Soliton dynamics in a nonlocal medium

Journal of the Optical Society of America B: Optical Physics

Volumn 16, Issue 2, 1999, Pages 236-239

  Mitchell, D John ^a   Snyder, Allan W ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033479405     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.16.000236     Document Type: Article

References (22)

1. A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
2. Y. R. Shen, Science 276, 1520 (1997).
3. A. W. Snyder and D. J. Mitchell, [ Opt. Lett. 22, 16 (1997)] describe the mighty morphing spatial solitons and bullets that are characteristic of a highly saturating medium. The In I law had been introduced previously, unbeknown to us, in a different context. See, for example, I. Bialynicki- Birula and J. Mycielski, Phys. Scr. 20, 539 (1979). But no one seems to have recognized its relevance to optical spatial solitons, possibly because of its singularity at I = 0. However, Gausian beams in a In I medium induce parabolic index waveguides, which are a standard model in linear optics. Coming at the problem, as we do, from the linear perspective shows from the outset that In I is, like the parabolic index fiber, a good approximation.
4. A. W. Snyder and D. J. Mitchell, [ Opt. Lett. 22, 16 (1997)] describe the mighty morphing spatial solitons and bullets that are characteristic of a highly saturating medium. The In I law had been introduced previously, unbeknown to us, in a different context. See, for example, I. Bialynicki-Birula and J. Mycielski, Phys. Scr. 20, 539 (1979). But no one seems to have recognized its relevance to optical spatial solitons, possibly because of its singularity at I = 0. However, Gausian beams in a In I medium induce parabolic index waveguides, which are a standard model in linear optics. Coming at the problem, as we do, from the linear perspective shows from the outset that In I is, like the parabolic index fiber, a good approximation.
5. M. Segev, B. Crosignani, A. Yariv, and B. Fisher, Phys. Rev. Lett. 68, 923 (1993).
6. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
7. F. C. Khoo, Prog. Opt. 26, 107 (1988).
8. M. Mitchell and M. Segev, Nature (London) 387, 880 (1997).
9. V. Tikhonenko, Opt. Lett. 23, 594 (1998).
10. A. W. Snyder and A. P. Sheppard, Opt. Lett. 18, 482 (1993). A simple qualitative theory is advanced here to predict when annihilation, fusion, or birth occurs.
11. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992); B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, and G. Salamo, J. Opt. Soc. Am. B 10, 440 (1993); D. N. Christodoulides and M. I. Carvalho, Opt. Lett. 19, 1714 (1994); M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (1994); N. Fressegeas, J. Maufoy, and G. Kugel, Phys. Rev. E 54, 6866 (1996).
12. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992); B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, and G. Salamo, J. Opt. Soc. Am. B 10, 440 (1993); D. N. Christodoulides and M. I. Carvalho, Opt. Lett. 19, 1714 (1994); M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (1994); N. Fressegeas, J. Maufoy, and G. Kugel, Phys. Rev. E 54, 6866 (1996).
13. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992); B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, and G. Salamo, J. Opt. Soc. Am. B 10, 440 (1993); D. N. Christodoulides and M. I. Carvalho, Opt. Lett. 19, 1714 (1994); M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (1994); N. Fressegeas, J. Maufoy, and G. Kugel, Phys. Rev. E 54, 6866 (1996).
14. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992); B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, and G. Salamo, J. Opt. Soc. Am. B 10, 440 (1993); D. N. Christodoulides and M. I. Carvalho, Opt. Lett. 19, 1714 (1994); M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (1994); N. Fressegeas, J. Maufoy, and G. Kugel, Phys. Rev. E 54, 6866 (1996).
15. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992); B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, and G. Salamo, J. Opt. Soc. Am. B 10, 440 (1993); D. N. Christodoulides and M. I. Carvalho, Opt. Lett. 19, 1714 (1994); M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (1994); N. Fressegeas, J. Maufoy, and G. Kugel, Phys. Rev. E 54, 6866 (1996).
16. Section 8 of Ref. 12 shows that Maxwell's equations for transverse field E are equivalent to the Schrödinger equation, provided only that the medium is homogeneous. This is so because the maximum nonlinear induced refractive-index change is small.
17. A. W. Snyder, D. J. Mitchell, and Yu. S. Kivshar, Mod. Phys. Lett. B 9, 1479 (1995).
18. 2) = 0. Equation (4) follows immediately.
19. min immediately yields Eq. (10).
20. y satisfy Eq. (4).
21. M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996).
22. W. Krolikowski and S. A. Holmstrom, Opt. Lett. 22, 369 (1997).