Abstract

We consider theoretically two coupled optical waveguides' with a varying barrier height along the waveguides direction. The barrier could be constructed by the elongated island with a reduced refractive index (that acts as a potential barrier), such that in the middle region it splits a waveguide into two weakly coupled parts. It is predicted by numerical simulations and analytical consideration that the presence of some imperfection of the system parameters can cause splitting of the injected laser beam and one will observe two intensity maximums at the output, while for small imperfections the input and output beam intensity distributions will be the same. The switching between two regimes could be achieved by changing the spectral width of the beam or the refractive index of the island. This nontrivial effect is explained by the possibility of transitions between the different eigenstates of the system in the region of large potential barrier heights. The mentioned effect could be used for all-optical readdressing and filtering purposes.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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  9. R. Khomeriki, “Nonlinear band gap transmission in optical waveguide arrays,” Phys. Rev. Lett. 92, 063905 (2004).
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  13. R. Khomeriki and S. Ruffo, “Nonadiabatic Landau-Zener tunneling in waveguide arrays with a step in the refractive index,” Phys. Rev. Lett. 94, 113904 (2005).
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  14. S. Longhi, “Landau-Zener dynamics in a curved optical directional coupler,” Acoust. Hologr. 7, L9-L12 (2005).
  15. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Optically induced Zener tunneling in one-dimensional lattices,” Opt. Lett. 31, 790-792 (2006).
    [CrossRef] [PubMed]
  16. A. S. Desyatnikov, Y. S. Kivshar, V. S. Shchesnovich, S. B. Cavalcanti, and J. M. Hickmann, “Resonant Zener tunneling in two-dimensional periodic photonic lattices,” Opt. Lett. 32, 325-327 (2007).
    [CrossRef] [PubMed]
  17. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
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  21. R. Khomeriki, J. Leon, and S. Ruffo, “Coexistence of Josephson oscillations and a novel self-trapping regime in optical waveguide arrays,” Phys. Rev. Lett. 97, 143902 (2006).
    [CrossRef] [PubMed]
  22. A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, “Signal processing by opto-optical interactions between self-localized and free propagating beams in liquid crystals,” Appl. Phys. Lett. 87, 261104 (2005).
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  23. L. Davidovich, “Sub-Poissonian processes in quantum optics,” Rev. Mod. Phys. 68, 127-173 (1996).
    [CrossRef]
  24. M. J. Ablowitz and Z. H. Musslimani, “Discrete spatial solitons in a diffraction-managed nonlinear waveguide array: a unified approach,” Physica D 184, 276303 (2003).
    [CrossRef]
  25. A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates,” Phys. Rev. Lett. 79, 4950-4953 (1997).
    [CrossRef]
  26. S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59, 620-633 (1999).
    [CrossRef]
  27. T. Kapitula and P. G. Kevrekidis, “Bose-Einstein condensates in the presence of a magnetic trap and optical lattice: two-mode approximation,” Nonlinearity 18, 2491-2512 (2005).
    [CrossRef]
  28. P. G. Kevrekidis, Zhigang Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, “Spontaneous symmetry breaking in photonic lattices: theory and experiment,” Phys. Lett. A 340, 275-280 (2005).
    [CrossRef]
  29. M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson Junction,” Phys. Rev. Lett. 95, 010402 (2005).
    [CrossRef] [PubMed]
  30. A. Ugulava, L. Chotorlishvili, and K. Nickoladze, “Quantum-mechanical research on nonlinear resonance and the problem of quantum chaos,” Phys. Rev. E 70, 026219 (2004).
    [CrossRef]
  31. A. Ugulava, L. Chotorlishvili, and K. Nickoladze, “Overlapping of nonlinear resonances and the problem of quantum chaos,” Phys. Rev. E 68, 026216 (2003).
    [CrossRef]

2007 (2)

T. Schwartz, G. Bartal, Sh. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52-55 (2007).
[CrossRef] [PubMed]

A. S. Desyatnikov, Y. S. Kivshar, V. S. Shchesnovich, S. B. Cavalcanti, and J. M. Hickmann, “Resonant Zener tunneling in two-dimensional periodic photonic lattices,” Opt. Lett. 32, 325-327 (2007).
[CrossRef] [PubMed]

2006 (2)

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Optically induced Zener tunneling in one-dimensional lattices,” Opt. Lett. 31, 790-792 (2006).
[CrossRef] [PubMed]

R. Khomeriki, J. Leon, and S. Ruffo, “Coexistence of Josephson oscillations and a novel self-trapping regime in optical waveguide arrays,” Phys. Rev. Lett. 97, 143902 (2006).
[CrossRef] [PubMed]

2005 (8)

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, “Signal processing by opto-optical interactions between self-localized and free propagating beams in liquid crystals,” Appl. Phys. Lett. 87, 261104 (2005).
[CrossRef]

R. S. Tasgal, Y. B. Band, and B. A. Malomed, “Gap solitons in a medium with third-harmonic generation,” Phys. Rev. E 72, 016624 (2005).
[CrossRef]

R. Khomeriki and J. Leon, “Light detectors bistable nonlinear waveguide arrays,” Phys. Rev. Lett. 94, 243902 (2005).
[CrossRef]

R. Khomeriki and S. Ruffo, “Nonadiabatic Landau-Zener tunneling in waveguide arrays with a step in the refractive index,” Phys. Rev. Lett. 94, 113904 (2005).
[CrossRef] [PubMed]

S. Longhi, “Landau-Zener dynamics in a curved optical directional coupler,” Acoust. Hologr. 7, L9-L12 (2005).

T. Kapitula and P. G. Kevrekidis, “Bose-Einstein condensates in the presence of a magnetic trap and optical lattice: two-mode approximation,” Nonlinearity 18, 2491-2512 (2005).
[CrossRef]

P. G. Kevrekidis, Zhigang Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, “Spontaneous symmetry breaking in photonic lattices: theory and experiment,” Phys. Lett. A 340, 275-280 (2005).
[CrossRef]

M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson Junction,” Phys. Rev. Lett. 95, 010402 (2005).
[CrossRef] [PubMed]

2004 (5)

A. Ugulava, L. Chotorlishvili, and K. Nickoladze, “Quantum-mechanical research on nonlinear resonance and the problem of quantum chaos,” Phys. Rev. E 70, 026219 (2004).
[CrossRef]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, “Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices,” Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

R. Khomeriki, “Nonlinear band gap transmission in optical waveguide arrays,” Phys. Rev. Lett. 92, 063905 (2004).
[CrossRef] [PubMed]

D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618 (2004).
[CrossRef]

2003 (3)

M. J. Ablowitz and Z. H. Musslimani, “Discrete spatial solitons in a diffraction-managed nonlinear waveguide array: a unified approach,” Physica D 184, 276303 (2003).
[CrossRef]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

A. Ugulava, L. Chotorlishvili, and K. Nickoladze, “Overlapping of nonlinear resonances and the problem of quantum chaos,” Phys. Rev. E 68, 026216 (2003).
[CrossRef]

2002 (1)

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

1999 (3)

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59, 620-633 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, A. Braüer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752-4755 (1999).
[CrossRef]

1998 (1)

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]

1997 (1)

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates,” Phys. Rev. Lett. 79, 4950-4953 (1997).
[CrossRef]

1996 (1)

L. Davidovich, “Sub-Poissonian processes in quantum optics,” Rev. Mod. Phys. 68, 127-173 (1996).
[CrossRef]

1988 (1)

1982 (1)

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. 18, 1568-1571 (1982).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz and Z. H. Musslimani, “Discrete spatial solitons in a diffraction-managed nonlinear waveguide array: a unified approach,” Physica D 184, 276303 (2003).
[CrossRef]

Agrawall, G. P.

Y. S. Kivshar and G. P. Agrawall, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Aitchison, J. S.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

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]

Alberucci, A.

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, “Signal processing by opto-optical interactions between self-localized and free propagating beams in liquid crystals,” Appl. Phys. Lett. 87, 261104 (2005).
[CrossRef]

Albiez, M.

M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson Junction,” Phys. Rev. Lett. 95, 010402 (2005).
[CrossRef] [PubMed]

Assanto, G.

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Optically induced Zener tunneling in one-dimensional lattices,” Opt. Lett. 31, 790-792 (2006).
[CrossRef] [PubMed]

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, “Signal processing by opto-optical interactions between self-localized and free propagating beams in liquid crystals,” Appl. Phys. Lett. 87, 261104 (2005).
[CrossRef]

Band, Y. B.

R. S. Tasgal, Y. B. Band, and B. A. Malomed, “Gap solitons in a medium with third-harmonic generation,” Phys. Rev. E 72, 016624 (2005).
[CrossRef]

Bartal, G.

T. Schwartz, G. Bartal, Sh. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52-55 (2007).
[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]

Brauer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Braüer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Braüer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752-4755 (1999).
[CrossRef]

Brzdakiewicz, K. A.

Cavalcanti, S. B.

Chen, Zhigang

P. G. Kevrekidis, Zhigang Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, “Spontaneous symmetry breaking in photonic lattices: theory and experiment,” Phys. Lett. A 340, 275-280 (2005).
[CrossRef]

Chotorlishvili, L.

A. Ugulava, L. Chotorlishvili, and K. Nickoladze, “Quantum-mechanical research on nonlinear resonance and the problem of quantum chaos,” Phys. Rev. E 70, 026219 (2004).
[CrossRef]

A. Ugulava, L. Chotorlishvili, and K. Nickoladze, “Overlapping of nonlinear resonances and the problem of quantum chaos,” Phys. Rev. E 68, 026216 (2003).
[CrossRef]

Christodoulides, D. N.

Cristiani, M.

M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson Junction,” Phys. Rev. Lett. 95, 010402 (2005).
[CrossRef] [PubMed]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Braüer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752-4755 (1999).
[CrossRef]

Davidovich, L.

L. Davidovich, “Sub-Poissonian processes in quantum optics,” Rev. Mod. Phys. 68, 127-173 (1996).
[CrossRef]

Desyatnikov, A. S.

Eisenberg, H. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

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]

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, A. Braüer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752-4755 (1999).
[CrossRef]

Fantoni, S.

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59, 620-633 (1999).
[CrossRef]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates,” Phys. Rev. Lett. 79, 4950-4953 (1997).
[CrossRef]

Fishman, Sh.

T. Schwartz, G. Bartal, Sh. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52-55 (2007).
[CrossRef] [PubMed]

Folling, J.

M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson Junction,” Phys. Rev. Lett. 95, 010402 (2005).
[CrossRef] [PubMed]

Frantzeskakis, D. J.

P. G. Kevrekidis, Zhigang Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, “Spontaneous symmetry breaking in photonic lattices: theory and experiment,” Phys. Lett. A 340, 275-280 (2005).
[CrossRef]

Fratalocchi, A.

Gati, R.

M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson Junction,” Phys. Rev. Lett. 95, 010402 (2005).
[CrossRef] [PubMed]

Giovanazzi, S.

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates,” Phys. Rev. Lett. 79, 4950-4953 (1997).
[CrossRef]

Hickmann, J. M.

Hunsmann, S.

M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson Junction,” Phys. Rev. Lett. 95, 010402 (2005).
[CrossRef] [PubMed]

Jensen, S. M.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. 18, 1568-1571 (1982).
[CrossRef]

Joseph, R. I.

Kapitula, T.

T. Kapitula and P. G. Kevrekidis, “Bose-Einstein condensates in the presence of a magnetic trap and optical lattice: two-mode approximation,” Nonlinearity 18, 2491-2512 (2005).
[CrossRef]

Karpierz, M. A.

Kevrekidis, P. G.

P. G. Kevrekidis, Zhigang Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, “Spontaneous symmetry breaking in photonic lattices: theory and experiment,” Phys. Lett. A 340, 275-280 (2005).
[CrossRef]

T. Kapitula and P. G. Kevrekidis, “Bose-Einstein condensates in the presence of a magnetic trap and optical lattice: two-mode approximation,” Nonlinearity 18, 2491-2512 (2005).
[CrossRef]

Khomeriki, R.

R. Khomeriki, J. Leon, and S. Ruffo, “Coexistence of Josephson oscillations and a novel self-trapping regime in optical waveguide arrays,” Phys. Rev. Lett. 97, 143902 (2006).
[CrossRef] [PubMed]

R. Khomeriki and J. Leon, “Light detectors bistable nonlinear waveguide arrays,” Phys. Rev. Lett. 94, 243902 (2005).
[CrossRef]

R. Khomeriki and S. Ruffo, “Nonadiabatic Landau-Zener tunneling in waveguide arrays with a step in the refractive index,” Phys. Rev. Lett. 94, 113904 (2005).
[CrossRef] [PubMed]

R. Khomeriki, “Nonlinear band gap transmission in optical waveguide arrays,” Phys. Rev. Lett. 92, 063905 (2004).
[CrossRef] [PubMed]

Kivshar, Y. S.

A. S. Desyatnikov, Y. S. Kivshar, V. S. Shchesnovich, S. B. Cavalcanti, and J. M. Hickmann, “Resonant Zener tunneling in two-dimensional periodic photonic lattices,” Opt. Lett. 32, 325-327 (2007).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, “Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices,” Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

Y. S. Kivshar and G. P. Agrawall, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Kivshar, Yu. S.

D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618 (2004).
[CrossRef]

Krolikowski, W.

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, “Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices,” Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

Lederer, F.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Braüer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752-4755 (1999).
[CrossRef]

Leon, J.

R. Khomeriki, J. Leon, and S. Ruffo, “Coexistence of Josephson oscillations and a novel self-trapping regime in optical waveguide arrays,” Phys. Rev. Lett. 97, 143902 (2006).
[CrossRef] [PubMed]

R. Khomeriki and J. Leon, “Light detectors bistable nonlinear waveguide arrays,” Phys. Rev. Lett. 94, 243902 (2005).
[CrossRef]

Longhi, S.

S. Longhi, “Landau-Zener dynamics in a curved optical directional coupler,” Acoust. Hologr. 7, L9-L12 (2005).

Malomed, B. A.

P. G. Kevrekidis, Zhigang Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, “Spontaneous symmetry breaking in photonic lattices: theory and experiment,” Phys. Lett. A 340, 275-280 (2005).
[CrossRef]

R. S. Tasgal, Y. B. Band, and B. A. Malomed, “Gap solitons in a medium with third-harmonic generation,” Phys. Rev. E 72, 016624 (2005).
[CrossRef]

Mandelik, D.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

Morandotti, R.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

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]

Musslimani, Z. H.

M. J. Ablowitz and Z. H. Musslimani, “Discrete spatial solitons in a diffraction-managed nonlinear waveguide array: a unified approach,” Physica D 184, 276303 (2003).
[CrossRef]

Neshev, D.

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, “Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices,” Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

Nickoladze, K.

A. Ugulava, L. Chotorlishvili, and K. Nickoladze, “Quantum-mechanical research on nonlinear resonance and the problem of quantum chaos,” Phys. Rev. E 70, 026219 (2004).
[CrossRef]

A. Ugulava, L. Chotorlishvili, and K. Nickoladze, “Overlapping of nonlinear resonances and the problem of quantum chaos,” Phys. Rev. E 68, 026216 (2003).
[CrossRef]

Oberthaler, M. K.

M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson Junction,” Phys. Rev. Lett. 95, 010402 (2005).
[CrossRef] [PubMed]

Pasquazi, A.

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, “Signal processing by opto-optical interactions between self-localized and free propagating beams in liquid crystals,” Appl. Phys. Lett. 87, 261104 (2005).
[CrossRef]

Peccianti, M.

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, “Signal processing by opto-optical interactions between self-localized and free propagating beams in liquid crystals,” Appl. Phys. Lett. 87, 261104 (2005).
[CrossRef]

Pelinovsky, D. E.

D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618 (2004).
[CrossRef]

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Braüer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752-4755 (1999).
[CrossRef]

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

Raghavan, S.

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59, 620-633 (1999).
[CrossRef]

Ruffo, S.

R. Khomeriki, J. Leon, and S. Ruffo, “Coexistence of Josephson oscillations and a novel self-trapping regime in optical waveguide arrays,” Phys. Rev. Lett. 97, 143902 (2006).
[CrossRef] [PubMed]

R. Khomeriki and S. Ruffo, “Nonadiabatic Landau-Zener tunneling in waveguide arrays with a step in the refractive index,” Phys. Rev. Lett. 94, 113904 (2005).
[CrossRef] [PubMed]

Schwartz, T.

T. Schwartz, G. Bartal, Sh. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52-55 (2007).
[CrossRef] [PubMed]

Segev, M.

T. Schwartz, G. Bartal, Sh. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52-55 (2007).
[CrossRef] [PubMed]

Shchesnovich, V. S.

Shenoy, S. R.

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59, 620-633 (1999).
[CrossRef]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates,” Phys. Rev. Lett. 79, 4950-4953 (1997).
[CrossRef]

Silberberg, Y.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

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]

Smerzi, A.

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59, 620-633 (1999).
[CrossRef]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates,” Phys. Rev. Lett. 79, 4950-4953 (1997).
[CrossRef]

Sukhorukov, A. A.

D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618 (2004).
[CrossRef]

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, “Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices,” Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

Tasgal, R. S.

R. S. Tasgal, Y. B. Band, and B. A. Malomed, “Gap solitons in a medium with third-harmonic generation,” Phys. Rev. E 72, 016624 (2005).
[CrossRef]

Ugulava, A.

A. Ugulava, L. Chotorlishvili, and K. Nickoladze, “Quantum-mechanical research on nonlinear resonance and the problem of quantum chaos,” Phys. Rev. E 70, 026219 (2004).
[CrossRef]

A. Ugulava, L. Chotorlishvili, and K. Nickoladze, “Overlapping of nonlinear resonances and the problem of quantum chaos,” Phys. Rev. E 68, 026216 (2003).
[CrossRef]

Weinstein, M. I.

P. G. Kevrekidis, Zhigang Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, “Spontaneous symmetry breaking in photonic lattices: theory and experiment,” Phys. Lett. A 340, 275-280 (2005).
[CrossRef]

Yariv, A.

A. Yariv, Optical Electronics, 4th ed. (Saunders College, 1991).

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Acoust. Hologr. (1)

S. Longhi, “Landau-Zener dynamics in a curved optical directional coupler,” Acoust. Hologr. 7, L9-L12 (2005).

Appl. Phys. Lett. (1)

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, “Signal processing by opto-optical interactions between self-localized and free propagating beams in liquid crystals,” Appl. Phys. Lett. 87, 261104 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. 18, 1568-1571 (1982).
[CrossRef]

Nature (1)

T. Schwartz, G. Bartal, Sh. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52-55 (2007).
[CrossRef] [PubMed]

Nonlinearity (1)

T. Kapitula and P. G. Kevrekidis, “Bose-Einstein condensates in the presence of a magnetic trap and optical lattice: two-mode approximation,” Nonlinearity 18, 2491-2512 (2005).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

P. G. Kevrekidis, Zhigang Chen, B. A. Malomed, D. J. Frantzeskakis, and M. I. Weinstein, “Spontaneous symmetry breaking in photonic lattices: theory and experiment,” Phys. Lett. A 340, 275-280 (2005).
[CrossRef]

Phys. Rev. A (1)

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59, 620-633 (1999).
[CrossRef]

Phys. Rev. E (4)

A. Ugulava, L. Chotorlishvili, and K. Nickoladze, “Quantum-mechanical research on nonlinear resonance and the problem of quantum chaos,” Phys. Rev. E 70, 026219 (2004).
[CrossRef]

A. Ugulava, L. Chotorlishvili, and K. Nickoladze, “Overlapping of nonlinear resonances and the problem of quantum chaos,” Phys. Rev. E 68, 026216 (2003).
[CrossRef]

R. S. Tasgal, Y. B. Band, and B. A. Malomed, “Gap solitons in a medium with third-harmonic generation,” Phys. Rev. E 72, 016624 (2005).
[CrossRef]

D. E. Pelinovsky, A. A. Sukhorukov, and Yu. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E 70, 036618 (2004).
[CrossRef]

Phys. Rev. Lett. (13)

R. Khomeriki and J. Leon, “Light detectors bistable nonlinear waveguide arrays,” Phys. Rev. Lett. 94, 243902 (2005).
[CrossRef]

R. Khomeriki and S. Ruffo, “Nonadiabatic Landau-Zener tunneling in waveguide arrays with a step in the refractive index,” Phys. Rev. Lett. 94, 113904 (2005).
[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]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, “Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices,” Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

R. Khomeriki, “Nonlinear band gap transmission in optical waveguide arrays,” Phys. Rev. Lett. 92, 063905 (2004).
[CrossRef] [PubMed]

R. Khomeriki, J. Leon, and S. Ruffo, “Coexistence of Josephson oscillations and a novel self-trapping regime in optical waveguide arrays,” Phys. Rev. Lett. 97, 143902 (2006).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, A. Braüer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752-4755 (1999).
[CrossRef]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates,” Phys. Rev. Lett. 79, 4950-4953 (1997).
[CrossRef]

M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson Junction,” Phys. Rev. Lett. 95, 010402 (2005).
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Physica D (1)

M. J. Ablowitz and Z. H. Musslimani, “Discrete spatial solitons in a diffraction-managed nonlinear waveguide array: a unified approach,” Physica D 184, 276303 (2003).
[CrossRef]

Rev. Mod. Phys. (1)

L. Davidovich, “Sub-Poissonian processes in quantum optics,” Rev. Mod. Phys. 68, 127-173 (1996).
[CrossRef]

Other (2)

A. Yariv, Optical Electronics, 4th ed. (Saunders College, 1991).

Y. S. Kivshar and G. P. Agrawall, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

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Figures (3)

Fig. 1
Fig. 1

Suggested experimental setup for observation of the self-chaotization process between two eigenstates. In the proposed device there is an elongated area with a smaller refractive index ( n < n 0 ) and a spatial length Δ z splitting the waveguide into two parts in the middle region. The light is polarized linearly along the transverse y direction. (a) Upper panel: the low imperfections of the system are considered and as a result the intensity distributions across the waveguide (axis x) are the same at both the input and output. The lower panel represents the situation for larger imperfections and the picture is different: instead of a single intensity maximum at the output one should observe the splitting of the injected beam. (b) Input–output intensity distributions in the case of large imperfections.

Fig. 2
Fig. 2

Dependence of the propagation constants E 1 0 and E 2 0 of the first two modes on the barrier height v of the double harmonic well potential. As seen, for large v’s the eigenvalues E 1 0 and E 2 0 are very close. Insets display the form of linear modes in the double well potential for zero barrier and large barrier heights.

Fig. 3
Fig. 3

Three-dimensional graphs of the intensity distribution describing the numerical simulations on Eq. (4). The runs are averaged over random distributions of H H s + H a [see Eq. (4)]. Particularly, for (a) the distribution is taken such that K 2 δ E 1 δ E 2 0.0002 , while for (b) it is K 2 δ E 1 δ E 2 0.002 . For the larger fluctuations two intensity maximums at the output part of (b) are clearly seen. The inset in (a) shows the variation of the potential barrier height v along the waveguide in both the large and small fluctuation cases.

Equations (21)

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× × E + 1 c 2 2 t 2 { n 2 E } = 0 ,
E ( r , t ) = e ̂ y ( Ψ ( x , z ) e i ( ω t k z ) + c.c. ) ,
2 i k Ψ z + 2 Ψ x 2 k 2 ( 1 [ n ( z , x ) ] 2 n 0 2 ) Ψ = 0 .
i Ψ z = ( H 0 + H ) Ψ , H 0 = 1 4 2 x 2 + 4 v ( z ) V ( x ) ,
H 0 Φ + = E 1 0 Φ + , H 0 Φ = E 2 0 Φ .
L L ( Φ + ) 2 d x = 1 , L L ( Φ ) 2 d x = 1 , L L Φ + Φ d x = 0 .
Φ + = ( 1 L ) cos ( π x 2 L ) , Φ = ( 1 L ) sin ( π x L ) .
Ψ ( x , z ) = ψ 1 ( z ) Φ + ( x ) + ψ 2 ( z ) Φ ( x ) ,
i ψ 1 z = E 1 ψ 1 + K ψ 2 , i ψ 2 z = E 2 ψ 2 + K ψ 1 ,
L L Φ ± H s Φ ± d x = δ E 1 , 2 , L L Φ ± H a Φ ± d x = 0 ,
L L Φ + H 0 Φ d x = 0 ,
L L Φ + H s Φ d x = 0 , L L Φ + H a Φ d x K .
ψ 1 2 = 1 ψ 2 2 , ψ 2 2 = 4 K 2 sin 2 [ ( z 2 ) 4 K 2 + Δ E 2 ] 4 K 2 + Δ E 2 ,
ϕ 2 = E 1 + E 2 2 z , ϕ 1 = ϕ 2 + ϕ , cos ϕ = Δ E ψ 2 2 K ψ 1 .
ψ 1 = cos ( K z ) e i E 1 z , ψ 2 = i sin ( K z ) e i E 2 z .
ψ 2 = e i E 1 ( z Δ z ) cos ( K Δ z ) Φ + i e i E 2 ( z Δ z ) sin ( K Δ z ) Φ 2 = cos 2 ( K Δ z ) Φ + 2 + sin 2 ( K Δ z ) Φ 2 sin ( 2 K Δ z ) sin ( Δ E ( z Δ z ) ) Φ + Φ .
cos ( K z ) 1 , cos 2 ( K z ) 1 ,
sin ( K z ) 0 , sin 2 ( K z ) 0 ,
Ψ Φ + ( x ) , Ψ 2 Φ + 2 ( x ) .
cos 2 ( K Δ z ) = sin 2 ( K Δ z ) = 1 2 , sin ( 2 K Δ z ) = 0 ,
Ψ 2 = 1 2 ( Φ + 2 ( x ) + Φ 2 ( x ) ) .

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