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)

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

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

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]

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

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

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)

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

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

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

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

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]

Physica D (Amsterdam) (1)

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

Science (2)

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

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

Other (3)

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).

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

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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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