf, "Nondiffracting X waves--exact solutions to free-space scalar wave equation and their finite aperture realizations," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19-31 (1992).
[Crossref] [PubMed]

1989 (1)

R. W. Ziolkowski, D. K. Lewis, and B. D. Cook, "Evidence of localized wave transmission," Phys. Rev. Lett. 62, 147-150 (1989).
[Crossref] [PubMed]

1986 (1)

B. Yurke and D. Stoler, "Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion," Phys. Rev. Lett. 57, 13-16 (1986).
[Crossref] [PubMed]

1985 (1)

B. Yurke, "Wideband photon counting and homodyne detection," Phys. Rev. A 32, 311-323 (1985).
[Crossref] [PubMed]

Bellanca, G.

Bergé, L.

L. Bergé, K. Germaschewski, R. Grauer, and J. J. Rasmussen, "Hyperbolic shock waves of the optical self-focusing with normal group-velocity dispersion," Phys. Rev. Lett. 89, 153902 (2002).
[Crossref] [PubMed]

Butkus, R.

R. Butkus, S. Orlov, A. Piskarskas, V. Smilgevicius, and A. Stabinis, "Phase matching of optical X-waves in nonlinear crystals," Opt. Commun. 244, 411-421 (2005).
[Crossref]

Christodoulides, D. N.

Y. Lahini, E. Frumker, Y. Silberberg, S. Droulias, K. Hizanidis, R. Morandotti, and D. N. Christodoulides, "Discrete X-wave formation in nonlinear waveguide arrays," Phys. Rev. Lett. 98, 023901 (2007).
[Crossref] [PubMed]

O. Manela, M. Segev, and D. N. Christodoulides, "Nondiffracting beams in periodic media," Opt. Lett. 30, 2611-2613 (2005).
[Crossref] [PubMed]

Ciattoni, A.

A. Ciattoni, C. Conti, and P. Di Porto, "Vector electromagnetic X waves," Phys. Rev. E 69, 036608 (2004).
[Crossref]

A. Ciattoni and P. Di Porto, "Electromagnetic nondiffracting pulses in lossless isotropic plasmalike media," Phys. Rev. E 70, 035601(R) (2004).
[Crossref]

Clerici, M.

O. Jedrkiewicz, A. Picozzi, M. Clerici, D. Faccio, and P. D. Trapani, "Emergence of X-shaped spatiotemporal coherence in optical waves," Phys. Rev. Lett. 97, 243903 (2006).
[Crossref]

Conti, C.

C. Conti, arXiv.org:quant-ph/0409130 (2004).

A. Ciattoni, C. Conti, and P. Di Porto, "Vector electromagnetic X waves," Phys. Rev. E 69, 036608 (2004).
[Crossref]

C. Conti and S. Trillo, "Nonspreading wave packets in three dimensions formed by an ultracold Bose gas in an optical lattice," Phys. Rev. Lett. 92, 120404 (2004).
[Crossref] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

C. Conti, arXiv:quant-ph/0309069v3 (2003).

C. Conti and S. Trillo, "X waves generated at the second harmonic," Opt. Lett. 28, 1251-1253 (2003).
[Crossref] [PubMed]

S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, "Colored conical emission by means of second-harmonic generation," Opt. Lett. 27, 1451-1453 (2002).
[Crossref]

Cook, B. D.

R. W. Ziolkowski, D. K. Lewis, and B. D. Cook, "Evidence of localized wave transmission," Phys. Rev. Lett. 62, 147-150 (1989).
[Crossref] [PubMed]

Di Porto, P.

A. Ciattoni, C. Conti, and P. Di Porto, "Vector electromagnetic X waves," Phys. Rev. E 69, 036608 (2004).
[Crossref]

A. Ciattoni and P. Di Porto, "Electromagnetic nondiffracting pulses in lossless isotropic plasmalike media," Phys. Rev. E 70, 035601(R) (2004).
[Crossref]

Di Trapani, P.

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

Droulias, S.

Y. Lahini, E. Frumker, Y. Silberberg, S. Droulias, K. Hizanidis, R. Morandotti, and D. N. Christodoulides, "Discrete X-wave formation in nonlinear waveguide arrays," Phys. Rev. Lett. 98, 023901 (2007).
[Crossref] [PubMed]

Faccio, D.

O. Jedrkiewicz, A. Picozzi, M. Clerici, D. Faccio, and P. D. Trapani, "Emergence of X-shaped spatiotemporal coherence in optical waves," Phys. Rev. Lett. 97, 243903 (2006).
[Crossref]

Frumker, E.

Y. Lahini, E. Frumker, Y. Silberberg, S. Droulias, K. Hizanidis, R. Morandotti, and D. N. Christodoulides, "Discrete X-wave formation in nonlinear waveguide arrays," Phys. Rev. Lett. 98, 023901 (2007).
[Crossref] [PubMed]

Germaschewski, K.

L. Bergé, K. Germaschewski, R. Grauer, and J. J. Rasmussen, "Hyperbolic shock waves of the optical self-focusing with normal group-velocity dispersion," Phys. Rev. Lett. 89, 153902 (2002).
[Crossref] [PubMed]

Grauer, R.

L. Bergé, K. Germaschewski, R. Grauer, and J. J. Rasmussen, "Hyperbolic shock waves of the optical self-focusing with normal group-velocity dispersion," Phys. Rev. Lett. 89, 153902 (2002).
[Crossref] [PubMed]

Greenleaf, J. F.

J. Lu and J. F. Greenleaf, "Nondiffracting X waves--exact solutions to free-space scalar wave equation and their finite aperture realizations," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19-31 (1992).
[Crossref] [PubMed]

Haelterman, M.

A. Picozzi and M. Haelterman, "Hidden coherence along space-time trajectories in parametric wave mixing," Phys. Rev. Lett. 88, 083901 (2002).
[Crossref] [PubMed]

Hernandez-Figueroa, H. E.

E. Recami, M. Zamboni-Rached, and H. E. Hernandez-Figueroa, Localized Waves (Wiley-Interscience, 2007).

Hizanidis, K.

Y. Lahini, E. Frumker, Y. Silberberg, S. Droulias, K. Hizanidis, R. Morandotti, and D. N. Christodoulides, "Discrete X-wave formation in nonlinear waveguide arrays," Phys. Rev. Lett. 98, 023901 (2007).
[Crossref] [PubMed]

Jedrkiewicz, O.

O. Jedrkiewicz, A. Picozzi, M. Clerici, D. Faccio, and P. D. Trapani, "Emergence of X-shaped spatiotemporal coherence in optical waves," Phys. Rev. Lett. 97, 243903 (2006).
[Crossref]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, "Colored conical emission by means of second-harmonic generation," Opt. Lett. 27, 1451-1453 (2002).
[Crossref]

Lahini, Y.

Y. Lahini, E. Frumker, Y. Silberberg, S. Droulias, K. Hizanidis, R. Morandotti, and D. N. Christodoulides, "Discrete X-wave formation in nonlinear waveguide arrays," Phys. Rev. Lett. 98, 023901 (2007).
[Crossref] [PubMed]

Lewis, D. K.

R. W. Ziolkowski, D. K. Lewis, and B. D. Cook, "Evidence of localized wave transmission," Phys. Rev. Lett. 62, 147-150 (1989).
[Crossref] [PubMed]

Longhi, S.

S. Longhi, "Spatial-temporal Gauss-Laguerre waves in dispersive media," Phys. Rev. E 68, 066612 (2004).
[Crossref]

S. Longhi, "Parametric amplification of spatiotemporal localized envelope waves," Phys. Rev. E 69, 016606 (2004).
[Crossref]

Loudon, R.

R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford U. Press, 2000).

Lu, J.

J. Lu and J. F. Greenleaf, "Nondiffracting X waves--exact solutions to free-space scalar wave equation and their finite aperture realizations," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19-31 (1992).
[Crossref] [PubMed]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Manela, O.

Menert, M.

P. Saari, M. Menert, and H. Valtna, "Photon localization barrier can be overcome," Opt. Commun. 246, 445-450 (2005).
[Crossref]

Morandotti, R.

Y. Lahini, E. Frumker, Y. Silberberg, S. Droulias, K. Hizanidis, R. Morandotti, and D. N. Christodoulides, "Discrete X-wave formation in nonlinear waveguide arrays," Phys. Rev. Lett. 98, 023901 (2007).
[Crossref] [PubMed]

Orlov, S.

R. Butkus, S. Orlov, A. Piskarskas, V. Smilgevicius, and A. Stabinis, "Phase matching of optical X-waves in nonlinear crystals," Opt. Commun. 244, 411-421 (2005).
[Crossref]

S. Orlov, A. Piskarskas, and A. Stabinis, "Focus wave modes in optical parametric generators," Opt. Lett. 27, 2103-2105 (2002).
[Crossref]

Picozzi, A.

O. Jedrkiewicz, A. Picozzi, M. Clerici, D. Faccio, and P. D. Trapani, "Emergence of X-shaped spatiotemporal coherence in optical waves," Phys. Rev. Lett. 97, 243903 (2006).
[Crossref]

A. Picozzi and M. Haelterman, "Hidden coherence along space-time trajectories in parametric wave mixing," Phys. Rev. Lett. 88, 083901 (2002).
[Crossref] [PubMed]

Piskarskas, A.

R. Butkus, S. Orlov, A. Piskarskas, V. Smilgevicius, and A. Stabinis, "Phase matching of optical X-waves in nonlinear crystals," Opt. Commun. 244, 411-421 (2005).
[Crossref]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

S. Orlov, A. Piskarskas, and A. Stabinis, "Focus wave modes in optical parametric generators," Opt. Lett. 27, 2103-2105 (2002).
[Crossref]

Rasmussen, J. J.

L. Bergé, K. Germaschewski, R. Grauer, and J. J. Rasmussen, "Hyperbolic shock waves of the optical self-focusing with normal group-velocity dispersion," Phys. Rev. Lett. 89, 153902 (2002).
[Crossref] [PubMed]

Recami, E.

E. Recami, M. Zamboni-Rached, and H. E. Hernandez-Figueroa, Localized Waves (Wiley-Interscience, 2007).

Reivelt, K.

P. Saari and K. Reivelt, "Evidence of X-shaped propagation-invariant localized light waves," Phys. Rev. Lett. 79, 4135-4138 (1997).
[Crossref]

Saari, P.

P. Saari, M. Menert, and H. Valtna, "Photon localization barrier can be overcome," Opt. Commun. 246, 445-450 (2005).
[Crossref]

P. Saari and K. Reivelt, "Evidence of X-shaped propagation-invariant localized light waves," Phys. Rev. Lett. 79, 4135-4138 (1997).
[Crossref]

H. Sonajalg and P. Saari, "Suppression of temporal spread of ultrashort pulses in dispersive media by Bessel beam generators," Opt. Lett. 21, 1162-1164 (1996).
[Crossref] [PubMed]

Sanders, B. C.

B. C. Sanders, "Entangled coherent states," Phys. Rev. A 45, 6811-6815 (1992).
[Crossref] [PubMed]

Segev, M.

Silberberg, Y.

Y. Lahini, E. Frumker, Y. Silberberg, S. Droulias, K. Hizanidis, R. Morandotti, and D. N. Christodoulides, "Discrete X-wave formation in nonlinear waveguide arrays," Phys. Rev. Lett. 98, 023901 (2007).
[Crossref] [PubMed]

Smilgevicius, V.

R. Butkus, S. Orlov, A. Piskarskas, V. Smilgevicius, and A. Stabinis, "Phase matching of optical X-waves in nonlinear crystals," Opt. Commun. 244, 411-421 (2005).
[Crossref]

Sonajalg, H.

Stabinis, A.

R. Butkus, S. Orlov, A. Piskarskas, V. Smilgevicius, and A. Stabinis, "Phase matching of optical X-waves in nonlinear crystals," Opt. Commun. 244, 411-421 (2005).
[Crossref]

S. Orlov, A. Piskarskas, and A. Stabinis, "Focus wave modes in optical parametric generators," Opt. Lett. 27, 2103-2105 (2002).
[Crossref]

Staliunas, K.

K. Staliunas and M. Tlidi, "Hyperbolic transverse patterns in nonlinear optical resonators," Phys. Rev. Lett. 94, 133902 (2005).
[Crossref] [PubMed]

Stoler, D.

B. Yurke and D. Stoler, "Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion," Phys. Rev. Lett. 57, 13-16 (1986).
[Crossref] [PubMed]

Tlidi, M.

K. Staliunas and M. Tlidi, "Hyperbolic transverse patterns in nonlinear optical resonators," Phys. Rev. Lett. 94, 133902 (2005).
[Crossref] [PubMed]

Trapani, P. D.

O. Jedrkiewicz, A. Picozzi, M. Clerici, D. Faccio, and P. D. Trapani, "Emergence of X-shaped spatiotemporal coherence in optical waves," Phys. Rev. Lett. 97, 243903 (2006).
[Crossref]

S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, "Colored conical emission by means of second-harmonic generation," Opt. Lett. 27, 1451-1453 (2002).
[Crossref]

Trillo, S.

C. Conti and S. Trillo, "Nonspreading wave packets in three dimensions formed by an ultracold Bose gas in an optical lattice," Phys. Rev. Lett. 92, 120404 (2004).
[Crossref] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

C. Conti and S. Trillo, "X waves generated at the second harmonic," Opt. Lett. 28, 1251-1253 (2003).
[Crossref] [PubMed]

S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, "Colored conical emission by means of second-harmonic generation," Opt. Lett. 27, 1451-1453 (2002).
[Crossref]

Trull, J.

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, "Colored conical emission by means of second-harmonic generation," Opt. Lett. 27, 1451-1453 (2002).
[Crossref]

Valiulis, G.

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, "Colored conical emission by means of second-harmonic generation," Opt. Lett. 27, 1451-1453 (2002).
[Crossref]

Valtna, H.

P. Saari, M. Menert, and H. Valtna, "Photon localization barrier can be overcome," Opt. Commun. 246, 445-450 (2005).
[Crossref]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Yurke, B.

B. Yurke and D. Stoler, "Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion," Phys. Rev. Lett. 57, 13-16 (1986).
[Crossref] [PubMed]

B. Yurke, "Wideband photon counting and homodyne detection," Phys. Rev. A 32, 311-323 (1985).
[Crossref] [PubMed]

Zamboni-Rached, M.

E. Recami, M. Zamboni-Rached, and H. E. Hernandez-Figueroa, Localized Waves (Wiley-Interscience, 2007).

Ziolkowski, R. W.

R. W. Ziolkowski, D. K. Lewis, and B. D. Cook, "Evidence of localized wave transmission," Phys. Rev. Lett. 62, 147-150 (1989).
[Crossref] [PubMed]

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

J. Lu and J. F. Greenleaf, "Nondiffracting X waves--exact solutions to free-space scalar wave equation and their finite aperture realizations," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19-31 (1992).
[Crossref] [PubMed]

Opt. Commun. (2)

P. Saari, M. Menert, and H. Valtna, "Photon localization barrier can be overcome," Opt. Commun. 246, 445-450 (2005).
[Crossref]

R. Butkus, S. Orlov, A. Piskarskas, V. Smilgevicius, and A. Stabinis, "Phase matching of optical X-waves in nonlinear crystals," Opt. Commun. 244, 411-421 (2005).
[Crossref]

Opt. Lett. (5)

Phys. Rev. A (2)

B. Yurke, "Wideband photon counting and homodyne detection," Phys. Rev. A 32, 311-323 (1985).
[Crossref] [PubMed]

B. C. Sanders, "Entangled coherent states," Phys. Rev. A 45, 6811-6815 (1992).
[Crossref] [PubMed]

Phys. Rev. E (4)

S. Longhi, "Spatial-temporal Gauss-Laguerre waves in dispersive media," Phys. Rev. E 68, 066612 (2004).
[Crossref]

A. Ciattoni and P. Di Porto, "Electromagnetic nondiffracting pulses in lossless isotropic plasmalike media," Phys. Rev. E 70, 035601(R) (2004).
[Crossref]

S. Longhi, "Parametric amplification of spatiotemporal localized envelope waves," Phys. Rev. E 69, 016606 (2004).
[Crossref]

A. Ciattoni, C. Conti, and P. Di Porto, "Vector electromagnetic X waves," Phys. Rev. E 69, 036608 (2004).
[Crossref]

Phys. Rev. Lett. (10)

R. W. Ziolkowski, D. K. Lewis, and B. D. Cook, "Evidence of localized wave transmission," Phys. Rev. Lett. 62, 147-150 (1989).
[Crossref] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

K. Staliunas and M. Tlidi, "Hyperbolic transverse patterns in nonlinear optical resonators," Phys. Rev. Lett. 94, 133902 (2005).
[Crossref] [PubMed]

C. Conti and S. Trillo, "Nonspreading wave packets in three dimensions formed by an ultracold Bose gas in an optical lattice," Phys. Rev. Lett. 92, 120404 (2004).
[Crossref] [PubMed]

Y. Lahini, E. Frumker, Y. Silberberg, S. Droulias, K. Hizanidis, R. Morandotti, and D. N. Christodoulides, "Discrete X-wave formation in nonlinear waveguide arrays," Phys. Rev. Lett. 98, 023901 (2007).
[Crossref] [PubMed]

P. Saari and K. Reivelt, "Evidence of X-shaped propagation-invariant localized light waves," Phys. Rev. Lett. 79, 4135-4138 (1997).
[Crossref]

O. Jedrkiewicz, A. Picozzi, M. Clerici, D. Faccio, and P. D. Trapani, "Emergence of X-shaped spatiotemporal coherence in optical waves," Phys. Rev. Lett. 97, 243903 (2006).
[Crossref]

A. Picozzi and M. Haelterman, "Hidden coherence along space-time trajectories in parametric wave mixing," Phys. Rev. Lett. 88, 083901 (2002).
[Crossref] [PubMed]

L. Bergé, K. Germaschewski, R. Grauer, and J. J. Rasmussen, "Hyperbolic shock waves of the optical self-focusing with normal group-velocity dispersion," Phys. Rev. Lett. 89, 153902 (2002).
[Crossref] [PubMed]

B. Yurke and D. Stoler, "Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion," Phys. Rev. Lett. 57, 13-16 (1986).
[Crossref] [PubMed]

Other (5)

C. Conti, arXiv:quant-ph/0309069v3 (2003).

C. Conti, arXiv.org:quant-ph/0409130 (2004).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford U. Press, 2000).

E. Recami, M. Zamboni-Rached, and H. E. Hernandez-Figueroa, Localized Waves (Wiley-Interscience, 2007).

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Equations (15)

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E x ( r , t ) = R 0 d k f ( k ) J 0 ( sin θ 0 k r ) e i k cos θ 0 [ z ( c cos θ 0 ) ] ,
E ̂ ( r , t ) = k , s c k 2 ε 0 L 3 i a ̂ k , s e i ( k r c k t ) e k , s + h.c. ,
X = k , s D ̂ k , s [ Δ θ 0 ( k ) β ( k , s ) ] 0 ,
X E ̂ X = R [ k , s Δ θ 0 ( k ) 2 c k ε 0 L 3 i β ( k , s ) e i ( k r c k t ) e k , s ] ,
β ( k , s ) = ( 2 π ) 3 i δ θ ε 0 2 c k L 3 k k f s ( k ) ,
X E ̂ X = R { 0 d k k 2 0 2 π d ϕ [ f 1 ( k ) e k 1 + f 2 ( k ) e k 2 ] e i ( k r c k t ) } ,
X E ̂ X = R 0 d k f ( k ) [ J 0 ( sin θ 0 k r ) e x x tan θ 0 r J 1 ( sin θ 0 k r ) e z ] e i k cos θ 0 ( z V t ) ,
X E = k , s Δ θ 0 ( k ) Φ ( k , s ) D ̂ k , s [ α ( k , s ) ] 0 ,
X E a ̂ k s X E = Δ θ 0 ( k ) α ( k , s ) Q ( k , s ) ,
Q ( k , s ) = Φ ( k , s ) 2 + Φ ( k , s ) e ( 1 2 ) α ( k , s ) 2 k k , s s Δ θ 0 ( k ) Φ * ( k , s ) e ( 1 2 ) α ( k , s ) 2 ,
X E E ̂ X E = R [ k , s Δ θ 0 ( k ) G ( k , s ) e i ( k r c k t ) e k , s ] ,
X E projected = α 1 + Φ E 0 ,
x α 2 = e x 2 π [ 1 + Φ E 2 + 2 Φ E cos ( 2 α 1 x arg Φ E ) ] .
X out = e ( 1 2 ) r = 0 M α r 2 n 1 , n 2 , , n M = 0 e ( i 2 ) χ t m , p = 0 M n m n p q = 1 , 2 , , M α q n q n q ! n q .
X out = 1 2 ( e i π 4 X + e i π 4 X ) ,

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