Abstract

We investigate the propagation of optical solitons interacting with linear defects in the medium. We show that solitons exhibit a wave-particle dualism versus power, i.e., depending on the relative size of soliton and defect, responsible for a soliton trajectory dependent on its waist.

© 2011 Optical Society of America

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References

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  1. W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2006).
    [CrossRef]
  2. G. Della Valle, M. Savoini, M. Ornigotti, P. Laporta, V. Foglietti, M. Finazzi, L. Duò, and S. Longhi, Phys. Rev. Lett. 102, 180402 (2009).
    [CrossRef] [PubMed]
  3. F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, Phys. Rev. Lett. 105, 143902(2010).
    [CrossRef]
  4. T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, Science 319, 1367 (2008).
    [CrossRef] [PubMed]
  5. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
    [CrossRef]
  6. S.-C. Lei, T.-K. Ng, and R.-K. Lee, Opt. Express 18, 14586 (2010).
    [CrossRef] [PubMed]
  7. Y. S. Kivshar and G. P. Agrawal, Optical Solitons(Academic, 2003).
  8. R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
    [CrossRef]
  9. A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  10. G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
    [CrossRef] [PubMed]
  11. C. Conti and G. Assanto, in Encyclopedia of Modern Optics (Elsevier, 2004), Vol.  5, p. 43.
  12. J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, 1994).
  13. D. J. Mitchell, A. W. Snyder, and L. Poladian, Phys. Rev. Lett. 77, 271 (1996).
    [CrossRef] [PubMed]
  14. J. S. Roman, C. Ruiz, J. A. Perez, D. Delgado, C. Mendez, L. Plaja, and L. Roso, Opt. Express 14, 2817 (2006).
    [CrossRef]
  15. X. D. Cao and B. A. Malomed, Phys. Lett. A 206, 177(1995).
    [CrossRef]
  16. R. H. Goodman, P. J. Holmes, and M. I. Weinstein, Physica D (Amsterdam) 192, 215 (2004).
    [CrossRef]
  17. Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, Phys. Rev. Lett. 99, 133901 (2007).
    [CrossRef] [PubMed]
  18. S. Burtsev, D. J. Kaup, and B. A. Malomed, Phys. Rev. E 52, 4474 (1995).
    [CrossRef]
  19. A. Fratalocchi and G. Assanto, Opt. Lett. 31, 1489(2006).
    [CrossRef] [PubMed]
  20. A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
    [CrossRef] [PubMed]
  21. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
    [CrossRef]
  22. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Phys. Rev. Lett. 101, 153902 (2008).
    [CrossRef] [PubMed]
  23. A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, Phys. Rev. Lett. 100, 153901 (2008).
    [CrossRef] [PubMed]
  24. E. N. Tsoy and C. M. de Sterke, Phys. Lett. A 372, 1856 (2008).
    [CrossRef]

2010 (2)

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, Phys. Rev. Lett. 105, 143902(2010).
[CrossRef]

S.-C. Lei, T.-K. Ng, and R.-K. Lee, Opt. Express 18, 14586 (2010).
[CrossRef] [PubMed]

2009 (1)

G. Della Valle, M. Savoini, M. Ornigotti, P. Laporta, V. Foglietti, M. Finazzi, L. Duò, and S. Longhi, Phys. Rev. Lett. 102, 180402 (2009).
[CrossRef] [PubMed]

2008 (4)

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, Science 319, 1367 (2008).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Phys. Rev. Lett. 101, 153902 (2008).
[CrossRef] [PubMed]

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, Phys. Rev. Lett. 100, 153901 (2008).
[CrossRef] [PubMed]

E. N. Tsoy and C. M. de Sterke, Phys. Lett. A 372, 1856 (2008).
[CrossRef]

2007 (1)

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, Phys. Rev. Lett. 99, 133901 (2007).
[CrossRef] [PubMed]

2006 (4)

2004 (1)

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, Physica D (Amsterdam) 192, 215 (2004).
[CrossRef]

1999 (2)

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

1996 (1)

D. J. Mitchell, A. W. Snyder, and L. Poladian, Phys. Rev. Lett. 77, 271 (1996).
[CrossRef] [PubMed]

1995 (2)

X. D. Cao and B. A. Malomed, Phys. Lett. A 206, 177(1995).
[CrossRef]

S. Burtsev, D. J. Kaup, and B. A. Malomed, Phys. Rev. E 52, 4474 (1995).
[CrossRef]

1989 (1)

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

1973 (1)

A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Aceves, A. B.

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

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons(Academic, 2003).

Aimez, V.

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, Phys. Rev. Lett. 99, 133901 (2007).
[CrossRef] [PubMed]

Aitchison, J. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Ares, R.

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, Phys. Rev. Lett. 99, 133901 (2007).
[CrossRef] [PubMed]

Assanto, G.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Phys. Rev. Lett. 101, 153902 (2008).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

A. Fratalocchi and G. Assanto, Opt. Lett. 31, 1489(2006).
[CrossRef] [PubMed]

C. Conti and G. Assanto, in Encyclopedia of Modern Optics (Elsevier, 2004), Vol.  5, p. 43.

Bar-Ad, S.

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, Phys. Rev. Lett. 99, 133901 (2007).
[CrossRef] [PubMed]

Barak, A.

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, Phys. Rev. Lett. 100, 153901 (2008).
[CrossRef] [PubMed]

Burtsev, S.

S. Burtsev, D. J. Kaup, and B. A. Malomed, Phys. Rev. E 52, 4474 (1995).
[CrossRef]

Cao, X. D.

X. D. Cao and B. A. Malomed, Phys. Lett. A 206, 177(1995).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Conti, C.

C. Conti and G. Assanto, in Encyclopedia of Modern Optics (Elsevier, 2004), Vol.  5, p. 43.

de Sterke, C. M.

E. N. Tsoy and C. M. de Sterke, Phys. Lett. A 372, 1856 (2008).
[CrossRef]

Delgado, D.

Della Valle, G.

G. Della Valle, M. Savoini, M. Ornigotti, P. Laporta, V. Foglietti, M. Finazzi, L. Duò, and S. Longhi, Phys. Rev. Lett. 102, 180402 (2009).
[CrossRef] [PubMed]

Dreisow, F.

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, Phys. Rev. Lett. 105, 143902(2010).
[CrossRef]

Duò, L.

G. Della Valle, M. Savoini, M. Ornigotti, P. Laporta, V. Foglietti, M. Finazzi, L. Duò, and S. Longhi, Phys. Rev. Lett. 102, 180402 (2009).
[CrossRef] [PubMed]

Dyadyusha, A.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Phys. Rev. Lett. 101, 153902 (2008).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Eisenberg, H. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Finazzi, M.

G. Della Valle, M. Savoini, M. Ornigotti, P. Laporta, V. Foglietti, M. Finazzi, L. Duò, and S. Longhi, Phys. Rev. Lett. 102, 180402 (2009).
[CrossRef] [PubMed]

Fleischer, J. W.

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2006).
[CrossRef]

Foglietti, V.

G. Della Valle, M. Savoini, M. Ornigotti, P. Laporta, V. Foglietti, M. Finazzi, L. Duò, and S. Longhi, Phys. Rev. Lett. 102, 180402 (2009).
[CrossRef] [PubMed]

Fratalocchi, A.

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Goodman, R. H.

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, Physica D (Amsterdam) 192, 215 (2004).
[CrossRef]

Hasegawa, A.

A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Heinrich, M.

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, Phys. Rev. Lett. 105, 143902(2010).
[CrossRef]

Hill, S.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, Science 319, 1367 (2008).
[CrossRef] [PubMed]

Holmes, P. J.

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, Physica D (Amsterdam) 192, 215 (2004).
[CrossRef]

Jia, S.

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2006).
[CrossRef]

Kaczmarek, M.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Phys. Rev. Lett. 101, 153902 (2008).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Kaup, D. J.

S. Burtsev, D. J. Kaup, and B. A. Malomed, Phys. Rev. E 52, 4474 (1995).
[CrossRef]

Keil, R.

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, Phys. Rev. Lett. 105, 143902(2010).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons(Academic, 2003).

Konig, F.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, Science 319, 1367 (2008).
[CrossRef] [PubMed]

Kuklewicz, C.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, Science 319, 1367 (2008).
[CrossRef] [PubMed]

Laporta, P.

G. Della Valle, M. Savoini, M. Ornigotti, P. Laporta, V. Foglietti, M. Finazzi, L. Duò, and S. Longhi, Phys. Rev. Lett. 102, 180402 (2009).
[CrossRef] [PubMed]

Lee, R.-K.

Lei, S.-C.

Leonhardt, U.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, Science 319, 1367 (2008).
[CrossRef] [PubMed]

Linzon, Y.

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, Phys. Rev. Lett. 99, 133901 (2007).
[CrossRef] [PubMed]

Longhi, S.

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, Phys. Rev. Lett. 105, 143902(2010).
[CrossRef]

G. Della Valle, M. Savoini, M. Ornigotti, P. Laporta, V. Foglietti, M. Finazzi, L. Duò, and S. Longhi, Phys. Rev. Lett. 102, 180402 (2009).
[CrossRef] [PubMed]

Malomed, B. A.

X. D. Cao and B. A. Malomed, Phys. Lett. A 206, 177(1995).
[CrossRef]

S. Burtsev, D. J. Kaup, and B. A. Malomed, Phys. Rev. E 52, 4474 (1995).
[CrossRef]

Mendez, C.

Mitchell, D. J.

D. J. Mitchell, A. W. Snyder, and L. Poladian, Phys. Rev. Lett. 77, 271 (1996).
[CrossRef] [PubMed]

Moloney, J. V.

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

Morandotti, R.

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, Phys. Rev. Lett. 99, 133901 (2007).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Newell, A. C.

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

Ng, T.-K.

Nolte, S.

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, Phys. Rev. Lett. 105, 143902(2010).
[CrossRef]

Ornigotti, M.

G. Della Valle, M. Savoini, M. Ornigotti, P. Laporta, V. Foglietti, M. Finazzi, L. Duò, and S. Longhi, Phys. Rev. Lett. 102, 180402 (2009).
[CrossRef] [PubMed]

Peccianti, M.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Phys. Rev. Lett. 101, 153902 (2008).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Peleg, O.

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, Phys. Rev. Lett. 100, 153901 (2008).
[CrossRef] [PubMed]

Perez, J. A.

Peschel, U.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Philbin, T. G.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, Science 319, 1367 (2008).
[CrossRef] [PubMed]

Plaja, L.

Poladian, L.

D. J. Mitchell, A. W. Snyder, and L. Poladian, Phys. Rev. Lett. 77, 271 (1996).
[CrossRef] [PubMed]

Robertson, S.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, Science 319, 1367 (2008).
[CrossRef] [PubMed]

Roman, J. S.

Roso, L.

Ruiz, C.

Sakurai, J. J.

J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, 1994).

Savoini, M.

G. Della Valle, M. Savoini, M. Ornigotti, P. Laporta, V. Foglietti, M. Finazzi, L. Duò, and S. Longhi, Phys. Rev. Lett. 102, 180402 (2009).
[CrossRef] [PubMed]

Segev, M.

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, Phys. Rev. Lett. 100, 153901 (2008).
[CrossRef] [PubMed]

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Silberberg, Y.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Snyder, A. W.

D. J. Mitchell, A. W. Snyder, and L. Poladian, Phys. Rev. Lett. 77, 271 (1996).
[CrossRef] [PubMed]

Soffer, A.

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, Phys. Rev. Lett. 100, 153901 (2008).
[CrossRef] [PubMed]

Stegeman, G. I.

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Stucchio, C.

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, Phys. Rev. Lett. 100, 153901 (2008).
[CrossRef] [PubMed]

Szameit, A.

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, Phys. Rev. Lett. 105, 143902(2010).
[CrossRef]

Tappert, F.

A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Tsoy, E. N.

E. N. Tsoy and C. M. de Sterke, Phys. Lett. A 372, 1856 (2008).
[CrossRef]

Tünnermann, A.

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, Phys. Rev. Lett. 105, 143902(2010).
[CrossRef]

Volatier, M.

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, Phys. Rev. Lett. 99, 133901 (2007).
[CrossRef] [PubMed]

Wan, W.

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2006).
[CrossRef]

Weinstein, M. I.

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, Physica D (Amsterdam) 192, 215 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Nat. Phys. (2)

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2006).
[CrossRef]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Lett. A (2)

E. N. Tsoy and C. M. de Sterke, Phys. Lett. A 372, 1856 (2008).
[CrossRef]

X. D. Cao and B. A. Malomed, Phys. Lett. A 206, 177(1995).
[CrossRef]

Phys. Rev. A (1)

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

Phys. Rev. E (1)

S. Burtsev, D. J. Kaup, and B. A. Malomed, Phys. Rev. E 52, 4474 (1995).
[CrossRef]

Phys. Rev. Lett. (8)

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Phys. Rev. Lett. 101, 153902 (2008).
[CrossRef] [PubMed]

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, Phys. Rev. Lett. 100, 153901 (2008).
[CrossRef] [PubMed]

D. J. Mitchell, A. W. Snyder, and L. Poladian, Phys. Rev. Lett. 77, 271 (1996).
[CrossRef] [PubMed]

Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, Phys. Rev. Lett. 99, 133901 (2007).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

G. Della Valle, M. Savoini, M. Ornigotti, P. Laporta, V. Foglietti, M. Finazzi, L. Duò, and S. Longhi, Phys. Rev. Lett. 102, 180402 (2009).
[CrossRef] [PubMed]

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, Phys. Rev. Lett. 105, 143902(2010).
[CrossRef]

Physica D (Amsterdam) (1)

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, Physica D (Amsterdam) 192, 215 (2004).
[CrossRef]

Science (2)

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, Science 319, 1367 (2008).
[CrossRef] [PubMed]

Other (3)

Y. S. Kivshar and G. P. Agrawal, Optical Solitons(Academic, 2003).

C. Conti and G. Assanto, in Encyclopedia of Modern Optics (Elsevier, 2004), Vol.  5, p. 43.

J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, 1994).

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Figures (4)

Fig. 1
Fig. 1

(a) Soliton profiles for u 0 = 1 (blue solid curve), n L (red dashes), and n L / X (dashed-dotted black curve) versus X. (b) Force acting on soliton versus X and 1 / u 0 computed from Eq. (2). (c) Force versus soliton position X (solid and dashed curves correspond to all terms and terms up to m = 2 in Eq. (3), respectively) for soliton widths 1 / u 0 = 0.01 , 0.17 and 0.37, with narrower soliton corresponding to larger forces (in modulus). Here Δ = 1 .

Fig. 2
Fig. 2

Number of interference fringes in the soliton profile versus input for Δ = 1 (blue stars), 2 (green squares), 3 (red crosses) for X 0 = 2 . The insets show the corresponding profiles at Z = 20 for u 0 = 0.1 (left) and 2.5 (right), respectively.

Fig. 3
Fig. 3

Evolution in X Z for various input powers (legends) and beam positions X 0 = 0 (first row) and X 0 = 0.5 (second row), with Δ = 1 . The white rectangles indicate the defect location.

Fig. 4
Fig. 4

Soliton deflection versus power for X 0 = 0 (blue stars), 0.5 (black crosses), 1 (magenta circles), 1.5 (green squares), 2 (red diamonds) and Δ = 1 (solid curve), 2 (dashed curve), 3 (dash-dots).

Equations (3)

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

i u Z + 1 2 2 u X 2 + | u | 2 u p V eff ( X , Z ) u = 0 ,
d 2 X d Z 2 = p ψ V eff X d X .
d 2 X d Z 2 = p m = 0 W m ( X ) y m ψ ,

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