Abstract

We report the first observation of discrete quadratic surface solitons in self-focusing and defocusing periodically poled lithium niobate waveguide arrays. By operating on either side of the phase-matching condition and using the cascading nonlinearity, both in-phase and staggered discrete surface solitons were observed. This represents the first experimental demonstration of staggered/gap surface solitons at the interface of a semi-infinite nonlinear lattice. The experimental results were found to be in good agreement with theory.

© 2006 Optical Society of America

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  1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
    [CrossRef] [PubMed]
  2. D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988).
    [CrossRef] [PubMed]
  3. T. Peschel, U. Peschel, and F. Lederer, "Discrete bright solitary waves in quadratically nonlinear media," Phys. Rev. E 57, 1127-1133 (1998).
    [CrossRef]
  4. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66,046602 (2002).
    [CrossRef]
  5. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
    [CrossRef]
  6. R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
    [CrossRef] [PubMed]
  7. 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]
  8. A. Fratalocchi, G. Assanto, K. A. Brzdąkiewicz, and M. A. Karpierz, "Discrete light propagation and self-trapping in liquid crystals," Opt. Express. 13, 1808-1815 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-2468, (2005).
    [CrossRef] [PubMed]
  14. 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]
  15. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef] [PubMed]
  16. N. N. Akhmediev, V. I. Korneev, and Y. V. Kuz’menko, Sov. Phys. JETP 61, 62 (1985).
  17. R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Arrays of weakly coupled, periodically poled lithium niobate waveguides: beam propagation and discrete spatial quadratic solitons," Opto-Electron.Rev. 13, 113-121 (2005).
  18. R. Iwanow, G. I. Stegeman, R. Schiek, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Highly localized discrete quadratic solitons," Opt. Lett. 30, 1033-1035 (2005).
    [CrossRef] [PubMed]

2006 (2)

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]

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

2005 (4)

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Arrays of weakly coupled, periodically poled lithium niobate waveguides: beam propagation and discrete spatial quadratic solitons," Opto-Electron.Rev. 13, 113-121 (2005).

R. Iwanow, G. I. Stegeman, R. Schiek, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Highly localized discrete quadratic solitons," Opt. Lett. 30, 1033-1035 (2005).
[CrossRef] [PubMed]

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

A. Fratalocchi, G. Assanto, K. A. Brzdąkiewicz, and M. A. Karpierz, "Discrete light propagation and self-trapping in liquid crystals," Opt. Express. 13, 1808-1815 (2005).
[CrossRef] [PubMed]

2004 (1)

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

2003 (2)

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]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

2002 (1)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66,046602 (2002).
[CrossRef]

1998 (2)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

T. Peschel, U. Peschel, and F. Lederer, "Discrete bright solitary waves in quadratically nonlinear media," Phys. Rev. E 57, 1127-1133 (1998).
[CrossRef]

1988 (1)

1985 (2)

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

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guides by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. 21, 774-783, (1985).
[CrossRef]

1983 (1)

U. Langbein, F. Lederer, and H. E. Ponath, "A new type of nonlinear slab-guided waves," Opt. Commun. 46, 167-169, (1983).
[CrossRef]

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Akhmediev, N. N.

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

Assanto, G.

A. Fratalocchi, G. Assanto, K. A. Brzdąkiewicz, and M. A. Karpierz, "Discrete light propagation and self-trapping in liquid crystals," Opt. Express. 13, 1808-1815 (2005).
[CrossRef] [PubMed]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Brzdakiewicz, K. A.

A. Fratalocchi, G. Assanto, K. A. Brzdąkiewicz, and M. A. Karpierz, "Discrete light propagation and self-trapping in liquid crystals," Opt. Express. 13, 1808-1815 (2005).
[CrossRef] [PubMed]

Chilwell, J. T.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guides by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. 21, 774-783, (1985).
[CrossRef]

Christodoulides, D. N.

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, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-2468, (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]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66,046602 (2002).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988).
[CrossRef] [PubMed]

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]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66,046602 (2002).
[CrossRef]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[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]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66,046602 (2002).
[CrossRef]

Fratalocchi, A.

A. Fratalocchi, G. Assanto, K. A. Brzdąkiewicz, and M. A. Karpierz, "Discrete light propagation and self-trapping in liquid crystals," Opt. Express. 13, 1808-1815 (2005).
[CrossRef] [PubMed]

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]

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

Iwanow, R.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Arrays of weakly coupled, periodically poled lithium niobate waveguides: beam propagation and discrete spatial quadratic solitons," Opto-Electron.Rev. 13, 113-121 (2005).

R. Iwanow, G. I. Stegeman, R. Schiek, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Highly localized discrete quadratic solitons," Opt. Lett. 30, 1033-1035 (2005).
[CrossRef] [PubMed]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

Joseph, R. I.

Karpierz, M. A.

A. Fratalocchi, G. Assanto, K. A. Brzdąkiewicz, and M. A. Karpierz, "Discrete light propagation and self-trapping in liquid crystals," Opt. Express. 13, 1808-1815 (2005).
[CrossRef] [PubMed]

Kartashov, Y. V.

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

Korneev, V. I.

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

Kuz’menko, Y. V.

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

Langbein, U.

U. Langbein, F. Lederer, and H. E. Ponath, "A new type of nonlinear slab-guided waves," Opt. Commun. 46, 167-169, (1983).
[CrossRef]

Lederer, F.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Arrays of weakly coupled, periodically poled lithium niobate waveguides: beam propagation and discrete spatial quadratic solitons," Opto-Electron.Rev. 13, 113-121 (2005).

R. Iwanow, G. I. Stegeman, R. Schiek, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Highly localized discrete quadratic solitons," Opt. Lett. 30, 1033-1035 (2005).
[CrossRef] [PubMed]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

T. Peschel, U. Peschel, and F. Lederer, "Discrete bright solitary waves in quadratically nonlinear media," Phys. Rev. E 57, 1127-1133 (1998).
[CrossRef]

U. Langbein, F. Lederer, and H. E. Ponath, "A new type of nonlinear slab-guided waves," Opt. Commun. 46, 167-169, (1983).
[CrossRef]

Makris, K. 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]

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

Min, Y.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Arrays of weakly coupled, periodically poled lithium niobate waveguides: beam propagation and discrete spatial quadratic solitons," Opto-Electron.Rev. 13, 113-121 (2005).

R. Iwanow, G. I. Stegeman, R. Schiek, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Highly localized discrete quadratic solitons," Opt. Lett. 30, 1033-1035 (2005).
[CrossRef] [PubMed]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
[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]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Pertsch, T.

R. Iwanow, G. I. Stegeman, R. Schiek, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Highly localized discrete quadratic solitons," Opt. Lett. 30, 1033-1035 (2005).
[CrossRef] [PubMed]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Arrays of weakly coupled, periodically poled lithium niobate waveguides: beam propagation and discrete spatial quadratic solitons," Opto-Electron.Rev. 13, 113-121 (2005).

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

Peschel, T.

T. Peschel, U. Peschel, and F. Lederer, "Discrete bright solitary waves in quadratically nonlinear media," Phys. Rev. E 57, 1127-1133 (1998).
[CrossRef]

Peschel, U.

T. Peschel, U. Peschel, and F. Lederer, "Discrete bright solitary waves in quadratically nonlinear media," Phys. Rev. E 57, 1127-1133 (1998).
[CrossRef]

Ponath, H. E.

U. Langbein, F. Lederer, and H. E. Ponath, "A new type of nonlinear slab-guided waves," Opt. Commun. 46, 167-169, (1983).
[CrossRef]

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]

Schiek, R.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Arrays of weakly coupled, periodically poled lithium niobate waveguides: beam propagation and discrete spatial quadratic solitons," Opto-Electron.Rev. 13, 113-121 (2005).

R. Iwanow, G. I. Stegeman, R. Schiek, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Highly localized discrete quadratic solitons," Opt. Lett. 30, 1033-1035 (2005).
[CrossRef] [PubMed]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66,046602 (2002).
[CrossRef]

Seaton, C. T.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guides by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. 21, 774-783, (1985).
[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]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66,046602 (2002).
[CrossRef]

Shoemaker, R. L.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guides by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. 21, 774-783, (1985).
[CrossRef]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Smith, S. D.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guides by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. 21, 774-783, (1985).
[CrossRef]

Sohler, W.

R. Iwanow, G. I. Stegeman, R. Schiek, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Highly localized discrete quadratic solitons," Opt. Lett. 30, 1033-1035 (2005).
[CrossRef] [PubMed]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Arrays of weakly coupled, periodically poled lithium niobate waveguides: beam propagation and discrete spatial quadratic solitons," Opto-Electron.Rev. 13, 113-121 (2005).

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

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]

Stegeman, G. I.

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, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-2468, (2005).
[CrossRef] [PubMed]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Arrays of weakly coupled, periodically poled lithium niobate waveguides: beam propagation and discrete spatial quadratic solitons," Opto-Electron.Rev. 13, 113-121 (2005).

R. Iwanow, G. I. Stegeman, R. Schiek, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Highly localized discrete quadratic solitons," Opt. Lett. 30, 1033-1035 (2005).
[CrossRef] [PubMed]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guides by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. 21, 774-783, (1985).
[CrossRef]

Suntsov, S.

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, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-2468, (2005).
[CrossRef] [PubMed]

Torner, L.

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

Valera, J. D.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guides by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. 21, 774-783, (1985).
[CrossRef]

Vysloukh, V. A.

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

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]

IEEE J. Quantum Electron. (1)

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guides by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. 21, 774-783, (1985).
[CrossRef]

Nature (2)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[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]

Opt. Commun. (1)

U. Langbein, F. Lederer, and H. E. Ponath, "A new type of nonlinear slab-guided waves," Opt. Commun. 46, 167-169, (1983).
[CrossRef]

Opt. Express. (1)

A. Fratalocchi, G. Assanto, K. A. Brzdąkiewicz, and M. A. Karpierz, "Discrete light propagation and self-trapping in liquid crystals," Opt. Express. 13, 1808-1815 (2005).
[CrossRef] [PubMed]

Opt. Lett. (3)

Phys. Rev. E (2)

T. Peschel, U. Peschel, and F. Lederer, "Discrete bright solitary waves in quadratically nonlinear media," Phys. Rev. E 57, 1127-1133 (1998).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66,046602 (2002).
[CrossRef]

Phys. Rev. Lett. (4)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
[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]

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

Rev. (1)

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Arrays of weakly coupled, periodically poled lithium niobate waveguides: beam propagation and discrete spatial quadratic solitons," Opto-Electron.Rev. 13, 113-121 (2005).

Sov. Phys. JETP (1)

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

Other (2)

A. A. Maradudin, "Nonlinear surface electromagnetic waves," in Optical and Acoustic Waves in Solids-Modern Topics, (World Scientific, Singapore, 1983), Chap. 2.

A. D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, "Third-order nonlinear electromagnetic TE and TM guided waves," in Nonlinear Surface Electromagnetic Phenomena," H. E. Ponath, and G. I. Stegeman, eds. (North-Holland, Amsterdam, 1991) p. 73-287.

Supplementary Material (2)

» Media 1: AVI (2355 KB)     
» Media 2: AVI (1876 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

(upper) Simple model for the discrete array-continuous medium interface. (lower) Actual sample structure showing the index distribution, the fundamental fields and the harmonic fields. The index distribution and fields are overlapped in space but have been separated for clarity.

Fig. 2.
Fig. 2.

(a) Surface soliton existence curves for in-phase solitons for 36π (red curve) and -15.5π (blue curve). (b), (c) Intensity profiles for low, and high powers for FW (blue) and SH (red), in the case of positive mismatch 36π, respectively, and (d) Intensity profiles for high powers for FH (blue) and SH (red), in the case of negative mismatch -15.5π. The SH powers of both solitons are overlapped for large nonlinear wavevector shifts.

Fig. 3.
Fig. 3.

(a) Surface soliton existence curves for staggered solitons for a mismatch of -15.5π (red curve) and 36π (blue curve). (b), (c) Intensity profiles for low, and high powers for FH (blue) and SH (red), in the case of negative mismatch -15.5π, respectively, and (d) Intensity profiles for high powers for FH (blue) and SH (red), in the case of positive mismatch 36π. The SH powers of both solitons are overlapped for large nonlinear wavevector shifts.

Fig. 4 .
Fig. 4 .

Experimental set-up: MO-microscope objective; PPLN-periodically poled lithium niobate; Pol-Polarizer;λ/2-half-wave plate.

Fig. 5.
Fig. 5.

Linear diffraction when only n=0 is excited, experiment (blue) and theory (red).

Fig. 6.
Fig. 6.

The evolution of the output intensity distribution with increasing input peak power of the fundamental for single channel excitation (n=0) (positive phase mismatch=+36π) [Media 1]

Fig. 7.
Fig. 7.

The evolution of the output intensity distributions versus input peak power of the fundamental for single channel excitation (n=0) (negative phase mismatch=-15.5π) [Media 2]

Fig. 8.
Fig. 8.

Measured (let-hand-side) and calculated (right-hand-side) output field distributions for single channel excitation for two input power levels corresponding to partial collapse into a surface soliton for FH (first row) and full collapse into a surface soliton for FH (second row) and SH (last row). Phase mismatch=+36π(self-focusing nonlinearity). The red curves represent theoretical results (at 435 W and 441 W) and the blue experimental data (at 430 W, and 600W) FW input powers.

Fig. 9.
Fig. 9.

Measured (let-hand-side) and calculated (right-hand-side) output field distributions for single channel excitation for two input power levels corresponding to partial collapse into a surface soliton for FH (first row) and full collapse into a surface soliton for FH (second row) and SH (last row). Phase mismatch=-15.5π(self-defocusing nonlinearity). The red curves represent theoretical results (at 310 W and 321 W) and the blue experimental data (at 420 W, and 580W) FW peak input powers.

Equations (2)

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{ i u 0 z + cu 1 + γ u 0 * v 0 = 0 , for n = 0 i u n z + c ( u n + 1 + u n 1 ) + γ u n * v n = 0 , for n 1
i v n z Δ β v n + γ u n 2 = 0 , for n 0

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