Bright and dark solitary waves in the presence of third-harmonic generation

Journal of the Optical Society of America B: Optical Physics

Volumn 15, Issue 5, 1998, Pages 1488-1496

  Sammut, Rowland A ^a,b   Buryak, Alexander V ^a,b   Kivshar, Yuri S ^b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032400322     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.15.001488     Document Type: Article

References (32)

1. D. L. Mills, Nonlinear Optics: Basic Concepts (Springer-Verlag, Berlin, 1991); R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).
2. D. L. Mills, Nonlinear Optics: Basic Concepts (Springer-Verlag, Berlin, 1991); R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).
3. I. V. Tomov and M. C. Richardson, IEEE J. Quantum Electron. 12, 521 (1976).
4. (2) materials, G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
5. Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976); A. A. Kanashov and A. M. Rubenchik, Physica D 4, 122 (1981); R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993); A. V. Buryak and Yu. S. Kivshar, Opt. Lett. 19, 1612 (1994); L. Torner, C. R. Menyuk, and G. I. Stegeman, Opt. Lett. 19, 1615 (1994).
6. Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976); A. A. Kanashov and A. M. Rubenchik, Physica D 4, 122 (1981); R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993); A. V. Buryak and Yu. S. Kivshar, Opt. Lett. 19, 1612 (1994); L. Torner, C. R. Menyuk, and G. I. Stegeman, Opt. Lett. 19, 1615 (1994).
7. Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976); A. A. Kanashov and A. M. Rubenchik, Physica D 4, 122 (1981); R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993); A. V. Buryak and Yu. S. Kivshar, Opt. Lett. 19, 1612 (1994); L. Torner, C. R. Menyuk, and G. I. Stegeman, Opt. Lett. 19, 1615 (1994).
8. Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976); A. A. Kanashov and A. M. Rubenchik, Physica D 4, 122 (1981); R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993); A. V. Buryak and Yu. S. Kivshar, Opt. Lett. 19, 1612 (1994); L. Torner, C. R. Menyuk, and G. I. Stegeman, Opt. Lett. 19, 1615 (1994).
9. Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976); A. A. Kanashov and A. M. Rubenchik, Physica D 4, 122 (1981); R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993); A. V. Buryak and Yu. S. Kivshar, Opt. Lett. 19, 1612 (1994); L. Torner, C. R. Menyuk, and G. I. Stegeman, Opt. Lett. 19, 1615 (1994).
10. A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).
11. D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
12. A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996).
13. A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).
14. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996); R. A. Furst, D. M. Baboiu, B. L. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
15. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996); R. A. Furst, D. M. Baboiu, B. L. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
16. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996); R. A. Furst, D. M. Baboiu, B. L. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
17. S. Saltiel, S. Tanev, and A. D. Boardman, Opt. Lett. 22, 148 (1997).
18. See, e.g., R. W. Micallef, V. V. Afanasjev, Yu. S. Kivshar, and J. D. Love, Phys. Rev. E 54, 2936 (1996) and references therein.
19. N. A. Ansari, R. A. Sammut, and H. T. Tran, J. Opt. Soc. Am. B 13, 1419 (1996); 14, 298 (1997).
20. N. A. Ansari, R. A. Sammut, and H. T. Tran, J. Opt. Soc. Am. B 13, 1419 (1996); 14, 298 (1997).
21. This exact solution has been presented previously in the papers by K. Hayata and M. Koshiba, Opt. Lett. 19, 1717 (1994), and Y. Chen, Phys. Rev. A 50, 5145 (1994). However, unlike the theory of solitary waves in quadratic media, in the case of third-harmonic generation the exact hyperbolic-secant-like solution does not give any useful information about the families of proper (stable) two-wave solitary waves.
22. This exact solution has been presented previously in the papers by K. Hayata and M. Koshiba, Opt. Lett. 19, 1717 (1994), and Y. Chen, Phys. Rev. A 50, 5145 (1994). However, unlike the theory of solitary waves in quadratic media, in the case of third-harmonic generation the exact hyperbolic-secant-like solution does not give any useful information about the families of proper (stable) two-wave solitary waves.
23. A. E. Kaplan, Phys. Rev. Lett. 55, 1291 (1985); IEEE J. Quantum Electron. 21, 1538 (1985).
24. A. E. Kaplan, Phys. Rev. Lett. 55, 1291 (1985); IEEE J. Quantum Electron. 21, 1538 (1985).
25. A. W. Snyder, D. J. Mitchell, and A. V. Buryak, J. Opt. Soc. Am. B 13, 1146 (1996).
26. Yu. S. Kivshar and W. Krolikowski, Opt. Lett. 20, 1527 (1995); Yu. S. Kivshar and V. V. Afanasjev, Opt. Lett. 21, 1135 (1996); D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, Phys. Rev. E 54, 2015 (1996).
27. Yu. S. Kivshar and W. Krolikowski, Opt. Lett. 20, 1527 (1995); Yu. S. Kivshar and V. V. Afanasjev, Opt. Lett. 21, 1135 (1996); D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, Phys. Rev. E 54, 2015 (1996).
28. Yu. S. Kivshar and W. Krolikowski, Opt. Lett. 20, 1527 (1995); Yu. S. Kivshar and V. V. Afanasjev, Opt. Lett. 21, 1135 (1996); D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, Phys. Rev. E 54, 2015 (1996).
29. See the review paper by Yu. S. Kivshar and B. Luther-Davies, "Dark optical solitons: physics and applications," Phys. Rep. (to be published).
30. A. V. Buryak, Phys. Rev. E 52, 1156 (1995); "Solitons due to second harmonic generation," Ph.D. dissertation (The Australian National University, Canberra, Australia, 1996).
31. A. V. Buryak, Phys. Rev. E 52, 1156 (1995); "Solitons due to second harmonic generation," Ph.D. dissertation (The Australian National University, Canberra, Australia, 1996).
32. A. V. Buryak and Yu. S. Kivshar, Phys. Rev. A 51, R41 (1995).