Abstract

We predict the existence of optical domain walls and quasi-rectangular localized modes in waveguide arrays with quadratic nonlinearity. An analytical criterion for the stability of these localized modes is derived and confirmed by direct numerical calculations. The instability gain near the respective boundaries is calculated. The instability predicted is controllable by input power and therefore has a potential for use in new all-optical switching schemes. Parameters of the waveguide arrays made from titanium-indiffused lithium niobate as well as the required power levels are estimated.

© 1999 Optical Society of America

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References

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  1. S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1982).
    [CrossRef]
  2. C. Schmidt-Hattenberger, U. Trutschel, and F. Lederer, “Nonlinear switching in multiple-core couplers,” Opt. Lett. 16, 294–296 (1991).
    [CrossRef] [PubMed]
  3. D. N. Cristodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988).
    [CrossRef]
  4. A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
    [CrossRef]
  5. O. Bang and P. D. Miller, “Exploiting discreteness for switching in waveguide arrays,” Opt. Lett. 21, 1105–1107 (1996).
    [CrossRef] [PubMed]
  6. W. Krolikowski and Y. S. Kivshar, “Soliton-based optical switching in waveguide arrays,” J. Opt. Soc. Am. B 13, 876–887 (1996).
    [CrossRef]
  7. T. Peschel, R. Muschall, and F. Lederer, “Power-controlled beam steering in nonequidistant arrays of nonlinear waveguides,” Opt. Commun. 136, 16–21 (1997).
    [CrossRef]
  8. P. Millar, J. S. Aitchison, J. U. Kang, G. I. Stegeman, A. Villeneuve, G. T. Kennedy, and W. Sibbett, “Nonlinear waveguide arrays in AlGaAs,” J. Opt. Soc. Am. B 14, 3224–3231 (1997).
    [CrossRef]
  9. 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]
  10. G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
    [CrossRef]
  11. R. Regener and W. Sohler, “Efficient second-harmonic generation in Ti:LiNbO3 channel waveguide resonators,” J. Opt. Soc. Am. B 5, 267–277 (1988).
    [CrossRef]
  12. R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 46, 940–942 (1996).
    [CrossRef]
  13. S. Darmanyan, A. Kobyakov, and F. Lederer, “Strongly localized modes in discrete systems with quadratic nonlinearity,” Phys. Rev. E 57, 2344–2349 (1998).
    [CrossRef]
  14. T. Peschel, U. Peschel, and F. Lederer, “Discrete bright solitary waves in quadratically nonlinear media,” Phys. Rev. E 57, 1127–1133 (1998).
    [CrossRef]
  15. P. D. Miller and O. Bang, “Macroscopic dynamics in quadratic nonlinear lattices,” Phys. Rev. E 57, 6038–6049 (1998).
    [CrossRef]
  16. S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520–3530 (1998).
    [CrossRef]
  17. J. B. Page, “Asymptotic solutions for localized vibrational modes in strongly anharmonic periodic systems,” Phys. Rev. B 41, 7835–7838 (1990).
    [CrossRef]
  18. S. Darmanyan, A. Kobyakov, F. Lederer, and L. Vázquez, “Discrete fronts and quasirectangular solitons,” Phys. Rev. B 59, 5994–5997 (1999).
    [CrossRef]
  19. R. Schiek, Y. Baek, and G. I. Stegeman, “Second-harmonic generation and cascaded nonlinearity in titanium-indiffused lithium niobate channel waveguides,” J. Opt. Soc. Am. B 15, 2255–2268 (1998).
    [CrossRef]
  20. E. Strake, G. P. Bava, and I. Montrosset, “Modes of channel waveguides: a novel quasi-analytical technique in comparison with the scalar finite-element method,” J. Lightwave Technol. 6, 1126–1135 (1988).
    [CrossRef]
  21. G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42–52 (1987).
    [CrossRef]
  22. V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991), pp. 74–76.
  23. M. M. Fejer, “Nonlinear optical frequency conversion: material requirements, engineered materials, and quasi-phasematching,” in Beam Shaping and Control with Nonlinear Optics (Plenum, New York, 1998), pp. 375–406.

1999

S. Darmanyan, A. Kobyakov, F. Lederer, and L. Vázquez, “Discrete fronts and quasirectangular solitons,” Phys. Rev. B 59, 5994–5997 (1999).
[CrossRef]

1998

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]

S. Darmanyan, A. Kobyakov, and F. Lederer, “Strongly localized modes in discrete systems with quadratic nonlinearity,” Phys. Rev. E 57, 2344–2349 (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]

P. D. Miller and O. Bang, “Macroscopic dynamics in quadratic nonlinear lattices,” Phys. Rev. E 57, 6038–6049 (1998).
[CrossRef]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520–3530 (1998).
[CrossRef]

R. Schiek, Y. Baek, and G. I. Stegeman, “Second-harmonic generation and cascaded nonlinearity in titanium-indiffused lithium niobate channel waveguides,” J. Opt. Soc. Am. B 15, 2255–2268 (1998).
[CrossRef]

1997

P. Millar, J. S. Aitchison, J. U. Kang, G. I. Stegeman, A. Villeneuve, G. T. Kennedy, and W. Sibbett, “Nonlinear waveguide arrays in AlGaAs,” J. Opt. Soc. Am. B 14, 3224–3231 (1997).
[CrossRef]

T. Peschel, R. Muschall, and F. Lederer, “Power-controlled beam steering in nonequidistant arrays of nonlinear waveguides,” Opt. Commun. 136, 16–21 (1997).
[CrossRef]

1996

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 46, 940–942 (1996).
[CrossRef]

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

W. Krolikowski and Y. S. Kivshar, “Soliton-based optical switching in waveguide arrays,” J. Opt. Soc. Am. B 13, 876–887 (1996).
[CrossRef]

O. Bang and P. D. Miller, “Exploiting discreteness for switching in waveguide arrays,” Opt. Lett. 21, 1105–1107 (1996).
[CrossRef] [PubMed]

1991

1990

J. B. Page, “Asymptotic solutions for localized vibrational modes in strongly anharmonic periodic systems,” Phys. Rev. B 41, 7835–7838 (1990).
[CrossRef]

1988

1987

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42–52 (1987).
[CrossRef]

1982

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1982).
[CrossRef]

Aceves, A. B.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[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]

P. Millar, J. S. Aitchison, J. U. Kang, G. I. Stegeman, A. Villeneuve, G. T. Kennedy, and W. Sibbett, “Nonlinear waveguide arrays in AlGaAs,” J. Opt. Soc. Am. B 14, 3224–3231 (1997).
[CrossRef]

Baek, Y.

R. Schiek, Y. Baek, and G. I. Stegeman, “Second-harmonic generation and cascaded nonlinearity in titanium-indiffused lithium niobate channel waveguides,” J. Opt. Soc. Am. B 15, 2255–2268 (1998).
[CrossRef]

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 46, 940–942 (1996).
[CrossRef]

Bang, O.

P. D. Miller and O. Bang, “Macroscopic dynamics in quadratic nonlinear lattices,” Phys. Rev. E 57, 6038–6049 (1998).
[CrossRef]

O. Bang and P. D. Miller, “Exploiting discreteness for switching in waveguide arrays,” Opt. Lett. 21, 1105–1107 (1996).
[CrossRef] [PubMed]

Baumann, I.

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 46, 940–942 (1996).
[CrossRef]

Bava, G. P.

E. Strake, G. P. Bava, and I. Montrosset, “Modes of channel waveguides: a novel quasi-analytical technique in comparison with the scalar finite-element method,” J. Lightwave Technol. 6, 1126–1135 (1988).
[CrossRef]

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42–52 (1987).
[CrossRef]

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]

Cristodoulides, D. N.

Darmanyan, S.

S. Darmanyan, A. Kobyakov, F. Lederer, and L. Vázquez, “Discrete fronts and quasirectangular solitons,” Phys. Rev. B 59, 5994–5997 (1999).
[CrossRef]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520–3530 (1998).
[CrossRef]

S. Darmanyan, A. Kobyakov, and F. Lederer, “Strongly localized modes in discrete systems with quadratic nonlinearity,” Phys. Rev. E 57, 2344–2349 (1998).
[CrossRef]

De Angelis, C.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[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]

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Jensen, S. M.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1982).
[CrossRef]

Joseph, R. I.

Kang, J. U.

Kennedy, G. T.

Kivshar, Y. S.

Kobyakov, A.

S. Darmanyan, A. Kobyakov, F. Lederer, and L. Vázquez, “Discrete fronts and quasirectangular solitons,” Phys. Rev. B 59, 5994–5997 (1999).
[CrossRef]

S. Darmanyan, A. Kobyakov, and F. Lederer, “Strongly localized modes in discrete systems with quadratic nonlinearity,” Phys. Rev. E 57, 2344–2349 (1998).
[CrossRef]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520–3530 (1998).
[CrossRef]

Krijnen, G.

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 46, 940–942 (1996).
[CrossRef]

Krolikowski, W.

Lederer, F.

S. Darmanyan, A. Kobyakov, F. Lederer, and L. Vázquez, “Discrete fronts and quasirectangular solitons,” Phys. Rev. B 59, 5994–5997 (1999).
[CrossRef]

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

S. Darmanyan, A. Kobyakov, and F. Lederer, “Strongly localized modes in discrete systems with quadratic nonlinearity,” Phys. Rev. E 57, 2344–2349 (1998).
[CrossRef]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520–3530 (1998).
[CrossRef]

T. Peschel, R. Muschall, and F. Lederer, “Power-controlled beam steering in nonequidistant arrays of nonlinear waveguides,” Opt. Commun. 136, 16–21 (1997).
[CrossRef]

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

C. Schmidt-Hattenberger, U. Trutschel, and F. Lederer, “Nonlinear switching in multiple-core couplers,” Opt. Lett. 16, 294–296 (1991).
[CrossRef] [PubMed]

Millar, P.

Miller, P. D.

P. D. Miller and O. Bang, “Macroscopic dynamics in quadratic nonlinear lattices,” Phys. Rev. E 57, 6038–6049 (1998).
[CrossRef]

O. Bang and P. D. Miller, “Exploiting discreteness for switching in waveguide arrays,” Opt. Lett. 21, 1105–1107 (1996).
[CrossRef] [PubMed]

Montrosset, I.

E. Strake, G. P. Bava, and I. Montrosset, “Modes of channel waveguides: a novel quasi-analytical technique in comparison with the scalar finite-element method,” J. Lightwave Technol. 6, 1126–1135 (1988).
[CrossRef]

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42–52 (1987).
[CrossRef]

Morandotti, 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]

Muschall, R.

T. Peschel, R. Muschall, and F. Lederer, “Power-controlled beam steering in nonequidistant arrays of nonlinear waveguides,” Opt. Commun. 136, 16–21 (1997).
[CrossRef]

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

Page, J. B.

J. B. Page, “Asymptotic solutions for localized vibrational modes in strongly anharmonic periodic systems,” Phys. Rev. B 41, 7835–7838 (1990).
[CrossRef]

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]

T. Peschel, R. Muschall, and F. Lederer, “Power-controlled beam steering in nonequidistant arrays of nonlinear waveguides,” Opt. Commun. 136, 16–21 (1997).
[CrossRef]

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[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]

Regener, R.

Schiek, R.

R. Schiek, Y. Baek, and G. I. Stegeman, “Second-harmonic generation and cascaded nonlinearity in titanium-indiffused lithium niobate channel waveguides,” J. Opt. Soc. Am. B 15, 2255–2268 (1998).
[CrossRef]

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 46, 940–942 (1996).
[CrossRef]

Schmidt, E.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520–3530 (1998).
[CrossRef]

Schmidt-Hattenberger, C.

Sibbett, W.

Silberberg, Y.

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]

Sohler, W.

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 46, 940–942 (1996).
[CrossRef]

R. Regener and W. Sohler, “Efficient second-harmonic generation in Ti:LiNbO3 channel waveguide resonators,” J. Opt. Soc. Am. B 5, 267–277 (1988).
[CrossRef]

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42–52 (1987).
[CrossRef]

Stegeman, G. I.

R. Schiek, Y. Baek, and G. I. Stegeman, “Second-harmonic generation and cascaded nonlinearity in titanium-indiffused lithium niobate channel waveguides,” J. Opt. Soc. Am. B 15, 2255–2268 (1998).
[CrossRef]

P. Millar, J. S. Aitchison, J. U. Kang, G. I. Stegeman, A. Villeneuve, G. T. Kennedy, and W. Sibbett, “Nonlinear waveguide arrays in AlGaAs,” J. Opt. Soc. Am. B 14, 3224–3231 (1997).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 46, 940–942 (1996).
[CrossRef]

Strake, E.

E. Strake, G. P. Bava, and I. Montrosset, “Modes of channel waveguides: a novel quasi-analytical technique in comparison with the scalar finite-element method,” J. Lightwave Technol. 6, 1126–1135 (1988).
[CrossRef]

Suche, H.

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42–52 (1987).
[CrossRef]

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Trillo, S.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

Trutschel, U.

Vázquez, L.

S. Darmanyan, A. Kobyakov, F. Lederer, and L. Vázquez, “Discrete fronts and quasirectangular solitons,” Phys. Rev. B 59, 5994–5997 (1999).
[CrossRef]

Villeneuve, A.

Wabnitz, S.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

IEEE J. Quantum Electron.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1982).
[CrossRef]

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42–52 (1987).
[CrossRef]

J. Lightwave Technol.

E. Strake, G. P. Bava, and I. Montrosset, “Modes of channel waveguides: a novel quasi-analytical technique in comparison with the scalar finite-element method,” J. Lightwave Technol. 6, 1126–1135 (1988).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

T. Peschel, R. Muschall, and F. Lederer, “Power-controlled beam steering in nonequidistant arrays of nonlinear waveguides,” Opt. Commun. 136, 16–21 (1997).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Phys. Rev. B

J. B. Page, “Asymptotic solutions for localized vibrational modes in strongly anharmonic periodic systems,” Phys. Rev. B 41, 7835–7838 (1990).
[CrossRef]

S. Darmanyan, A. Kobyakov, F. Lederer, and L. Vázquez, “Discrete fronts and quasirectangular solitons,” Phys. Rev. B 59, 5994–5997 (1999).
[CrossRef]

Phys. Rev. E

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[CrossRef]

S. Darmanyan, A. Kobyakov, and F. Lederer, “Strongly localized modes in discrete systems with quadratic nonlinearity,” Phys. Rev. E 57, 2344–2349 (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]

P. D. Miller and O. Bang, “Macroscopic dynamics in quadratic nonlinear lattices,” Phys. Rev. E 57, 6038–6049 (1998).
[CrossRef]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520–3530 (1998).
[CrossRef]

Phys. Rev. Lett.

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]

Other

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991), pp. 74–76.

M. M. Fejer, “Nonlinear optical frequency conversion: material requirements, engineered materials, and quasi-phasematching,” in Beam Shaping and Control with Nonlinear Optics (Plenum, New York, 1998), pp. 375–406.

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of a discrete domain wall and a Π-DS formed by two discrete domain walls. Upward- and downward-pointing arrows denote zero- and π-phase field oscillations, respectively.

Fig. 2
Fig. 2

Regions of stability, FI, and MI for Π-DS’s; s=cb/ca=0.2. Boundaries of the dark shaded regions correspond to the approximate analytical solution for MI [inequalities (16) and (17)], and a numerical solution of Eq. (14) is shown by dashed lines. No Π-DS exists for ν>2(2-s)x+2 [see inequality (9)].

Fig. 3
Fig. 3

Propagation of the perturbed FW component of the Π-DS; s=0.2, b=-1. (a) Stable solution (point S in Fig. 2), ca=0.24γ, β=-2γ; (b) decay that is due to MI (point M), ca=0.28γ, β=-2γ; (c) decay that is due to FI (point F), ca=0.33γ, β=8γ. The SH component has a similar form.

Fig. 4
Fig. 4

Dynamics of N=9 equally excited channels in (a) a stable (point S in Fig. 2) and (b) an unstable (point M) regime. Parameters are as in Figs. 3(a) and 3(b), respectively. γz=20.5.

Fig. 5
Fig. 5

Schematic of a quasi-phase-matched LiNbO3 waveguide array with the index profile induced by indiffusion of titanium stripes of width Ws=10 µm and separation Dg=20 µm. The calculated field profiles of the fundamental TE00 mode show strong coupling for the FW and negligible coupling for the SH.

Fig. 6
Fig. 6

Calculated propagation length for complete energy transfer of the FW between two waveguides (half-beat length, LA) as a function of the waveguide separation Dg (see Fig. 5).

Fig. 7
Fig. 7

Propagation of the FW amplitude of a rectangular excitation that comprises N=14 waveguides in a waveguide array with the decoupled SH (s=0, Fig. 5); β=-2γ, b=-1. (a) ca=0.22γ, (b) ca=0.3γ.

Equations (33)

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idAndZ+π2LA(An-1+An+1)+χAAn*Bn
×exp(-iΔkZ)=0,
idBndZ+π2LB(Bn-1+Bn+1)+χBAn2
×exp(iΔkZ)=0,
an=2AnBpeak,bn=BnBpeakexp(-iΔkZ),
z=ZL0,ca,b=πL02LA,B,β=-ΔkL0,
idandz+ca(an-1+an+1)+2γan*bn=0,
idbndz+cb(bn-1+bn+1)+βbn+γan2=0.
γ=ωdeff L0(20c3nω2n2ω)1/2BpeakΨ,
 Ψ=NL[eω(X, Y)]2e2ω*(X, Y)dXdY-+|eω(X, Y)|2dXdY-+|e2ω(X, Y)|2dXdY1/2
an=aun exp(ikz),bn=bvn exp(i2kz).
-kun+ca(un-1+un+1)+2γbunvn=0,
(β-2k)vn+cb(vn-1+vn+1)+γa2un2/b=0,
un(, 0, 0, 0, u4, u3, u2, u1, 1, 1, 1 ,),
vn(, 0, 0, 0, v4, v3, v2, v1, 1, 1, 1 ,),
a2=b(2k-2cb-β)/γ>0
k=2(γb+ca).
x=ca2γb,y=cb4γb-β,
u1=1-x24-3xy4,v1=1-x22-xy2,
u2=1+x+y2-3x28+1-ν2-νxy-3y28,
v2=1+x-x22+xy2,
u3=x-3x22+3xy2,v3=y+x2-ν2-νxy,
u4=x2,v4=y2,
ν=β/2γb.
detP-g1R01P+g0RR0T-g00R0T+g=0,
P=2(cos Q-1)x-1,
T=2(s cos Q-2)x-2+ν,
R2=4(2-s)x+4-2ν,s=cb/ca,
x>0,
x<0,ν<νMI2(3+s2+2s)x+2;
x>0,Q=π,GMI41+s-ν/26-νx1/2,
x<0,Q=π,
GMI(σ12+σ2)1/4 sin θ/2>GFI,

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