Abstract

We propose a mechanism by which a number of useful all-optical operations, such as switches, diodes, and logic gates, can be performed with a single device. An effective potential well is obtained by modulating the coupling between the waveguides through their separations. Depending on the power of a control soliton injected through the potential well, an incoming soliton will either completely transmit or reflect forming a controllable switch. We show that two such switches can work as AND, OR, NAND, and NOR logic gates. Furthermore, the same device may also function as a perfect soliton diode with adjustable polarity. We discuss the feasibility of realising such devices with current experimental setups.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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  12. Y. Wu, “New all-optical switch based on the spatial soliton repulsion,” Opt. Express 14(9), 4005–4012 (2006).
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  14. K. M. Aghdami, M. Golshani, and R. Kheradmand, “Two-dimensional discrete cavity solitons: switching and all-optical gates,” IEEE Photon. J. 4(4), 1147–1154 (2012).
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    [Crossref] [PubMed]
  23. A. Khare, S. V. Dmitriev, and A. Saxena, “Exact moving and stationary solutions of a generalized discrete nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 40(37), 11301–11317 (2007).
    [Crossref]
  24. A. Ankiewicz, N. Devine, M. Ünal, A. Chowdury, and N. Akhmediev, “Rogue waves and other solutions of single and coupled Ablowitz-Ladik and nonlinear Schrödinger equations,” J. Opt. 15(6), 064008 (2013).
    [Crossref]
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    [Crossref]
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    [Crossref]
  27. A. Maluckov, L. Hadžievski, and B. A. Malomed, “Staggered and moving localized modes in dynamical lattices with the cubic-quintic nonlinearity,” Phys. Rev. E. 77(33), 036604 (2008).
    [Crossref]
  28. M. Peyrard and M. D. Kruskal, “Kink dynamics in the highly discrete sine-Gordon system,” Physica D 14(1), 88–102 (1984).
    [Crossref]
  29. R. H. Goodman, P. J. Holmes, and M. I. Weinstein, “Strong NLS soliton-defect interactions,” Physica D 192(3–4), 215–248 (2004).
    [Crossref]
  30. C. Lee and J. Brand, “Enhanced quantum reflection of matter-wave solitons,” Europhys. Lett. 73(3), 321–327 (2006).
    [Crossref]
  31. T. Ernst and J. Brand, “Resonant trapping in the transport of a matter-wave soliton through a quantum well,” Phys. Rev. A. 81(3), 033614 (2010).
    [Crossref]
  32. M. Asad-uz-zaman and U. Al Khawaja, “Directional flow of solitons with asymmetric potential wells: soliton diode,” EPL 101(5), 50008 (2013).
    [Crossref]
  33. A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Express, , “Control of directional evanescent coupling in fs laser written waveguides,” Opt. Express 15(4), 1579–1587 (2007).
    [Crossref] [PubMed]
  34. M. Bellec, G. M. Nikolopoulos, and S. Tzortzakis, Optics Letters, “Faithful communication Hamiltonian in photonic lattices,” Opt. lett. 37(21), 4504–4506 (2012).
    [Crossref] [PubMed]
  35. A. A. Sukhorukov, “Reflectionless potentials and cavities in waveguide arrays and coupled-resonator structures,” Opt. lett. 35(7), 989–991 (2010).
    [Crossref] [PubMed]
  36. A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. A. Sukhorukov, “Realization of reflectionless potentials in photonic lattices,” Phys. Rev. Lett. 106, 193903 (2011).
    [Crossref] [PubMed]
  37. A. A. Sukhorukov, “Enhanced soliton transport in quasiperiodic lattices with introduced aperiodicity,” Phys. Rev. Lett. 96, 113902 (2006).
    [Crossref] [PubMed]
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    [Crossref]

2013 (3)

A. Ankiewicz, N. Devine, M. Ünal, A. Chowdury, and N. Akhmediev, “Rogue waves and other solutions of single and coupled Ablowitz-Ladik and nonlinear Schrödinger equations,” J. Opt. 15(6), 064008 (2013).
[Crossref]

C. Mejía-Cortés, R. A. Vicencio, and B. A. Malomed, “Mobility of solitons in one-dimensional lattices with the cubic-quintic nonlinearity,” Phys. Rev. E. 88(5), 052901 (2013).
[Crossref]

M. Asad-uz-zaman and U. Al Khawaja, “Directional flow of solitons with asymmetric potential wells: soliton diode,” EPL 101(5), 50008 (2013).
[Crossref]

2012 (2)

K. M. Aghdami, M. Golshani, and R. Kheradmand, “Two-dimensional discrete cavity solitons: switching and all-optical gates,” IEEE Photon. J. 4(4), 1147–1154 (2012).
[Crossref]

M. Bellec, G. M. Nikolopoulos, and S. Tzortzakis, Optics Letters, “Faithful communication Hamiltonian in photonic lattices,” Opt. lett. 37(21), 4504–4506 (2012).
[Crossref] [PubMed]

2011 (3)

A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. A. Sukhorukov, “Realization of reflectionless potentials in photonic lattices,” Phys. Rev. Lett. 106, 193903 (2011).
[Crossref] [PubMed]

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Sci. Rep. 1, 94 (2011).
[Crossref]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices”, Phys. Rev. Lett. 107(10), 103601 (2011).
[Crossref] [PubMed]

2010 (5)

A. Szameit and S. Nolte, “Discrete optics in femtosecond-laser-written photonic structures,” J. Phys. B 43(16), 163001 (2010).
[Crossref]

T. Ernst and J. Brand, “Resonant trapping in the transport of a matter-wave soliton through a quantum well,” Phys. Rev. A. 81(3), 033614 (2010).
[Crossref]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Soliton gating and switching in liquid crystal light valve,” Appl. Phys. Lett. 96(7), 071104 (2010).
[Crossref]

U. Al Khawaja, “A comparative analysis of Painlevé, Lax pair, and similarity transformation methods in obtaining the integrability conditions of nonlinear Schrödinger equations,” J. Math. Phys. 51(5), 053506 (2010).
[Crossref]

A. A. Sukhorukov, “Reflectionless potentials and cavities in waveguide arrays and coupled-resonator structures,” Opt. lett. 35(7), 989–991 (2010).
[Crossref] [PubMed]

2008 (3)

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

A. Maluckov, L. Hadžievski, and B. A. Malomed, “Staggered and moving localized modes in dynamical lattices with the cubic-quintic nonlinearity,” Phys. Rev. E. 77(33), 036604 (2008).
[Crossref]

2007 (4)

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[Crossref] [PubMed]

A. Khare, S. V. Dmitriev, and A. Saxena, “Exact moving and stationary solutions of a generalized discrete nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 40(37), 11301–11317 (2007).
[Crossref]

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Express, , “Control of directional evanescent coupling in fs laser written waveguides,” Opt. Express 15(4), 1579–1587 (2007).
[Crossref] [PubMed]

Y. Wu, M. Huang, M. Chen, and R. Tasy, “All-optical switch based on the local nonlinear Mach-Zehnder interferometer,” Opt. Express 15(16), 9883–9892 (2007).
[Crossref] [PubMed]

2006 (4)

Y. Wu, “New all-optical switch based on the spatial soliton repulsion,” Opt. Express 14(9), 4005–4012 (2006).
[Crossref] [PubMed]

A. A. Sukhorukov, “Enhanced soliton transport in quasiperiodic lattices with introduced aperiodicity,” Phys. Rev. Lett. 96, 113902 (2006).
[Crossref] [PubMed]

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

C. Lee and J. Brand, “Enhanced quantum reflection of matter-wave solitons,” Europhys. Lett. 73(3), 321–327 (2006).
[Crossref]

2005 (2)

Y. Wu, “All-optical logic gates by using multibranch waveguide structure with localized optical nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 11(2), 307–312 (2005).
[Crossref]

J. Scheuer and M. Orenstein, “All-optical gates facilitated by soliton interactions in multilayered Kerr medium”, J. Opt. Soc. Am. B 22, 1260 (2005).
[Crossref]

2004 (1)

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, “Strong NLS soliton-defect interactions,” Physica D 192(3–4), 215–248 (2004).
[Crossref]

2003 (2)

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” IEEE J. Quantum Electron. 39(31), 31–55 (2003).
[Crossref]

I. E. Papacharalampous, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, “Soliton collisions in the discrete nonlinear Schrödinger equation,” Phys. Rev. E 68(42), 046604 (2003).
[Crossref]

2002 (1)

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81(18), 3335–3337 (2002).
[Crossref]

2001 (1)

D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete Solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001).
[Crossref] [PubMed]

1996 (1)

1995 (1)

1989 (1)

J. P. Sabini, N. Finlayson, and G. I. Stegeman, “All-optical switching In nonlinear X junctions,” Appl. Phys. Lett. 55(12), 1176–1178 (1989).
[Crossref]

1984 (1)

M. Peyrard and M. D. Kruskal, “Kink dynamics in the highly discrete sine-Gordon system,” Physica D 14(1), 88–102 (1984).
[Crossref]

Aghdami, K. M.

K. M. Aghdami, M. Golshani, and R. Kheradmand, “Two-dimensional discrete cavity solitons: switching and all-optical gates,” IEEE Photon. J. 4(4), 1147–1154 (2012).
[Crossref]

Akhmediev, N.

A. Ankiewicz, N. Devine, M. Ünal, A. Chowdury, and N. Akhmediev, “Rogue waves and other solutions of single and coupled Ablowitz-Ladik and nonlinear Schrödinger equations,” J. Opt. 15(6), 064008 (2013).
[Crossref]

Akhmediev, N.N.

N.N. Akhmediev and A. Ankiexicz, Solitons: Nonlinear Pulses and Beams (Chapman and Hall, 1997).

Al Khawaja, U.

M. Asad-uz-zaman and U. Al Khawaja, “Directional flow of solitons with asymmetric potential wells: soliton diode,” EPL 101(5), 50008 (2013).
[Crossref]

U. Al Khawaja, “A comparative analysis of Painlevé, Lax pair, and similarity transformation methods in obtaining the integrability conditions of nonlinear Schrödinger equations,” J. Math. Phys. 51(5), 053506 (2010).
[Crossref]

Alberucci, A.

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Soliton gating and switching in liquid crystal light valve,” Appl. Phys. Lett. 96(7), 071104 (2010).
[Crossref]

Ankiewicz, A.

A. Ankiewicz, N. Devine, M. Ünal, A. Chowdury, and N. Akhmediev, “Rogue waves and other solutions of single and coupled Ablowitz-Ladik and nonlinear Schrödinger equations,” J. Opt. 15(6), 064008 (2013).
[Crossref]

Ankiexicz, A.

N.N. Akhmediev and A. Ankiexicz, Solitons: Nonlinear Pulses and Beams (Chapman and Hall, 1997).

Asad-uz-zaman, M.

M. Asad-uz-zaman and U. Al Khawaja, “Directional flow of solitons with asymmetric potential wells: soliton diode,” EPL 101(5), 50008 (2013).
[Crossref]

Assanto, G.

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Soliton gating and switching in liquid crystal light valve,” Appl. Phys. Lett. 96(7), 071104 (2010).
[Crossref]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81(18), 3335–3337 (2002).
[Crossref]

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[Crossref] [PubMed]

Bellec, M.

Bortolozzo, U.

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Soliton gating and switching in liquid crystal light valve,” Appl. Phys. Lett. 96(7), 071104 (2010).
[Crossref]

Brand, J.

T. Ernst and J. Brand, “Resonant trapping in the transport of a matter-wave soliton through a quantum well,” Phys. Rev. A. 81(3), 033614 (2010).
[Crossref]

C. Lee and J. Brand, “Enhanced quantum reflection of matter-wave solitons,” Europhys. Lett. 73(3), 321–327 (2006).
[Crossref]

Chen, M.

Chowdury, A.

A. Ankiewicz, N. Devine, M. Ünal, A. Chowdury, and N. Akhmediev, “Rogue waves and other solutions of single and coupled Ablowitz-Ladik and nonlinear Schrödinger equations,” J. Opt. 15(6), 064008 (2013).
[Crossref]

Christodoulides, D. N.

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Sci. Rep. 1, 94 (2011).
[Crossref]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices”, Phys. Rev. Lett. 107(10), 103601 (2011).
[Crossref] [PubMed]

D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete Solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001).
[Crossref] [PubMed]

Chu, P. L.

Conti, C.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81(18), 3335–3337 (2002).
[Crossref]

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

De Luca, A.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81(18), 3335–3337 (2002).
[Crossref]

Desyatnikov, A.

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

Devine, N.

A. Ankiewicz, N. Devine, M. Ünal, A. Chowdury, and N. Akhmediev, “Rogue waves and other solutions of single and coupled Ablowitz-Ladik and nonlinear Schrödinger equations,” J. Opt. 15(6), 064008 (2013).
[Crossref]

Dmitriev, S. V.

A. Khare, S. V. Dmitriev, and A. Saxena, “Exact moving and stationary solutions of a generalized discrete nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 40(37), 11301–11317 (2007).
[Crossref]

Dreisow, F.

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices”, Phys. Rev. Lett. 107(10), 103601 (2011).
[Crossref] [PubMed]

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Sci. Rep. 1, 94 (2011).
[Crossref]

A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. A. Sukhorukov, “Realization of reflectionless potentials in photonic lattices,” Phys. Rev. Lett. 106, 193903 (2011).
[Crossref] [PubMed]

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Express, , “Control of directional evanescent coupling in fs laser written waveguides,” Opt. Express 15(4), 1579–1587 (2007).
[Crossref] [PubMed]

Eisenberg, H. S.

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” IEEE J. Quantum Electron. 39(31), 31–55 (2003).
[Crossref]

Ernst, T.

T. Ernst and J. Brand, “Resonant trapping in the transport of a matter-wave soliton through a quantum well,” Phys. Rev. A. 81(3), 033614 (2010).
[Crossref]

Eugenieva, E. D.

D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete Solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001).
[Crossref] [PubMed]

Finlayson, N.

J. P. Sabini, N. Finlayson, and G. I. Stegeman, “All-optical switching In nonlinear X junctions,” Appl. Phys. Lett. 55(12), 1176–1178 (1989).
[Crossref]

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[Crossref] [PubMed]

Frantzeskakis, D. J.

I. E. Papacharalampous, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, “Soliton collisions in the discrete nonlinear Schrödinger equation,” Phys. Rev. E 68(42), 046604 (2003).
[Crossref]

Gattass, R. R.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

Golshani, M.

K. M. Aghdami, M. Golshani, and R. Kheradmand, “Two-dimensional discrete cavity solitons: switching and all-optical gates,” IEEE Photon. J. 4(4), 1147–1154 (2012).
[Crossref]

Goodman, R. H.

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, “Strong NLS soliton-defect interactions,” Physica D 192(3–4), 215–248 (2004).
[Crossref]

Gordon, J.P.

L.F. Mollenauer and J.P. Gordon, Solitons in Optical Fibers (Acadamic, 2006).

Hadžievski, L.

A. Maluckov, L. Hadžievski, and B. A. Malomed, “Staggered and moving localized modes in dynamical lattices with the cubic-quintic nonlinearity,” Phys. Rev. E. 77(33), 036604 (2008).
[Crossref]

Hasegawa, A.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford University, 1995).

Heinrich, M.

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Sci. Rep. 1, 94 (2011).
[Crossref]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices”, Phys. Rev. Lett. 107(10), 103601 (2011).
[Crossref] [PubMed]

A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. A. Sukhorukov, “Realization of reflectionless potentials in photonic lattices,” Phys. Rev. Lett. 106, 193903 (2011).
[Crossref] [PubMed]

Holmes, P. J.

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, “Strong NLS soliton-defect interactions,” Physica D 192(3–4), 215–248 (2004).
[Crossref]

Huang, M.

Keil, R.

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Sci. Rep. 1, 94 (2011).
[Crossref]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices”, Phys. Rev. Lett. 107(10), 103601 (2011).
[Crossref] [PubMed]

Kevrekidis, P. G.

I. E. Papacharalampous, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, “Soliton collisions in the discrete nonlinear Schrödinger equation,” Phys. Rev. E 68(42), 046604 (2003).
[Crossref]

Khare, A.

A. Khare, S. V. Dmitriev, and A. Saxena, “Exact moving and stationary solutions of a generalized discrete nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 40(37), 11301–11317 (2007).
[Crossref]

Kheradmand, R.

K. M. Aghdami, M. Golshani, and R. Kheradmand, “Two-dimensional discrete cavity solitons: switching and all-optical gates,” IEEE Photon. J. 4(4), 1147–1154 (2012).
[Crossref]

Kivshar, Y.

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

Kivshar, Y. S.

Kodama, Y.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford University, 1995).

Krolikowski, W.

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

Królikowski, W.

Kruskal, M. D.

M. Peyrard and M. D. Kruskal, “Kink dynamics in the highly discrete sine-Gordon system,” Physica D 14(1), 88–102 (1984).
[Crossref]

Lederer, F.

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

Lee, C.

C. Lee and J. Brand, “Enhanced quantum reflection of matter-wave solitons,” Europhys. Lett. 73(3), 321–327 (2006).
[Crossref]

Malomed, B. A.

C. Mejía-Cortés, R. A. Vicencio, and B. A. Malomed, “Mobility of solitons in one-dimensional lattices with the cubic-quintic nonlinearity,” Phys. Rev. E. 88(5), 052901 (2013).
[Crossref]

A. Maluckov, L. Hadžievski, and B. A. Malomed, “Staggered and moving localized modes in dynamical lattices with the cubic-quintic nonlinearity,” Phys. Rev. E. 77(33), 036604 (2008).
[Crossref]

I. E. Papacharalampous, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, “Soliton collisions in the discrete nonlinear Schrödinger equation,” Phys. Rev. E 68(42), 046604 (2003).
[Crossref]

P. L. Chu, Y. S. Kivshar, B. A. Malomed, G. Peng, and M. L. Quiroga-Teixeiro, “Soliton controlling, switching, and splitting in nonlinear fused-fiber couplers,” J. Opt. Soc. Am. B 12(5), 898–903 (1995).
[Crossref]

Maluckov, A.

A. Maluckov, L. Hadžievski, and B. A. Malomed, “Staggered and moving localized modes in dynamical lattices with the cubic-quintic nonlinearity,” Phys. Rev. E. 77(33), 036604 (2008).
[Crossref]

Mazur, E.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

Mejía-Cortés, C.

C. Mejía-Cortés, R. A. Vicencio, and B. A. Malomed, “Mobility of solitons in one-dimensional lattices with the cubic-quintic nonlinearity,” Phys. Rev. E. 88(5), 052901 (2013).
[Crossref]

Mollenauer, L.F.

L.F. Mollenauer and J.P. Gordon, Solitons in Optical Fibers (Acadamic, 2006).

Moya-Cessa, H.

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices”, Phys. Rev. Lett. 107(10), 103601 (2011).
[Crossref] [PubMed]

Neshev, D.

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

Nikolopoulos, G. M.

Nolte, S.

A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. A. Sukhorukov, “Realization of reflectionless potentials in photonic lattices,” Phys. Rev. Lett. 106, 193903 (2011).
[Crossref] [PubMed]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices”, Phys. Rev. Lett. 107(10), 103601 (2011).
[Crossref] [PubMed]

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Sci. Rep. 1, 94 (2011).
[Crossref]

A. Szameit and S. Nolte, “Discrete optics in femtosecond-laser-written photonic structures,” J. Phys. B 43(16), 163001 (2010).
[Crossref]

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Express, , “Control of directional evanescent coupling in fs laser written waveguides,” Opt. Express 15(4), 1579–1587 (2007).
[Crossref] [PubMed]

O’Brien, J. L.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

Orenstein, M.

Papacharalampous, I. E.

I. E. Papacharalampous, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, “Soliton collisions in the discrete nonlinear Schrödinger equation,” Phys. Rev. E 68(42), 046604 (2003).
[Crossref]

Peccianti, M.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81(18), 3335–3337 (2002).
[Crossref]

Peng, G.

Perez-Leija, A.

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices”, Phys. Rev. Lett. 107(10), 103601 (2011).
[Crossref] [PubMed]

Pertsch, T.

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Sci. Rep. 1, 94 (2011).
[Crossref]

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Express, , “Control of directional evanescent coupling in fs laser written waveguides,” Opt. Express 15(4), 1579–1587 (2007).
[Crossref] [PubMed]

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

Peschel, U.

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

Peyrard, M.

M. Peyrard and M. D. Kruskal, “Kink dynamics in the highly discrete sine-Gordon system,” Physica D 14(1), 88–102 (1984).
[Crossref]

Piccardi, A.

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Soliton gating and switching in liquid crystal light valve,” Appl. Phys. Lett. 96(7), 071104 (2010).
[Crossref]

Politi, A.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

Quiroga-Teixeiro, M. L.

Rarity, J. G.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

Residori, S.

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Soliton gating and switching in liquid crystal light valve,” Appl. Phys. Lett. 96(7), 071104 (2010).
[Crossref]

Sabini, J. P.

J. P. Sabini, N. Finlayson, and G. I. Stegeman, “All-optical switching In nonlinear X junctions,” Appl. Phys. Lett. 55(12), 1176–1178 (1989).
[Crossref]

Saxena, A.

A. Khare, S. V. Dmitriev, and A. Saxena, “Exact moving and stationary solutions of a generalized discrete nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 40(37), 11301–11317 (2007).
[Crossref]

Scheuer, J.

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[Crossref] [PubMed]

Segev, M.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[Crossref] [PubMed]

Silberberg, Y.

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” IEEE J. Quantum Electron. 39(31), 31–55 (2003).
[Crossref]

Stegeman, G. I.

J. P. Sabini, N. Finlayson, and G. I. Stegeman, “All-optical switching In nonlinear X junctions,” Appl. Phys. Lett. 55(12), 1176–1178 (1989).
[Crossref]

Sukhorukov, A.

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

Sukhorukov, A. A.

A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. A. Sukhorukov, “Realization of reflectionless potentials in photonic lattices,” Phys. Rev. Lett. 106, 193903 (2011).
[Crossref] [PubMed]

A. A. Sukhorukov, “Reflectionless potentials and cavities in waveguide arrays and coupled-resonator structures,” Opt. lett. 35(7), 989–991 (2010).
[Crossref] [PubMed]

A. A. Sukhorukov, “Enhanced soliton transport in quasiperiodic lattices with introduced aperiodicity,” Phys. Rev. Lett. 96, 113902 (2006).
[Crossref] [PubMed]

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” IEEE J. Quantum Electron. 39(31), 31–55 (2003).
[Crossref]

Szameit, A.

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices”, Phys. Rev. Lett. 107(10), 103601 (2011).
[Crossref] [PubMed]

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Sci. Rep. 1, 94 (2011).
[Crossref]

A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. A. Sukhorukov, “Realization of reflectionless potentials in photonic lattices,” Phys. Rev. Lett. 106, 193903 (2011).
[Crossref] [PubMed]

A. Szameit and S. Nolte, “Discrete optics in femtosecond-laser-written photonic structures,” J. Phys. B 43(16), 163001 (2010).
[Crossref]

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Express, , “Control of directional evanescent coupling in fs laser written waveguides,” Opt. Express 15(4), 1579–1587 (2007).
[Crossref] [PubMed]

Tasy, R.

Trompeter, H.

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

Tünnermann, A.

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Sci. Rep. 1, 94 (2011).
[Crossref]

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Express, , “Control of directional evanescent coupling in fs laser written waveguides,” Opt. Express 15(4), 1579–1587 (2007).
[Crossref] [PubMed]

Tzortzakis, S.

Umeton, C.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81(18), 3335–3337 (2002).
[Crossref]

Ünal, M.

A. Ankiewicz, N. Devine, M. Ünal, A. Chowdury, and N. Akhmediev, “Rogue waves and other solutions of single and coupled Ablowitz-Ladik and nonlinear Schrödinger equations,” J. Opt. 15(6), 064008 (2013).
[Crossref]

Vicencio, R. A.

C. Mejía-Cortés, R. A. Vicencio, and B. A. Malomed, “Mobility of solitons in one-dimensional lattices with the cubic-quintic nonlinearity,” Phys. Rev. E. 88(5), 052901 (2013).
[Crossref]

Weinstein, M. I.

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, “Strong NLS soliton-defect interactions,” Physica D 192(3–4), 215–248 (2004).
[Crossref]

Wu, Y.

Yu, S.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

Appl. Phys. Lett. (3)

J. P. Sabini, N. Finlayson, and G. I. Stegeman, “All-optical switching In nonlinear X junctions,” Appl. Phys. Lett. 55(12), 1176–1178 (1989).
[Crossref]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81(18), 3335–3337 (2002).
[Crossref]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Soliton gating and switching in liquid crystal light valve,” Appl. Phys. Lett. 96(7), 071104 (2010).
[Crossref]

EPL (1)

M. Asad-uz-zaman and U. Al Khawaja, “Directional flow of solitons with asymmetric potential wells: soliton diode,” EPL 101(5), 50008 (2013).
[Crossref]

Europhys. Lett. (1)

C. Lee and J. Brand, “Enhanced quantum reflection of matter-wave solitons,” Europhys. Lett. 73(3), 321–327 (2006).
[Crossref]

IEEE J. Quantum Electron. (1)

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” IEEE J. Quantum Electron. 39(31), 31–55 (2003).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. Wu, “All-optical logic gates by using multibranch waveguide structure with localized optical nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 11(2), 307–312 (2005).
[Crossref]

IEEE Photon. J. (1)

K. M. Aghdami, M. Golshani, and R. Kheradmand, “Two-dimensional discrete cavity solitons: switching and all-optical gates,” IEEE Photon. J. 4(4), 1147–1154 (2012).
[Crossref]

J. Math. Phys. (1)

U. Al Khawaja, “A comparative analysis of Painlevé, Lax pair, and similarity transformation methods in obtaining the integrability conditions of nonlinear Schrödinger equations,” J. Math. Phys. 51(5), 053506 (2010).
[Crossref]

J. Opt. (1)

A. Ankiewicz, N. Devine, M. Ünal, A. Chowdury, and N. Akhmediev, “Rogue waves and other solutions of single and coupled Ablowitz-Ladik and nonlinear Schrödinger equations,” J. Opt. 15(6), 064008 (2013).
[Crossref]

J. Opt. Soc. Am. B (3)

J. Phys. A: Math. Theor. (1)

A. Khare, S. V. Dmitriev, and A. Saxena, “Exact moving and stationary solutions of a generalized discrete nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 40(37), 11301–11317 (2007).
[Crossref]

J. Phys. B (1)

A. Szameit and S. Nolte, “Discrete optics in femtosecond-laser-written photonic structures,” J. Phys. B 43(16), 163001 (2010).
[Crossref]

Nat. Photonics (1)

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

Nature (1)

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[Crossref] [PubMed]

Opt. Express (3)

Opt. lett. (2)

Phys. Rev. A. (1)

T. Ernst and J. Brand, “Resonant trapping in the transport of a matter-wave soliton through a quantum well,” Phys. Rev. A. 81(3), 033614 (2010).
[Crossref]

Phys. Rev. E (1)

I. E. Papacharalampous, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, “Soliton collisions in the discrete nonlinear Schrödinger equation,” Phys. Rev. E 68(42), 046604 (2003).
[Crossref]

Phys. Rev. E. (2)

C. Mejía-Cortés, R. A. Vicencio, and B. A. Malomed, “Mobility of solitons in one-dimensional lattices with the cubic-quintic nonlinearity,” Phys. Rev. E. 88(5), 052901 (2013).
[Crossref]

A. Maluckov, L. Hadžievski, and B. A. Malomed, “Staggered and moving localized modes in dynamical lattices with the cubic-quintic nonlinearity,” Phys. Rev. E. 77(33), 036604 (2008).
[Crossref]

Phys. Rev. Lett. (5)

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices”, Phys. Rev. Lett. 107(10), 103601 (2011).
[Crossref] [PubMed]

A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. A. Sukhorukov, “Realization of reflectionless potentials in photonic lattices,” Phys. Rev. Lett. 106, 193903 (2011).
[Crossref] [PubMed]

A. A. Sukhorukov, “Enhanced soliton transport in quasiperiodic lattices with introduced aperiodicity,” Phys. Rev. Lett. 96, 113902 (2006).
[Crossref] [PubMed]

D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete Solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001).
[Crossref] [PubMed]

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96(5), 053903 (2006).
[Crossref] [PubMed]

Physica D (2)

M. Peyrard and M. D. Kruskal, “Kink dynamics in the highly discrete sine-Gordon system,” Physica D 14(1), 88–102 (1984).
[Crossref]

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, “Strong NLS soliton-defect interactions,” Physica D 192(3–4), 215–248 (2004).
[Crossref]

Sci. Rep. (1)

R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Sci. Rep. 1, 94 (2011).
[Crossref]

Science (1)

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

Other (3)

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford University, 1995).

L.F. Mollenauer and J.P. Gordon, Solitons in Optical Fibers (Acadamic, 2006).

N.N. Akhmediev and A. Ankiexicz, Solitons: Nonlinear Pulses and Beams (Chapman and Hall, 1997).

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Figures (8)

Fig. 1
Fig. 1 Soliton speed versus time for different coupling strength and initial speeds.
Fig. 2
Fig. 2 Transmission coefficients versus soliton initial velocity and amplitude. Reflection (R) is shown with the solid (red) curve, transmission (T) with dashed (green) curve, and trapping (L) with dotted (black) curve. Coupling used: Cn = C + sinh(1.5) sech(1.5(n – 32)) with C = 0.45 in the v-curves and C ranging between 0.45 and 0.39 in the A-curve. The parameter A is the amplitude of the numerically-found stationary soliton. Signal and control solitons are found numerically by solving the time-independent version of Eq. (1) with C = 0.45 and γ = 1 and initial location at 22 and 32, respectively. The total number of wave guides is N = 63. The amplitude of the control soliton is multiplied by the power control parameter r = 0.16.
Fig. 3
Fig. 3 Schematic figure showing the proposal of injecting a control soliton into a potential well in order to control the scattering of the signal soliton.
Fig. 4
Fig. 4 Soliton scattering off a single potential well for different control soliton powers. Left: Reflectance in terms of soliton initial speed for different values of r. Right: critical speed, vc, for quantum reflection versus power control parameter r. All other parameters are the same as in Fig. 2.
Fig. 5
Fig. 5 Diode behaviour shown with soliton scattering off a double potential well from both directions. Solid curves correspond to scattering from the left and dashed curves correspond to scattering from the right shown with reflection (R) in red, transmission (T) in green and trapping (T) in black. The two potential wells are centerd at 30 and 34 with total waveguides N = 63, the power control parameter used is r = 0.3 and all other parameters are the same as in Fig. 2.
Fig. 6
Fig. 6 Logic gates performance shown with soliton scattering off a double potential wells behaving. Red curves correspond to reflection (R), green curves correspond to transmission (T), and black curves correspond to trapping (L). Filled circles correspond to the presence of control solitons in both wells (11). Up and lower triangles correspond to the presence of a control soliton in the left or right well (10 or 01), respectively. Empty circles correspond to the absence of control solitons from both wells (00). The two potentials are separated by 4 waveguides, the power control parameter used is r = 0.16, total number of waveguides is N = 124, and all other parameters are the same as in Fig. 2.
Fig. 7
Fig. 7 Density plots corresponding to two selected points from Fig. 6 showing the AND and NAND gates, with initial signal soliton speed v = 0.19, in the upper panel and the OR and NOR gates, with initial signal soliton speed v = 0.215, in the lower panel. In each subfigure waveguides range from 1 to 124 and time ranges from 0 to 375. All other parameters are the same as those of Fig. 6.
Fig. 8
Fig. 8 Waveguides separation, Dn,n+1, and the corresponding coupling Cn,n+1. The calibration values D0 = 24μm and C0 = 0.45mm−1 were taken from the experiment of [33] for the λ = 543 nm pulse.

Tables (1)

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Table 1 Logic gates obtained by scattering a soliton off a double potential well with two control solitons. Input corresponds to the presence (1) or nonpresence (0) of a control soliton such that, for instance, 10 corresponds to a control soliton in the left well and no soliton in the right well. Output is taken from the reflected or transmitted signal soliton. The two potential wells are separated by 4 waveguides and the power control parameter used is r = 0.16.

Equations (16)

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i ψ n z + C n , n 1 ψ n 1 + C n , n + 1 ψ n + 1 + γ | ψ n | 2 ψ n = 0 ,
C n , n + 1 = C + V ( n 1 ) , C n , n + 1 = C + V ( n + 1 ) ,
i ψ n z + C ψ n 1 + C ψ n + 1 + V ( n 1 ) ψ n 1 + V ( n + 1 ) ψ n + 1 + γ | ψ n | 2 ψ n = 0 .
i ψ n z + ( ψ n 1 + ψ n + 1 ) ( C + | ψ n | 2 ) = 0 ,
ψ n AL = C sinh ( μ ) sech [ μ ( n n 0 ) ] exp ( i β z ) ,
C n , n ± 1 = C + | ψ n ± 1 AL | 2 ,
i ψ n z = C ( ψ n 1 + ψ n + 1 ) | ψ n 1 AL | 2 ψ n 1 | ψ n + 1 AL | 2 ψ n + 1 γ | ψ n | 2 ψ n .
C n , n ± 1 S = ( C + | ψ n | 2 ) ( C + | ψ n ± 1 | 2 ) .
i ψ n z = C n 1 S ψ n 1 C n + 1 S ψ n + 1 γ | ψ n | 2 ψ n ,
C n ± 1 S = ( C + | ψ n AL | 2 ) ( C + | ψ n ± 1 AL | 2 ) .
C n , n ± 1 S = C exp ( 1 D n , n ± 1 D 0 ) ,
D n , n ± 1 = D 0 [ 1 log ( C n , n ± 1 S C ) ] .
C n ± 1 S = C { [ 1 + sinh 2 ( μ ) sech 2 μ ( n n 0 ) ] × [ 1 + sinh 2 ( μ ) sech 2 μ ( n ± 1 n 0 ) ] } 1 / 2 .
D n , n ± 1 = D 0 [ 1 1 2 log [ 1 + sinh 2 ( μ ) sech 2 ( μ ( n n 0 ) ) ] 1 2 log [ 1 + sinh 2 ( μ ) sech 2 ( μ ( n ± 1 n 0 ) ) ] ] .
C n , n ± 1 S = [ ( C + | ψ 1 , n AL | 2 + | ψ 2 , n AL | 2 ) × ( C + | ψ 1 , n ± 1 AL | 2 + | ψ 2 , n ± 1 AL | 2 ) ] 1 / 2 ,
ψ i , n AL = C sinh ( μ i ) sech [ μ i ( n n i ) ] exp ( i β i z ) , i = 1 , 2 ,

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