Abstract

Reflection and refraction of spatial solitons at dielectric interfaces, accommodating arbitrarily angles of incidence, is studied. Analysis is based on Helmholtz soliton theory, which eliminates the angular restriction associated with the paraxial approximation. A novel generalization of Snell’s law is discovered that is valid for collimated light beams and the entire angular domain. Our new theoretical predictions are shown to be in excellent agreement with full numerical simulations. New qualitative features of soliton refraction and limitations of previous paraxial analyses are highlighted.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. S. McDonald and W. J. Firth, J. Opt. Soc. Am. B 7, 1328 (1990).
    [CrossRef]
  2. G. S. McDonald and W. J. Firth, J. Mod. Opt. 34, 612 (1990).
  3. P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Opt. Soc. Am. B 19, 1216 (2002).
    [CrossRef]
  4. P. Chamorro-Posada and G. S. McDonald, Phys. Rev. E 74, (2006).
    [CrossRef]
  5. S. Chi and Q. Guo, Opt. Lett. 20, 1598 (1995).
    [CrossRef] [PubMed]
  6. B. Crosignani, A. Yariv, and S. Mookherjea, Opt. Lett. 29, 1254 (2004).
    [CrossRef] [PubMed]
  7. A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
    [CrossRef] [PubMed]
  8. L. A. Nesterov, Opt. Spektrosk. 64, 1166 (1988).
  9. Yu. S. Kivshar, A. M. Kosevich, and A. O. Chubykalo, Phys. Rev. A 41, 1677 (1990).
    [CrossRef] [PubMed]
  10. Yu. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, Phys. Rev. E 53, 5409 (1996).
    [CrossRef]
  11. A. I. Smirnov and A. A. Zharov, in Soliton-Driven Photonics, A.D.Boardman and A.P.Sukhorukov, eds. (Kluwer Academic, 2001), pp. 141-167.
    [CrossRef]
  12. A. D. Boardman, P. Bontemps, W. Ilecki, and A. A. Zharov, J. Mod. Opt. 47, 1941 (2000).
  13. P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 45, 1111 (1998).
    [CrossRef]
  14. P. Chamorro-Posada and G. S. McDonald, Opt. Lett. 28, 825 (2003).
    [CrossRef] [PubMed]
  15. P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 47, 1877 (2000).
  16. P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, Opt. Commun. 192, 1 (2001).
    [CrossRef]

2006 (1)

P. Chamorro-Posada and G. S. McDonald, Phys. Rev. E 74, (2006).
[CrossRef]

2004 (1)

2003 (1)

2002 (1)

2001 (1)

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, Opt. Commun. 192, 1 (2001).
[CrossRef]

2000 (2)

A. D. Boardman, P. Bontemps, W. Ilecki, and A. A. Zharov, J. Mod. Opt. 47, 1941 (2000).

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 47, 1877 (2000).

1998 (1)

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 45, 1111 (1998).
[CrossRef]

1996 (1)

Yu. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, Phys. Rev. E 53, 5409 (1996).
[CrossRef]

1995 (1)

1990 (3)

G. S. McDonald and W. J. Firth, J. Opt. Soc. Am. B 7, 1328 (1990).
[CrossRef]

G. S. McDonald and W. J. Firth, J. Mod. Opt. 34, 612 (1990).

Yu. S. Kivshar, A. M. Kosevich, and A. O. Chubykalo, Phys. Rev. A 41, 1677 (1990).
[CrossRef] [PubMed]

1989 (1)

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef] [PubMed]

1988 (1)

L. A. Nesterov, Opt. Spektrosk. 64, 1166 (1988).

Aceves, A. B.

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef] [PubMed]

Aliev, Yu. M.

Yu. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, Phys. Rev. E 53, 5409 (1996).
[CrossRef]

Boardman, A. D.

A. D. Boardman, P. Bontemps, W. Ilecki, and A. A. Zharov, J. Mod. Opt. 47, 1941 (2000).

Yu. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, Phys. Rev. E 53, 5409 (1996).
[CrossRef]

Bontemps, P.

A. D. Boardman, P. Bontemps, W. Ilecki, and A. A. Zharov, J. Mod. Opt. 47, 1941 (2000).

Chamorro-Posada, P.

P. Chamorro-Posada and G. S. McDonald, Phys. Rev. E 74, (2006).
[CrossRef]

P. Chamorro-Posada and G. S. McDonald, Opt. Lett. 28, 825 (2003).
[CrossRef] [PubMed]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Opt. Soc. Am. B 19, 1216 (2002).
[CrossRef]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, Opt. Commun. 192, 1 (2001).
[CrossRef]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 47, 1877 (2000).

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 45, 1111 (1998).
[CrossRef]

Chi, S.

Chubykalo, A. O.

Yu. S. Kivshar, A. M. Kosevich, and A. O. Chubykalo, Phys. Rev. A 41, 1677 (1990).
[CrossRef] [PubMed]

Crosignani, B.

Firth, W. J.

G. S. McDonald and W. J. Firth, J. Mod. Opt. 34, 612 (1990).

G. S. McDonald and W. J. Firth, J. Opt. Soc. Am. B 7, 1328 (1990).
[CrossRef]

Guo, Q.

Ilecki, W.

A. D. Boardman, P. Bontemps, W. Ilecki, and A. A. Zharov, J. Mod. Opt. 47, 1941 (2000).

Kivshar, Yu. S.

Yu. S. Kivshar, A. M. Kosevich, and A. O. Chubykalo, Phys. Rev. A 41, 1677 (1990).
[CrossRef] [PubMed]

Kosevich, A. M.

Yu. S. Kivshar, A. M. Kosevich, and A. O. Chubykalo, Phys. Rev. A 41, 1677 (1990).
[CrossRef] [PubMed]

McDonald, G. S.

P. Chamorro-Posada and G. S. McDonald, Phys. Rev. E 74, (2006).
[CrossRef]

P. Chamorro-Posada and G. S. McDonald, Opt. Lett. 28, 825 (2003).
[CrossRef] [PubMed]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Opt. Soc. Am. B 19, 1216 (2002).
[CrossRef]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, Opt. Commun. 192, 1 (2001).
[CrossRef]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 47, 1877 (2000).

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 45, 1111 (1998).
[CrossRef]

G. S. McDonald and W. J. Firth, J. Mod. Opt. 34, 612 (1990).

G. S. McDonald and W. J. Firth, J. Opt. Soc. Am. B 7, 1328 (1990).
[CrossRef]

Moloney, J. V.

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef] [PubMed]

Mookherjea, S.

Nesterov, L. A.

L. A. Nesterov, Opt. Spektrosk. 64, 1166 (1988).

New, G. H. C.

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Opt. Soc. Am. B 19, 1216 (2002).
[CrossRef]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, Opt. Commun. 192, 1 (2001).
[CrossRef]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 47, 1877 (2000).

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 45, 1111 (1998).
[CrossRef]

Newell, A. C.

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef] [PubMed]

Smirnov, A. I.

Yu. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, Phys. Rev. E 53, 5409 (1996).
[CrossRef]

A. I. Smirnov and A. A. Zharov, in Soliton-Driven Photonics, A.D.Boardman and A.P.Sukhorukov, eds. (Kluwer Academic, 2001), pp. 141-167.
[CrossRef]

Xie, K.

Yu. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, Phys. Rev. E 53, 5409 (1996).
[CrossRef]

Yariv, A.

Zharov, A. A.

A. D. Boardman, P. Bontemps, W. Ilecki, and A. A. Zharov, J. Mod. Opt. 47, 1941 (2000).

Yu. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, Phys. Rev. E 53, 5409 (1996).
[CrossRef]

A. I. Smirnov and A. A. Zharov, in Soliton-Driven Photonics, A.D.Boardman and A.P.Sukhorukov, eds. (Kluwer Academic, 2001), pp. 141-167.
[CrossRef]

J. Mod. Opt. (4)

G. S. McDonald and W. J. Firth, J. Mod. Opt. 34, 612 (1990).

A. D. Boardman, P. Bontemps, W. Ilecki, and A. A. Zharov, J. Mod. Opt. 47, 1941 (2000).

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 45, 1111 (1998).
[CrossRef]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 47, 1877 (2000).

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

Opt. Commun. (1)

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, Opt. Commun. 192, 1 (2001).
[CrossRef]

Opt. Lett. (3)

Opt. Spektrosk. (1)

L. A. Nesterov, Opt. Spektrosk. 64, 1166 (1988).

Phys. Rev. A (2)

Yu. S. Kivshar, A. M. Kosevich, and A. O. Chubykalo, Phys. Rev. A 41, 1677 (1990).
[CrossRef] [PubMed]

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef] [PubMed]

Phys. Rev. E (2)

P. Chamorro-Posada and G. S. McDonald, Phys. Rev. E 74, (2006).
[CrossRef]

Yu. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, Phys. Rev. E 53, 5409 (1996).
[CrossRef]

Other (1)

A. I. Smirnov and A. A. Zharov, in Soliton-Driven Photonics, A.D.Boardman and A.P.Sukhorukov, eds. (Kluwer Academic, 2001), pp. 141-167.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Geometry of the interface problem: a spatial soliton is incident on a planar boundary (located at x = 0 ).

Fig. 2
Fig. 2

Generalized Snell’s law for Helmholtz solitons incident on a linear (left) and nonlinear (right) interface: theory (solid curves) and full simulations (dots).

Fig. 3
Fig. 3

Critical angle for Helmholtz solitons: theory (solid curves) and numerics (dots).

Equations (7)

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

κ 2 u ζ 2 + i u ζ + 1 2 2 u ξ 2 + u 2 u = [ Δ 4 κ + ( 1 α ) u 2 ] H ( ξ ) u .
Δ 1 ( n 02 n 01 ) 2 , α α 2 α 1 ,
u ( ξ , ζ ) = η 0 sech [ η 0 α ξ + V ζ 1 + 2 κ V 2 ] × exp [ i 1 + 2 κ η 0 2 1 + 2 κ V 2 ( V ξ + ζ 2 κ ) ] × exp ( i ζ 2 κ ) ,
V = { V 2 1 2 κ 1 + 2 κ V 2 1 + 2 κ η 0 2 [ Δ + ( 1 α ) 2 κ η 0 2 ] } 1 2
γ n 01 cos θ i = n 02 cos θ t ,
γ [ 1 + 2 κ η 0 2 1 + 2 κ η 0 2 α ( 1 Δ ) 1 ] 1 2
tan ( θ C ) = [ Δ + 2 κ η 0 2 ( 1 α ) 1 Δ + 2 κ η 0 2 α ] 1 2 .

Metrics