Generation and nonlinear dynamics of X waves of the Schrödinger equation

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 70, Issue 4 2, 2004, Pages

  Conti, Claudio ^a  

^a ROMA TRE UNIVERSITY   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; DYNAMICS; FOURIER TRANSFORMS; MATHEMATICAL MODELS; NONLINEAR OPTICS; OPTICAL KERR EFFECT; PERTURBATION TECHNIQUES; QUANTUM THEORY; REFRACTIVE INDEX; SOLITONS; THREE DIMENSIONAL; WATER;

BEAM REPLENISHMENT; PULSE SPLITTING; SCHRÖDINGER EQUATION; THREE DIMENSIONAL SCHRÖDINGER MODEL; X WAVES;

ACOUSTIC WAVES;

EID: 41349112369     PISSN: 15393755     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.70.046613     Document Type: Article

References (65)

1. J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
2. J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 441 (1992).
3. J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
4. P. Saari, e-print physics/0103054.
5. E. Recami, M. Zamboni-Rached, K. Z. Nobrega, C. A. Dar tora, and H. E. Hernandez, IEEE J. Sel. Top. Quantum Electron. 9, 59 (2003).
6. G. Valiulis, J. Kilius, O. Jedrkiewicz, A. Bramati, S. Minardi, C. Conti, S. Trillo, A. Piskarskas, and P. Di Trapani, in Quantum Electronics and Laser Science Conference, Vol. 57 of Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2001).
7. P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
8. O. Jedrkiewicz, J. Trull, G. Valiulis, A. Piskarskas, C. Conti, S. Trillo, and P. Di Trapani, Phys. Rev. E 68, 026610 (2003).
9. J. Trull, O. Jedrkiewicz, P. Di Trapani, A. Matijosius, A. Varanavicius, G. Valiulis, R. Danielius, E. Kucinskas, A. Piskarskas, and S. Trillo, Phys. Rev. E 69, 026607 (2004).
10. D. Faccio, P. Di Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, and A. Matijosius, e-print physics/0405086v1.
11. C. Conti, S. Trillo, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, and P. Di Trapani, Phys. Rev. Lett. 90, 170406 (2003).
12. S. Trillo, C. Conti, P. D. Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, Opt. Lett. 27, 1451 (2002).
13. S. Orlov, A. Piskarskas, and A. Stabinis, Opt. Lett. 27, 2103 (2002).
14. S. Orlov, A. Piskarskas, and A. Stabinis, Opt. Lett. 27, 2167 (2002).
15. C. Conti and S. Trillo, Opt. Lett. 28, 1251 (2002).
16. M. A. Porras, S. Trillo, C. Conti, and P. Di Trapani, Opt. Lett. 28, 1090 (2003).
17. M. A. Porras and P. Di Trapani, e-print physics/0309084v1.
18. M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
19. A. Ciattoni, C. Conti, and P. Di Porto, J. Opt. Soc. Am. A 21, 451 (2004).
20. S. Longhi, Phys. Rev. E 68, 066612 (2004).
21. S. Longhi, Phys. Rev. E 69, 016606 (2004).
22. S. Longhi, Opt. Lett. 29, 147 (2004).
23. R. Butkus, S. Orlov, A. Piskarskas, V. Smilgevičius, and A. Stabinis, Opt. Commun. 227, 237 (2003).
24. C. Conti, e-print quant-ph/0309069v3.
25. R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, J. Opt. Soc. Am. A 10, 75 (1993).
26. P. Saari and K. Reivelt, Phys. Rev. Lett. 79, 4135 (1997).
27. A. M. Shaarawi, J. Opt. Soc. Am. A 14, 1804 (1997).
28. K. Reivelt and P. Saari, J. Opt. Soc. Am. A 17, 1785 (2000).
29. C. J. R. Sheppard, J. Opt. Soc. Am. A 19, 2218 (2002).
30. R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, Phys. Rev. A 67, 063820 (2003).
31. A. Ciattoni, C. Conti, and P. Di Porto, Phys. Rev. E 69, 036608 (2004).
32. C. Conti and S. Trillo, Phys. Rev. Lett. 92, 120404 (2004).
33. C. Conti, Phys. Rev. E 68, 016606 (2003).
34. A. Dubietis, G. Tamosauskas, I. Diomin, and A. Varanavicius, Opt. Lett. 28, 1269 (2003).
35. M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
36. P. Chernev and V. Petrov, Opt. Lett. 17, 172 (1992).
37. J. Rothenberg, Opt. Lett. 17, 583 (1992).
38. J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, Phys. Rev. Lett. 77, 3783 (1996).
39. L. Bergé, J. J. Rasmussen, E. G. Shapiro, and S. K. Turitsyn, J. Opt. Soc. Am. B 13, 1879 (1996).
40. T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997).
41. M. Trippenbach and Y. B. Band, Phys. Rev. A 56, 4242 (1997).
42. S. A. Diddams, H. K. Eaton, A. A. Zozulya, and T. S. Clement, Opt. Lett. 23, 379 (1998).
43. J. T. Manassah and B. Gross, Opt. Commun. 158, 105 (1998).
44. A. G. Litvak, V. A. Mironov, and E. M. Sher, Phys. Rev. E 61, 891 (2000).
45. L. Bergé, K. Germaschewski, R. Grauer, and J. J. Rasmussen, Phys. Rev. Lett. 89, 153902 (2002).
46. A. Matijosius, J. Trull, P. Di Trapani, A. Dubietis, R. Piskars-kas, A. Varanavicius, and A. Piskarskas, e-print physics/ 0312036v1.
47. E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. France, F. Salin, and A. Mysyrowicz, Opt. Lett. 21, 62 (1996).
48. O. G. Kosareva, V. P. Kandidov, C. Y. Brodeur, A. Chien, and S. L. Chin, Opt. Lett. 22, 1332 (1997).
49. H. Zeng, J. Wu, H. Xu, K. Wu, and E. Wu, Phys. Rev. Lett. 92, 143903 (2004).
50. 0, it is V=1/(β+k′).
51. In this paper the term X wave is defined by the mathematical expression. Different definitions can be found in the literature; (see the cited references) however, they are not directly useful in the presence of material dispersion or of nonlinearity, or for envelope X waves.
52. C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1985).
53. J. Lu and A. Liu, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1472 (2000).
54. J. Salo and M. M. Salomaa, J. Phys. A 34, 9319 (2001).
55. In principle, even the harmonic generation by a pump X wave, traveling at a given velocity could be considered.
56. Phys. Rev. Focus 12 (2003), story 7 (http://focus.aps.org/story/ v12/st7).
57. W. Torruellas, Y. S. Kivshar, and G. I. Stegeman, in Spatial Solitons, edited by S. Trillo and W. Torruellas (Springer-Verlag, Berlin, 2001).
58. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integral and Series (Taylor & Francis, New York, 1986), Vol. 2.
59. J. Moloney and A. Newell, Nonlinear Optics (Westview Press, New York, 2003).
60. G. Kaiser, Phys. Lett. A 168, 28 (1992).
61. Care is needed because of the use of the inverse functions and corresponding branch cuts. The use of the complex ln(z) enables treating together the branches μ<0 and μ>0.
62. G. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, New York, 2001).
63. M. Zamboni-Rached, H. E. Hernandez-Figueroa, and E. Re-cami, e-print physics/0405059v2.
64. A. M. Shaarawi, I. M. Besieris, and T. M. Said, J. Opt. Soc. Am. A 20, 1658 (2003).
65. M. Zamboni-Rached, A. M. Shaarawi, and E. Recami, e-print physics/0309098v1.