Abstract

We investigate light-beam propagation along the interface between linear and nonlinear media with parity–time symmetry. A novel class of two-dimensional localized surface modes (LSMs) is found analytically and numerically. If the potential is parity–time invariant along the direction parallel to the interface between the two media, stable LSMs can exist. Otherwise, if the potential is parity–time invariant along the direction perpendicular to the interface between the two media, there are no stable LSMs.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. J. Tomlinson, Opt. Lett. 5, 323 (1980).
    [CrossRef]
  2. N. N. Akhmediev, V. I. Korneev, and Y. V. Kuzmenko, Sov. Phys. JETP 61, 62 (1985).
  3. K. M. Leung, Phys. Rev. B 32, 5093 (1985).
    [CrossRef]
  4. A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, Phys. Rev. A 35, 1159 (1987).
    [CrossRef]
  5. K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (2006).
    [CrossRef]
  6. Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, Opt. Express 14, 4049 (2006).
    [CrossRef]
  7. Y. V. Kartashov and L. Torner, Opt. Lett. 31, 2172 (2006).
    [CrossRef]
  8. X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
    [CrossRef]
  9. A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 797 (2009).
    [CrossRef]
  10. C. M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998).
    [CrossRef]
  11. C. E. Rüter, K. G. Makris, R. Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
    [CrossRef]
  12. A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
    [CrossRef]
  13. J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, Phys. Rev. A 84, 040101(R) (2011).
    [CrossRef]
  14. X. Luo, J. Huang, H. Zhong, X. Qin, Q. Xie, Yu. S. Kivshar, and C. Lee, Phys. Rev. Lett. 110, 243902 (2013).
    [CrossRef]
  15. B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G.-L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014).
    [CrossRef]
  16. Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
    [CrossRef]
  17. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
    [CrossRef]
  18. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. A 81, 063807 (2010).
    [CrossRef]
  19. O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, Phys. Rev. Lett. 103, 030402 (2009).
    [CrossRef]
  20. A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, and D. N. Christodoulides, Nature 488, 167 (2012).
    [CrossRef]
  21. Y. He, D. Mihalache, X. Zhu, L. Guo, and Y. V. Kartashov, Opt. Lett. 37, 2526 (2012).
    [CrossRef]
  22. Y. Sun, W. Tan, H. Q. Li, J. S. Li, and H. Chen, Phys. Rev. Lett. 112, 143903 (2014).
    [CrossRef]
  23. Z. Xu, Y. V. Kartashov, and L. Torner, Opt. Lett. 30, 3171 (2005).
    [CrossRef]
  24. M. J. Ablowitz and Z. H. Musslimani, Opt. Lett. 30, 2140 (2005).
    [CrossRef]
  25. S. Nixon, L. Ge, and J. Yang, Phys. Rev. A 85, 023822 (2012).
    [CrossRef]
  26. Z. Ahmed, Phys. Lett. A 282, 343 (2001).
    [CrossRef]
  27. L. Berge, Phys. Rep. 303, 259 (1998).
    [CrossRef]
  28. J. Yang and T. I. Lakoba, Stud. Appl. Math. 118, 153 (2007).
    [CrossRef]

2014

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G.-L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014).
[CrossRef]

Y. Sun, W. Tan, H. Q. Li, J. S. Li, and H. Chen, Phys. Rev. Lett. 112, 143903 (2014).
[CrossRef]

2013

X. Luo, J. Huang, H. Zhong, X. Qin, Q. Xie, Yu. S. Kivshar, and C. Lee, Phys. Rev. Lett. 110, 243902 (2013).
[CrossRef]

2012

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, and D. N. Christodoulides, Nature 488, 167 (2012).
[CrossRef]

Y. He, D. Mihalache, X. Zhu, L. Guo, and Y. V. Kartashov, Opt. Lett. 37, 2526 (2012).
[CrossRef]

S. Nixon, L. Ge, and J. Yang, Phys. Rev. A 85, 023822 (2012).
[CrossRef]

2011

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, Phys. Rev. A 84, 040101(R) (2011).
[CrossRef]

2010

C. E. Rüter, K. G. Makris, R. Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. A 81, 063807 (2010).
[CrossRef]

2009

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 797 (2009).
[CrossRef]

2008

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

2007

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef]

J. Yang and T. I. Lakoba, Stud. Appl. Math. 118, 153 (2007).
[CrossRef]

2006

2005

2001

Z. Ahmed, Phys. Lett. A 282, 343 (2001).
[CrossRef]

1998

L. Berge, Phys. Rep. 303, 259 (1998).
[CrossRef]

C. M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998).
[CrossRef]

1987

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef]

1985

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuzmenko, Sov. Phys. JETP 61, 62 (1985).

K. M. Leung, Phys. Rev. B 32, 5093 (1985).
[CrossRef]

1980

Ablowitz, M. J.

Ahmed, Z.

Z. Ahmed, Phys. Lett. A 282, 343 (2001).
[CrossRef]

Aimez, V.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuzmenko, Sov. Phys. JETP 61, 62 (1985).

Bender, C. M.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G.-L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014).
[CrossRef]

C. M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998).
[CrossRef]

Bendix, O.

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

Berge, L.

L. Berge, Phys. Rep. 303, 259 (1998).
[CrossRef]

Bersch, C.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, and D. N. Christodoulides, Nature 488, 167 (2012).
[CrossRef]

Bezryadina, A.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef]

Boardman, A. D.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef]

Boettcher, S.

C. M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998).
[CrossRef]

Chen, H.

Y. Sun, W. Tan, H. Q. Li, J. S. Li, and H. Chen, Phys. Rev. Lett. 112, 143903 (2014).
[CrossRef]

Chen, Z.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef]

Christodoulides, D. N.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, and D. N. Christodoulides, Nature 488, 167 (2012).
[CrossRef]

C. E. Rüter, K. G. Makris, R. Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. A 81, 063807 (2010).
[CrossRef]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (2006).
[CrossRef]

Dreisow, F.

Duchesne, D.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

Egorov, A. A.

El-Ganainy, R.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. A 81, 063807 (2010).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

Ellis, F. M.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, Phys. Rev. A 84, 040101(R) (2011).
[CrossRef]

Fan, S.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G.-L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014).
[CrossRef]

Fleischmann, R.

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

Ganainy, R.

C. E. Rüter, K. G. Makris, R. Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Ge, L.

S. Nixon, L. Ge, and J. Yang, Phys. Rev. A 85, 023822 (2012).
[CrossRef]

Gianfreda, M.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G.-L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014).
[CrossRef]

Guo, A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

Guo, L.

He, Y.

Heinrich, M.

Huang, J.

X. Luo, J. Huang, H. Zhong, X. Qin, Q. Xie, Yu. S. Kivshar, and C. Lee, Phys. Rev. Lett. 110, 243902 (2013).
[CrossRef]

Hudock, J.

Kartashov, Y. V.

Kip, D.

C. E. Rüter, K. G. Makris, R. Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Kivshar, Yu. S.

X. Luo, J. Huang, H. Zhong, X. Qin, Q. Xie, Yu. S. Kivshar, and C. Lee, Phys. Rev. Lett. 110, 243902 (2013).
[CrossRef]

Korneev, V. I.

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuzmenko, Sov. Phys. JETP 61, 62 (1985).

Kottos, T.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, Phys. Rev. A 84, 040101(R) (2011).
[CrossRef]

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

Kuzmenko, Y. V.

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuzmenko, Sov. Phys. JETP 61, 62 (1985).

Lakoba, T. I.

J. Yang and T. I. Lakoba, Stud. Appl. Math. 118, 153 (2007).
[CrossRef]

Lederer, F.

Lee, C.

X. Luo, J. Huang, H. Zhong, X. Qin, Q. Xie, Yu. S. Kivshar, and C. Lee, Phys. Rev. Lett. 110, 243902 (2013).
[CrossRef]

Lei, F.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G.-L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014).
[CrossRef]

Leung, K. M.

K. M. Leung, Phys. Rev. B 32, 5093 (1985).
[CrossRef]

Li, A.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, Phys. Rev. A 84, 040101(R) (2011).
[CrossRef]

Li, H. Q.

Y. Sun, W. Tan, H. Q. Li, J. S. Li, and H. Chen, Phys. Rev. Lett. 112, 143903 (2014).
[CrossRef]

Li, J. S.

Y. Sun, W. Tan, H. Q. Li, J. S. Li, and H. Chen, Phys. Rev. Lett. 112, 143903 (2014).
[CrossRef]

Long, G.-L.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G.-L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014).
[CrossRef]

Luo, X.

X. Luo, J. Huang, H. Zhong, X. Qin, Q. Xie, Yu. S. Kivshar, and C. Lee, Phys. Rev. Lett. 110, 243902 (2013).
[CrossRef]

Makris, K. G.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. A 81, 063807 (2010).
[CrossRef]

C. E. Rüter, K. G. Makris, R. Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (2006).
[CrossRef]

Manela, O.

Maradudin, A. A.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef]

Mihalache, D.

Miri, M. A.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, and D. N. Christodoulides, Nature 488, 167 (2012).
[CrossRef]

Monifi, F.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G.-L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014).
[CrossRef]

Morandotti, R.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

Musslimani, Z. H.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. A 81, 063807 (2010).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

M. J. Ablowitz and Z. H. Musslimani, Opt. Lett. 30, 2140 (2005).
[CrossRef]

Nixon, S.

S. Nixon, L. Ge, and J. Yang, Phys. Rev. A 85, 023822 (2012).
[CrossRef]

Nolte, S.

Nori, F.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G.-L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014).
[CrossRef]

Onishchukov, G.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, and D. N. Christodoulides, Nature 488, 167 (2012).
[CrossRef]

Özdemir, S. K.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G.-L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014).
[CrossRef]

Peng, B.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G.-L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014).
[CrossRef]

Pertsch, T.

Qin, X.

X. Luo, J. Huang, H. Zhong, X. Qin, Q. Xie, Yu. S. Kivshar, and C. Lee, Phys. Rev. Lett. 110, 243902 (2013).
[CrossRef]

Regensburger, A.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, and D. N. Christodoulides, Nature 488, 167 (2012).
[CrossRef]

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Salamo, G. J.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

Schindler, J.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, Phys. Rev. A 84, 040101(R) (2011).
[CrossRef]

Segev, M.

C. E. Rüter, K. G. Makris, R. Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (2006).
[CrossRef]

Shapiro, B.

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

Siviloglou, G. A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

Stegeman, G. I.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (2006).
[CrossRef]

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef]

Sun, Y.

Y. Sun, W. Tan, H. Q. Li, J. S. Li, and H. Chen, Phys. Rev. Lett. 112, 143903 (2014).
[CrossRef]

Szameit, A.

Tan, W.

Y. Sun, W. Tan, H. Q. Li, J. S. Li, and H. Chen, Phys. Rev. Lett. 112, 143903 (2014).
[CrossRef]

Tomlinson, W. J.

Torner, L.

Tünnermann, A.

Twardowski, T.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef]

Volatier-Ravat, M.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

Vysloukh, V. A.

Wang, X.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef]

Wright, E. M.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef]

Xie, Q.

X. Luo, J. Huang, H. Zhong, X. Qin, Q. Xie, Yu. S. Kivshar, and C. Lee, Phys. Rev. Lett. 110, 243902 (2013).
[CrossRef]

Xu, Z.

Yang, J.

S. Nixon, L. Ge, and J. Yang, Phys. Rev. A 85, 023822 (2012).
[CrossRef]

J. Yang and T. I. Lakoba, Stud. Appl. Math. 118, 153 (2007).
[CrossRef]

Yang, L.

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G.-L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014).
[CrossRef]

Zheng, M. C.

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, Phys. Rev. A 84, 040101(R) (2011).
[CrossRef]

Zhong, H.

X. Luo, J. Huang, H. Zhong, X. Qin, Q. Xie, Yu. S. Kivshar, and C. Lee, Phys. Rev. Lett. 110, 243902 (2013).
[CrossRef]

Zhu, X.

Nat. Phys.

C. E. Rüter, K. G. Makris, R. Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G.-L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014).
[CrossRef]

Nature

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, and D. N. Christodoulides, Nature 488, 167 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

Z. Ahmed, Phys. Lett. A 282, 343 (2001).
[CrossRef]

Phys. Rep.

L. Berge, Phys. Rep. 303, 259 (1998).
[CrossRef]

Phys. Rev. A

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. A 81, 063807 (2010).
[CrossRef]

J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, Phys. Rev. A 84, 040101(R) (2011).
[CrossRef]

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef]

S. Nixon, L. Ge, and J. Yang, Phys. Rev. A 85, 023822 (2012).
[CrossRef]

Phys. Rev. B

K. M. Leung, Phys. Rev. B 32, 5093 (1985).
[CrossRef]

Phys. Rev. Lett.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef]

C. M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998).
[CrossRef]

X. Luo, J. Huang, H. Zhong, X. Qin, Q. Xie, Yu. S. Kivshar, and C. Lee, Phys. Rev. Lett. 110, 243902 (2013).
[CrossRef]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef]

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, Phys. Rev. Lett. 103, 030402 (2009).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

Y. Sun, W. Tan, H. Q. Li, J. S. Li, and H. Chen, Phys. Rev. Lett. 112, 143903 (2014).
[CrossRef]

Sov. Phys. JETP

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuzmenko, Sov. Phys. JETP 61, 62 (1985).

Stud. Appl. Math.

J. Yang and T. I. Lakoba, Stud. Appl. Math. 118, 153 (2007).
[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 (4)

Fig. 1.
Fig. 1.

Profile of the analytical LSM and the corresponding potential. (a) and (b) show the real and the imaginary parts, respectively, of R given by Eqs. (5) and (6). (c) is the profile of (1U)ΔG given by Eq. (7). (d) gives the intensity distribution of the analytical LSM [Eq. (8)]. (e) gives the distribution of the Poynting vector of (d). (f) Density profile after the initial LSM in (c) plus 5% noise propagates a distance of ζ=500. The dotted–dashed line displays the interface between the two media. Parameters are W0=0.3 and α=0.5.

Fig. 2.
Fig. 2.

Profile of the analytical LSM and the corresponding potential. (a) and (b) show the real and imaginary parts, respectively, of R given by Eqs. (10) and (11). (c) is the profile of (1U)ΔG given by Eq. (7). (d) gives the intensity distribution of the analytical LSM [Eq. (12)]. (e) gives the distribution of the Poynting vector of (d). (f) Density profile at ζ=500, evolved from the initial LSM in (c) with 5% noise. The dotted–dashed line displays the interface between the two media. Parameters are W0=0.3 and α=0.5.

Fig. 3.
Fig. 3.

(a) and (b) show the real and the imaginary parts of R=V+iW with σ=1.2843, respectively. (c) Intensity profiles for the LSMs with b=0.6. (d) Power P of the LSMs versus b. (e) Parameter σ versus b. The red circles correspond to the LSM in (c). (f) Density profile at ζ=500, evolved from the initial LSM in (c) with 5% noise. The dotted–dashed line displays the interface between the two media. Parameters are V0=2, W0=0.1, and ΔG=0.

Fig. 4.
Fig. 4.

(a) and (b) show the real and the imaginary parts of R=V+iW with ρ=1.2 and γ=0.1040, respectively. (c) Intensity profiles of the LSMs with b=8. (d) Power P of the LSMs versus b. (e) Parameter γ versus b. The red circles correspond to the LSM in (c). (f) Intensity profiles of the multibeam LSMs with b=8 and γ=0.1096. The dotted–dashed line displays the interface between the two media. Other parameters are chosen as V0=5, ρ=1.2, W0=0.05, and ΔG=5.

Equations (17)

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

i2ΓdEdz+2Ex2+2Ey2+(k02n012Γ2)E+2k02[n01(nr1+ini1)+n01n2|E|2]E=0,
i2ΓdEdz+2Ex2+2Ey2+(k02n022Γ2)E+2k02n02(nr2+ini2)E=0,
idqdζ+2q+Rq+(1U)ΔGq+U|q|2q=0,
U(x,y)={1,nonlinear medium,0,linear medium,
R(ξ,η)={2n01k02w02(nr1+ini1),nonlinear medium,2n02k02w02(nr2+ini2),linear medium.
2u+[R+(1U)ΔG]u+U|u|2ubu=0.
V=2(1+α)sech2(ξ)+(2+W029)sech2(η)(1+e2ξ)2αsech2(ξ)sech2(η),
W=W0sech(η)tanh(η),
(1U)ΔG=(α+α2)[tanh(ξ)+1]2.
u(ξ,η)=sech(ξ)sech(η)(1+e2ξ)αeiW03arctan[sinh(η)],
S⃗(ξ,η)=iW0sech2(ξ)2sech3(η)3(1+e2ξ)2α.
V=(2+2α+W029)sech2(ξ)+2sech2(η)(1+e2ξ)2αsech2(ξ)sech2(η),
W=W0sech(ξ){tanh(ξ)+2α[tanh(ξ)+1]3},
u(ξ,η)=sech(ξ)sech(η)(1+e2ξ)αeiW03arctan[sinh(ξ)],
W(ξ,η)={W0(2σ)ξeξ2η2,nonlinear medium,W0σξeξ2η2,linear medium.
V={V0[cos2(ξ+η)+cos2(ξη)],nonlinear medium,V0ρ[cos2(ξ+η)+cos2(ξη)],linear medium,
W={W0γ[sin(ξ+η0.5)+sin(ξη0.5)],nonlinear medium,W0[sin(ξ+η0.5)+sin(ξη0.5)],linear medium.

Metrics