Abstract

We report on the existence of surface defect gap solitons. Such new type of solitons can be well supported by an interface between the defect of optical lattice and the uniform media with focusing saturable nonlinearity. The surface defect of optical lattice can profoundly affect the properties of solitons. It is shown that for the positive defect, stable solitons exist at the first bandgap and their powers decrease with defect depth; while for negative defect, stable solitons exist at the second bandgap and their powers increase with defect depth. Such solitons with moderate power between lower and higher ones cannot stably existent at the first bandgap.

© 2006 Optical Society of America

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    [CrossRef]

2006

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of Surface Gap Solitons in Semi-InfiniteWaveguide Arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Y. H. Chen, G. Q. Liang, J. W. Dong, and H. Z. Wang, "Derivtion and characterization of dispersion of defect modes in photonic band gap from stacks of positive and negative index materials," Phys. Lett. A 351, 446-451 (2006).
[CrossRef]

Y. H. Chen, J. W. Dong and H. Z. Wang "Twin defect modes in one-dimensional photonic crystals with a single-negative defect," Appl. Phys. Lett. 89, 141101 (2006).
[CrossRef]

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, "Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures," Phys. Rev. E 74, 035601 (2006).
[CrossRef]

J. Yang and Z. Chen, "Defect solitons in photonic lattices," Phys. Rev. E 73, 026609 (2006).
[CrossRef]

Y. H. Chen, J. W. Dong, and H. Z. Wang, "Conditions of near-zero dispersion of defect modes in one-dimensional photonic crystal containing negative-index materials," J. Opt. Soc. Am. B 23, 776-781 (2006).
[CrossRef]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Surface vortex solitons," Opt. Express 14, 4049-4075 (2006).
[CrossRef] [PubMed]

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, "Surface multi-gap vector solitons," Opt. Express 14, 4780-4785 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, F. Ye, and L. Torner, "Vector mixed-gap surface solitons," Opt. Express 14, 4808-4824 (2006).
[CrossRef] [PubMed]

G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides and G. I. Stegeman, "Observation of discrete quadratic solitons," Opt. Express 14, 5508-5516 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, D. Mihalache, and L. Torner, "Generation of surface soliton arrays," Opt. Lett. 31, 2329-2331(2006).
[CrossRef] [PubMed]

M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, "Discrete surface solitons in semi-infinite binary waveguide arrays," Opt. Lett. 31, 2332-2334 (2006).
[CrossRef] [PubMed]

E. Smirnov, M. Stepić, C. E. Rüter, D. Kip, and V. Shandarov, "Observation of staggered surface solitary waves in one-dimensional waveguide arrays," Opt. Lett. 31, 2338-2340 (2006).
[CrossRef] [PubMed]

2005

2003

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, D. Dandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834-836 (2003).
[CrossRef] [PubMed]

2002

2001

A. A. Sukhorukov and Y. S. Kivshar, "Nonlinear Localized Waves in a Periodic Medium," Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef] [PubMed]

1999

J. Schöllmann, R. Scheibenzuber, A. S. Kovalev, A. P. Mayer, and A. A. Maradudin, "Stability of stationary gap solitary waves at periodically modulated surfaces," Phys. Rev. E 59, 4618 (1999).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-1350 (1999).
[CrossRef]

1995

1989

D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," Prog. Opt. 27, 229-313 (1989).

1985

G. I. Stegeman and C. T. Seaton, "Nonlinear integrated optics," J. Appl. Phys. 58, R57-R77 (1985);G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

G. I. Stegeman and C. T. Seaton, "Nonlinear integrated optics," J. Appl. Phys. 58, R57-R77 (1985);G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

1978

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32, 104-105 (1978).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, "Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures," Phys. Rev. E 74, 035601 (2006).
[CrossRef]

Aitchison, J. S.

R. Morandotti, H. S. Eisenberg, D. Dandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834-836 (2003).
[CrossRef] [PubMed]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-1350 (1999).
[CrossRef]

Bertolotti, M.

D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," Prog. Opt. 27, 229-313 (1989).

Chen, Y. H.

Y. H. Chen, J. W. Dong, and H. Z. Wang, "Conditions of near-zero dispersion of defect modes in one-dimensional photonic crystal containing negative-index materials," J. Opt. Soc. Am. B 23, 776-781 (2006).
[CrossRef]

Y. H. Chen, G. Q. Liang, J. W. Dong, and H. Z. Wang, "Derivtion and characterization of dispersion of defect modes in photonic band gap from stacks of positive and negative index materials," Phys. Lett. A 351, 446-451 (2006).
[CrossRef]

Y. H. Chen, J. W. Dong and H. Z. Wang "Twin defect modes in one-dimensional photonic crystals with a single-negative defect," Appl. Phys. Lett. 89, 141101 (2006).
[CrossRef]

J. W. Dong, Y. H. Chen, and H. Z. Wang, "Study on the dispersion and locazation of defect state in one-dimensional photonic crystal consisting of metamaterials," Acta.Phys. Sin. (In press).

Chen, Z.

J. Yang and Z. Chen, "Defect solitons in photonic lattices," Phys. Rev. E 73, 026609 (2006).
[CrossRef]

F. Fedele, J. Yang, and Z. Chen, "Properties of defect modes in one-dimensional optically induced photonic lattices," Stud. Appl. Math. 115, 277-299 (2005).
[CrossRef]

F. Fedele, J. Yang, and Z. Chen, "Defect modes in one-dimensional photonic lattices," Opt. Lett. 30, 1506-1508 (2005).
[CrossRef] [PubMed]

Z. Chen and K. Mccarthy, "Spatial soliton pixels from partially incoherent light," Opt. Lett. 27, 2019-2021 (2002).
[CrossRef]

Cho, A. Y.

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32, 104-105 (1978).
[CrossRef]

Christodoulides, D. N.

G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides and G. I. Stegeman, "Observation of discrete quadratic solitons," Opt. Express 14, 5508-5516 (2006).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, "Discrete surface solitons," Opt. Lett. 30, 2466-2468 (2005).
[CrossRef] [PubMed]

J. Hudock, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, "Vector discrete nonlinear surface waves," Opt. Express 13, 7720-7725 (2005).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

Cronin-Golomb, M.

Dandelik, D.

Dong, J. W.

Y. H. Chen, G. Q. Liang, J. W. Dong, and H. Z. Wang, "Derivtion and characterization of dispersion of defect modes in photonic band gap from stacks of positive and negative index materials," Phys. Lett. A 351, 446-451 (2006).
[CrossRef]

Y. H. Chen, J. W. Dong and H. Z. Wang "Twin defect modes in one-dimensional photonic crystals with a single-negative defect," Appl. Phys. Lett. 89, 141101 (2006).
[CrossRef]

Y. H. Chen, J. W. Dong, and H. Z. Wang, "Conditions of near-zero dispersion of defect modes in one-dimensional photonic crystal containing negative-index materials," J. Opt. Soc. Am. B 23, 776-781 (2006).
[CrossRef]

J. W. Dong, Y. H. Chen, and H. Z. Wang, "Study on the dispersion and locazation of defect state in one-dimensional photonic crystal consisting of metamaterials," Acta.Phys. Sin. (In press).

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

Egorov, A. A.

Eisenberg, H. S.

R. Morandotti, H. S. Eisenberg, D. Dandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834-836 (2003).
[CrossRef] [PubMed]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-1350 (1999).
[CrossRef]

Fedele, F.

F. Fedele, J. Yang, and Z. Chen, "Properties of defect modes in one-dimensional optically induced photonic lattices," Stud. Appl. Math. 115, 277-299 (2005).
[CrossRef]

F. Fedele, J. Yang, and Z. Chen, "Defect modes in one-dimensional photonic lattices," Opt. Lett. 30, 1506-1508 (2005).
[CrossRef] [PubMed]

Finlayson, N.

G. I. Stegeman and C. T. Seaton, "Nonlinear integrated optics," J. Appl. Phys. 58, R57-R77 (1985);G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

Garanovich, I. L.

Hache, A.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Hudock, J.

Ilan, B.

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, "Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures," Phys. Rev. E 74, 035601 (2006).
[CrossRef]

Iwanow, R.

Kartashov, Y. V.

Kip, D.

Kivshar, Y. S.

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, "Surface multi-gap vector solitons," Opt. Express 14, 4780-4785 (2006).
[CrossRef] [PubMed]

M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, "Discrete surface solitons in semi-infinite binary waveguide arrays," Opt. Lett. 31, 2332-2334 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of Surface Gap Solitons in Semi-InfiniteWaveguide Arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

A. A. Sukhorukov and Y. S. Kivshar, "Nonlinear Localized Waves in a Periodic Medium," Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef] [PubMed]

Kovalev, A. S.

J. Schöllmann, R. Scheibenzuber, A. S. Kovalev, A. P. Mayer, and A. A. Maradudin, "Stability of stationary gap solitary waves at periodically modulated surfaces," Phys. Rev. E 59, 4618 (1999).
[CrossRef]

Krolikowski, W.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of Surface Gap Solitons in Semi-InfiniteWaveguide Arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Liang, G. Q.

Y. H. Chen, G. Q. Liang, J. W. Dong, and H. Z. Wang, "Derivtion and characterization of dispersion of defect modes in photonic band gap from stacks of positive and negative index materials," Phys. Lett. A 351, 446-451 (2006).
[CrossRef]

Makris, K. G.

Maradudin, A. A.

J. Schöllmann, R. Scheibenzuber, A. S. Kovalev, A. P. Mayer, and A. A. Maradudin, "Stability of stationary gap solitary waves at periodically modulated surfaces," Phys. Rev. E 59, 4618 (1999).
[CrossRef]

Mayer, A. P.

J. Schöllmann, R. Scheibenzuber, A. S. Kovalev, A. P. Mayer, and A. A. Maradudin, "Stability of stationary gap solitary waves at periodically modulated surfaces," Phys. Rev. E 59, 4618 (1999).
[CrossRef]

Mccarthy, K.

Mihalache, D.

Y. V. Kartashov, V. A. Vysloukh, D. Mihalache, and L. Torner, "Generation of surface soliton arrays," Opt. Lett. 31, 2329-2331(2006).
[CrossRef] [PubMed]

D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," Prog. Opt. 27, 229-313 (1989).

Mitchell, A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of Surface Gap Solitons in Semi-InfiniteWaveguide Arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Modotto, D.

Molina, M. I.

M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, "Discrete surface solitons in semi-infinite binary waveguide arrays," Opt. Lett. 31, 2332-2334 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of Surface Gap Solitons in Semi-InfiniteWaveguide Arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Morandotti, R.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, D. Dandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834-836 (2003).
[CrossRef] [PubMed]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-1350 (1999).
[CrossRef]

Neshev, D. N.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of Surface Gap Solitons in Semi-InfiniteWaveguide Arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Peschel, U.

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-1350 (1999).
[CrossRef]

Piestun, R.

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, "Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures," Phys. Rev. E 74, 035601 (2006).
[CrossRef]

Rosberg, C. R.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of Surface Gap Solitons in Semi-InfiniteWaveguide Arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Rüter, C. E.

Salamo, G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Scheibenzuber, R.

J. Schöllmann, R. Scheibenzuber, A. S. Kovalev, A. P. Mayer, and A. A. Maradudin, "Stability of stationary gap solitary waves at periodically modulated surfaces," Phys. Rev. E 59, 4618 (1999).
[CrossRef]

Schiek, R.

Schöllmann, J.

J. Schöllmann, R. Scheibenzuber, A. S. Kovalev, A. P. Mayer, and A. A. Maradudin, "Stability of stationary gap solitary waves at periodically modulated surfaces," Phys. Rev. E 59, 4618 (1999).
[CrossRef]

Schonbrun, E.

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, "Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures," Phys. Rev. E 74, 035601 (2006).
[CrossRef]

Seaton, C. T.

G. I. Stegeman and C. T. Seaton, "Nonlinear integrated optics," J. Appl. Phys. 58, R57-R77 (1985);G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

G. I. Stegeman and C. T. Seaton, "Nonlinear integrated optics," J. Appl. Phys. 58, R57-R77 (1985);G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

Segev, M.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

Shandarov, V.

Sibilia, C.

D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," Prog. Opt. 27, 229-313 (1989).

Silberberg, Y.

R. Morandotti, H. S. Eisenberg, D. Dandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834-836 (2003).
[CrossRef] [PubMed]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-1350 (1999).
[CrossRef]

Siviloglou, G. A.

Skryabin, D. V.

Smirnov, E.

Sorel, M.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, D. Dandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834-836 (2003).
[CrossRef] [PubMed]

Stanley, C. R.

Stegeman, G. I.

G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides and G. I. Stegeman, "Observation of discrete quadratic solitons," Opt. Express 14, 5508-5516 (2006).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, "Discrete surface solitons," Opt. Lett. 30, 2466-2468 (2005).
[CrossRef] [PubMed]

J. Hudock, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, "Vector discrete nonlinear surface waves," Opt. Express 13, 7720-7725 (2005).
[CrossRef] [PubMed]

G. I. Stegeman and C. T. Seaton, "Nonlinear integrated optics," J. Appl. Phys. 58, R57-R77 (1985);G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

G. I. Stegeman and C. T. Seaton, "Nonlinear integrated optics," J. Appl. Phys. 58, R57-R77 (1985);G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

Stepic, M.

Sukhorukov, A. A.

Suntsov, S.

Torner, L.

Vicencio, R. A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of Surface Gap Solitons in Semi-InfiniteWaveguide Arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Vysloukh, V. A.

Wang, H. Z.

Y. H. Chen, G. Q. Liang, J. W. Dong, and H. Z. Wang, "Derivtion and characterization of dispersion of defect modes in photonic band gap from stacks of positive and negative index materials," Phys. Lett. A 351, 446-451 (2006).
[CrossRef]

Y. H. Chen, J. W. Dong and H. Z. Wang "Twin defect modes in one-dimensional photonic crystals with a single-negative defect," Appl. Phys. Lett. 89, 141101 (2006).
[CrossRef]

Y. H. Chen, J. W. Dong, and H. Z. Wang, "Conditions of near-zero dispersion of defect modes in one-dimensional photonic crystal containing negative-index materials," J. Opt. Soc. Am. B 23, 776-781 (2006).
[CrossRef]

J. W. Dong, Y. H. Chen, and H. Z. Wang, "Study on the dispersion and locazation of defect state in one-dimensional photonic crystal consisting of metamaterials," Acta.Phys. Sin. (In press).

Wright, E. M.

G. I. Stegeman and C. T. Seaton, "Nonlinear integrated optics," J. Appl. Phys. 58, R57-R77 (1985);G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

Yang, H.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Yang, J.

J. Yang and Z. Chen, "Defect solitons in photonic lattices," Phys. Rev. E 73, 026609 (2006).
[CrossRef]

F. Fedele, J. Yang, and Z. Chen, "Defect modes in one-dimensional photonic lattices," Opt. Lett. 30, 1506-1508 (2005).
[CrossRef] [PubMed]

F. Fedele, J. Yang, and Z. Chen, "Properties of defect modes in one-dimensional optically induced photonic lattices," Stud. Appl. Math. 115, 277-299 (2005).
[CrossRef]

Yariv, A.

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32, 104-105 (1978).
[CrossRef]

Ye, F.

Yeh, P.

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32, 104-105 (1978).
[CrossRef]

Zanoni, R.

G. I. Stegeman and C. T. Seaton, "Nonlinear integrated optics," J. Appl. Phys. 58, R57-R77 (1985);G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

Appl. Phys. Lett.

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32, 104-105 (1978).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-1350 (1999).
[CrossRef]

Y. H. Chen, J. W. Dong and H. Z. Wang "Twin defect modes in one-dimensional photonic crystals with a single-negative defect," Appl. Phys. Lett. 89, 141101 (2006).
[CrossRef]

J. Appl. Phys.

G. I. Stegeman and C. T. Seaton, "Nonlinear integrated optics," J. Appl. Phys. 58, R57-R77 (1985);G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

J. Opt. Soc. Am. B

Nature

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Lett. A

Y. H. Chen, G. Q. Liang, J. W. Dong, and H. Z. Wang, "Derivtion and characterization of dispersion of defect modes in photonic band gap from stacks of positive and negative index materials," Phys. Lett. A 351, 446-451 (2006).
[CrossRef]

Phys. Rev. E

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, "Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures," Phys. Rev. E 74, 035601 (2006).
[CrossRef]

J. Yang and Z. Chen, "Defect solitons in photonic lattices," Phys. Rev. E 73, 026609 (2006).
[CrossRef]

J. Schöllmann, R. Scheibenzuber, A. S. Kovalev, A. P. Mayer, and A. A. Maradudin, "Stability of stationary gap solitary waves at periodically modulated surfaces," Phys. Rev. E 59, 4618 (1999).
[CrossRef]

Phys. Rev. Lett.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of Surface Gap Solitons in Semi-InfiniteWaveguide Arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

A. A. Sukhorukov and Y. S. Kivshar, "Nonlinear Localized Waves in a Periodic Medium," Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

Phys. Sin.

J. W. Dong, Y. H. Chen, and H. Z. Wang, "Study on the dispersion and locazation of defect state in one-dimensional photonic crystal consisting of metamaterials," Acta.Phys. Sin. (In press).

Prog. Opt.

D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," Prog. Opt. 27, 229-313 (1989).

Stud. Appl. Math.

F. Fedele, J. Yang, and Z. Chen, "Properties of defect modes in one-dimensional optically induced photonic lattices," Stud. Appl. Math. 115, 277-299 (2005).
[CrossRef]

Other

I. Makasyuk, Z. Chen, and J. Yang, Technical Digest Series, Conference on Nonlinear Guided Waves and Their Applications, (Optical Society of America, Dresden, Germany, 2005), TuC8.

S. Kawata, Near-Field Optics and Surface Plasmon Polaritons, (Springer, New York, 2001).
[CrossRef]

A. D. Boardman, M. Bertolotti, and T. Twardowski, eds., Nonlinear Waves in Solid State Physics, NATO ASI Vol. 247 (Plenum, New York 1989); Nonlinear Surface Electromagnetic Phenomena, H. E. Ponath and G. I. Stegeman eds., (North-Holland, Amsterdam, 1991).

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Figures (5)

Fig. 1.
Fig. 1.

Intensity distribution of optical lattices. (a) positive defect ε=0.5, (b) negative defect ε=-0.5 and (c) without defect ε=0.

Fig. 2.
Fig. 2.

Power versus the eigenvalue (blue regions are Bloch bands) for (a) ε=0.5 and (c) ε= -0.5. (b) The growth rate of (a) for -1.8<µ<-0.9. (d)–(f) SDGSs at points A, D, and B at the first bandgap for ε=0.5 with µ=-0.9, -2.25 and -1.4, respectively. (g)–(i) SDGSs propagation corresponding to (d)–(f). (j)–(l) SDGSs at points E, F, and G at the second bandgap for ε=-0.5 and the eigenvalues µ=-2.95, -3.1 and -3.64, respectively. (m)–(o) correspond to (j)–(l).

Fig. 3.
Fig. 3.

Stable propagation of SDGSs at the first bandgap with µ=-2.1at (a) ε=0.1, (b) ε=0.5, and (c) ε=0.7; (d)–(f) correspond to (a)–(c), respectively; and at the second bandgap with µ=-3.2 at (g) ε= -0.3, (h) ε= -0.5, and (i) ε= -0.9; (j)–(l) correspond to (g)–(i), respectively.

Fig. 4.
Fig. 4.

(a) and (b) Stable (grey shade) and unstable (white) regions of SDGSs at the first and the second bandgaps, respectively. (c) and (d) Powers versus eigenvalue µ for ε=0.5 and ε=-0.5, respectively.

Fig. 5.
Fig. 5.

SDGSs exist at the first bandgap. (a) The power versus the eigenvalue for the uniform lattice with (b) B: µ=-2.4 and (c) A: µ=-2.05. (d) and (e) correspond to (b) and (c), respectively.

Equations (3)

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

i q z + q xx E 0 1 + I L ( x ) + q 2 q = 0 ,
I L = I 0 cos 2 ( x Ω ) { 1 + ε g ( x ) } .
2 f x 2 E 0 1 + I L ( x ) + f 2 f μ f = 0 .

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