Abstract

We study self-localized second-band vortex states in two-dimensional photonic lattices and find stable ring solitons whose phase forms an array of counterrotating vortices. We also identify composite solitons in which a second-band vortex is jointly trapped with a mode arising from the first band and study their stability. When such a composite entity is unstable, it disintegrates while exchanging angular momentum between its constituents, eventually stabilizing into another form of composite soliton.

© 2004 Optical Society of America

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  1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  2. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  3. H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  4. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef]
  5. D. Neshev, E. Ostrovskaya, Yu. S. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  6. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
    [CrossRef]
  7. J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
    [CrossRef]
  8. N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
    [CrossRef]
  9. B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
    [CrossRef]
  10. J. Yang and Z. H. Musslimani, Opt. Lett. 28, 2094 (2003).
    [CrossRef] [PubMed]
  11. E. A. Ostrovskaya and Y. S. Kivshar, Opt. Express 12, 19 (2004), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  12. J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
    [CrossRef]
  13. N. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
    [CrossRef]
  14. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  15. J. W. Fleischer, G. Bartal, O. Chen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
    [CrossRef]
  16. D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
    [CrossRef]
  17. O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
    [CrossRef]
  18. V. I. Kruglov, Y. A. Logvin, and V. M. Volkov, J. Mod. Opt. 39, 2277 (1992).
    [CrossRef]
  19. A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
    [CrossRef]

2004 (3)

J. W. Fleischer, G. Bartal, O. Chen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef]

E. A. Ostrovskaya and Y. S. Kivshar, Opt. Express 12, 19 (2004), http://www.opticsexpress.org .
[CrossRef] [PubMed]

2003 (11)

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

D. Neshev, E. Ostrovskaya, Yu. S. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

J. Yang and Z. H. Musslimani, Opt. Lett. 28, 2094 (2003).
[CrossRef] [PubMed]

2002 (1)

N. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

2001 (1)

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

1998 (1)

H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

1992 (1)

V. I. Kruglov, Y. A. Logvin, and V. M. Volkov, J. Mod. Opt. 39, 2277 (1992).
[CrossRef]

1988 (1)

Aitchison, J.

H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Aitchison, J. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

Alexander, T. J.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef]

Bartal, G.

J. W. Fleischer, G. Bartal, O. Chen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef]

Boyd, A.

H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

Chen, O.

J. W. Fleischer, G. Bartal, O. Chen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef]

Chen, Z.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef]

Christodoulides, D. N.

J. W. Fleischer, G. Bartal, O. Chen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

N. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
[CrossRef] [PubMed]

Cohen, O.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

Efremidis, N.

N. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

Eisenberg, H.

H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Eisenberg, H. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, G. Bartal, O. Chen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

N. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Hudock, J.

J. W. Fleischer, G. Bartal, O. Chen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef]

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[CrossRef]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

Joseph, R. I.

Kevrekidis, P. G.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[CrossRef]

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Kivshar, Y. S.

Kivshar, Yu. S.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef]

D. Neshev, E. Ostrovskaya, Yu. S. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef]

Krolikowski, W.

Kruglov, V. I.

V. I. Kruglov, Y. A. Logvin, and V. M. Volkov, J. Mod. Opt. 39, 2277 (1992).
[CrossRef]

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Logvin, Y. A.

V. I. Kruglov, Y. A. Logvin, and V. M. Volkov, J. Mod. Opt. 39, 2277 (1992).
[CrossRef]

Malomed, B. A.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[CrossRef]

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Mandelik, D.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

Manela, O.

J. W. Fleischer, G. Bartal, O. Chen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef]

Martin, H.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef]

Meier, J.

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

Morandotti, R.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Musslimani, Z. H.

Neshev, D.

Neshev, D. N.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef]

Ostrovskaya, E.

Ostrovskaya, E. A.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef]

E. A. Ostrovskaya and Y. S. Kivshar, Opt. Express 12, 19 (2004), http://www.opticsexpress.org .
[CrossRef] [PubMed]

Schwartz, T.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

Sears, S.

N. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Segev, M.

J. W. Fleischer, G. Bartal, O. Chen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

N. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Silberberg, Y.

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Stegeman, G.

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

Sukhorukov, A. A.

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef]

Volkov, V. M.

V. I. Kruglov, Y. A. Logvin, and V. M. Volkov, J. Mod. Opt. 39, 2277 (1992).
[CrossRef]

Yang, J.

J. Mod. Opt. (1)

V. I. Kruglov, Y. A. Logvin, and V. M. Volkov, J. Mod. Opt. 39, 2277 (1992).
[CrossRef]

Nature (2)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. E (3)

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[CrossRef]

N. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Phys. Rev. Lett. (9)

J. W. Fleischer, G. Bartal, O. Chen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) First two bands of the transmission spectrum in a 2D square lattice with D=10. (b) High-symmetry points of the reciprocal lattice. (c) Phase structure of a counterrotating vortex array, with arrows showing the direction of increasing phase in each vortex.

Fig. 2
Fig. 2

(a), (b) Intensity and phase of a scalar second- band vortex lattice soliton. (c) Linear diffraction after z=100. (d) Intensity after propagation of z=10,000. (e) Total power of the soliton as a function of the propagation constant and peak soliton intensity for D=16 and V0=1.1. The dot represents the soliton shown in (a) and (b). The white circles in (b) and (c) indicate the waveguide boundaries.

Fig. 3
Fig. 3

Vector soliton: (a) intensity of first-band component and (b), (c) intensity and phase of the vortex component arising from the second band. (d) Evolution of the propagation constants of the two components (solid curves), and the propagation constants of the induced defect modes (dotted curves). When the composite entity destabilizes, its second (initially second-band) component transforms into a scalar first-band lattice soliton, whereas its first (initially first-band) component becomes localized by the defect induced by the second component.

Equations (1)

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iψz+2ψ+-11+Vx,y+Iψ=0,

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