Abstract

We show that, in a nonlinear centrally coupled circular array of evanescently coupled fibers, the coupling dynamics of a weak signal beam can be efficiently influenced by a high-power control beam that induces nonlinear defects. When the intense control beam is launched into the central core and one core in the periphery, then localized solitons are formed and cause the fibers with induced defects (defected fibers) to decouple from the other array elements. In the presence of a high-intensity control beam, the propagation of weak signal is restricted to the defected optical fibers. The weak signal periodically couples between the induced defects. This oscillatory behavior depends on the sign of the (Kerr-type) nonlinearity and the initial phase difference between the control fields injected to the central and one of the peripheral fibers. This all-optical network has the advantage of routing and switching the weak signal field in a controlled way by adjusting the parameters of intense control field.

© 2013 Optical Society of America

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  19. K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Localized modes in a circular array of coupled nonlinear optical waveguides,” Int. J. Bifurc. Chaos Appl. Sci. Eng. 16, 1739–1752 (2006).
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    [CrossRef]
  23. J. Hudgings, L. Molter, and M. Dutta, “Design and modeling of passive optical switches and power dividers using non-planar coupled fiber arrays,” IEEE J. Quantum Electron. 36, 1438–1444 (2000).
    [CrossRef]
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  25. D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988).
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  26. 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]
  27. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
    [CrossRef]
  28. S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. 18, 1580–1583 (1982).
    [CrossRef]
  29. B. Daino, G. Gregori, and S. Wabnitz, “Stability analysis of nonlinear coherent coupling,” J. Appl. Phys. 58, 4512–4514 (1985).
    [CrossRef]
  30. G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
    [CrossRef]
  31. A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, R. Keil, S. Nolte, A. Tnnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Nonlinearity-induced broadening of resonances in dynamically modulated couplers,” Opt. Lett. 34, 2700–2702 (2009).
    [CrossRef]

2012

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[CrossRef]

2011

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

2010

2009

2008

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assantoc, M. Segevd, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

2007

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

S. Longhi, “Light transfer control and diffraction management in circular fibre waveguide arrays,” J. Phys. B 40, 4477–4492 (2007).
[CrossRef]

2006

K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Localized modes in a circular array of coupled nonlinear optical waveguides,” Int. J. Bifurc. Chaos Appl. Sci. Eng. 16, 1739–1752 (2006).
[CrossRef]

2005

T. Pertsch, R. Iwanow, R. Schiek, G. I. Stegeman, U. Peschel, F. Lederer, Y. H. Min, and W. Sohler, “Spatial ultrafast switching and frequency conversion in lithium niobate waveguide arrays,” Opt. Lett. 30, 177–179 (2005).
[CrossRef]

Th. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).
[CrossRef]

2004

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Centrally coupled circular array of optical waveguides: the existence of stable steady-state continuous waves and breathing modes,” Phys. Scr. T107, 13–19 (2004).
[CrossRef]

2003

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

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

2001

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

A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose–Einstein condensates,” Phys. Rev. Lett. 86, 2353–2356 (2001).
[CrossRef]

2000

J. Hudgings, L. Molter, and M. Dutta, “Design and modeling of passive optical switches and power dividers using non-planar coupled fiber arrays,” IEEE J. Quantum Electron. 36, 1438–1444 (2000).
[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]

1996

1995

P. Marqui, J. M. Bilbault, and M. Remoissenet, “Observation of nonlinear localized modes in an electrical lattice,” Phys. Rev. E 51, 6127–6133 (1995).
[CrossRef]

1994

W. Królikowski, U. Trutschel, M. Cronin-Golomb, and C. Schmidt-Hattenberger, “Soliton-like optical switching in a circular fiber array,” Opt. Lett. 19, 320–322 (1994).
[CrossRef]

D. J. Jones and L. A. Molter, “Generalized switching properties of three-guide circular fiber arrays using coupled-mode analysis,” IEEE J. Quantum Electron. 30, 119–125 (1994).
[CrossRef]

1993

C. Schmidt-Hattenberger, R. Muschall, U. Trustschel, and F. Lederer, “A 1×7 fibre coupler with Kerr nonlinearity,” Opt. Quantum Electron. 25, 185–193 (1993).
[CrossRef]

M. P. Castanier and C. Pierre, “Individual and interactive mechanisms for localization and dissipation in a mono-coupled nearly-periodic structure,” J. Sound Vib. 168, 479–505 (1993).
[CrossRef]

1991

1988

1985

B. Daino, G. Gregori, and S. Wabnitz, “Stability analysis of nonlinear coherent coupling,” J. Appl. Phys. 58, 4512–4514 (1985).
[CrossRef]

A. C. Scott and M. Tabor, “Davydov solitons in polypeptides,” Philos. Trans. R. Soc. London 315, 423–436 (1985).
[CrossRef]

1982

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

1979

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42, 1698–1701 (1979).
[CrossRef]

1973

A. S. Davydov, “The theory of contraction of proteins under their excitation,” J. Theor. Biol. 38, 559–569 (1973).
[CrossRef]

Agrawal, G. P.

Y. S Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

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]

Albiez, M.

Th. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).
[CrossRef]

Anker, Th.

Th. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).
[CrossRef]

Assantoc, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assantoc, M. Segevd, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

Bang, O.

Bilbault, J. M.

P. Marqui, J. M. Bilbault, and M. Remoissenet, “Observation of nonlinear localized modes in an electrical lattice,” Phys. Rev. E 51, 6127–6133 (1995).
[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]

Castanier, M. P.

M. P. Castanier and C. Pierre, “Individual and interactive mechanisms for localization and dissipation in a mono-coupled nearly-periodic structure,” J. Sound Vib. 168, 479–505 (1993).
[CrossRef]

Christodoulides, D. N.

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

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assantoc, M. Segevd, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Localized modes in a circular array of coupled nonlinear optical waveguides,” Int. J. Bifurc. Chaos Appl. Sci. Eng. 16, 1739–1752 (2006).
[CrossRef]

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Centrally coupled circular array of optical waveguides: the existence of stable steady-state continuous waves and breathing modes,” Phys. Scr. T107, 13–19 (2004).
[CrossRef]

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

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

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

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

Cianci, E.

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

Cronin-Golomb, M.

Daino, B.

B. Daino, G. Gregori, and S. Wabnitz, “Stability analysis of nonlinear coherent coupling,” J. Appl. Phys. 58, 4512–4514 (1985).
[CrossRef]

Davydov, A. S.

A. S. Davydov, “The theory of contraction of proteins under their excitation,” J. Theor. Biol. 38, 559–569 (1973).
[CrossRef]

Della Valle, G.

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

Dimarcello, F. V.

Dreisow, F.

R. Keil, M. Heinrich, F. Dreisow, Th. Pertsch, A. Tunnermann, 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, Y. V. Kartashov, M. Heinrich, F. Dreisow, R. Keil, S. Nolte, A. Tnnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Nonlinearity-induced broadening of resonances in dynamically modulated couplers,” Opt. Lett. 34, 2700–2702 (2009).
[CrossRef]

Droulias, S.

K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Localized modes in a circular array of coupled nonlinear optical waveguides,” Int. J. Bifurc. Chaos Appl. Sci. Eng. 16, 1739–1752 (2006).
[CrossRef]

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Centrally coupled circular array of optical waveguides: the existence of stable steady-state continuous waves and breathing modes,” Phys. Scr. T107, 13–19 (2004).
[CrossRef]

Dutta, M.

J. Hudgings, L. Molter, and M. Dutta, “Design and modeling of passive optical switches and power dividers using non-planar coupled fiber arrays,” IEEE J. Quantum Electron. 36, 1438–1444 (2000).
[CrossRef]

Efremidis, N. K.

K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Localized modes in a circular array of coupled nonlinear optical waveguides,” Int. J. Bifurc. Chaos Appl. Sci. Eng. 16, 1739–1752 (2006).
[CrossRef]

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Centrally coupled circular array of optical waveguides: the existence of stable steady-state continuous waves and breathing modes,” Phys. Scr. T107, 13–19 (2004).
[CrossRef]

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

Eiermann, B.

Th. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).
[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]

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, 233901 (2001).
[CrossRef]

Fini, J. M.

Fishteyn, M.

Fleischer, J. W.

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

Foglietti, V.

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

Garanovich, I. L.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[CrossRef]

Gati, R.

Th. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).
[CrossRef]

Gregori, G.

B. Daino, G. Gregori, and S. Wabnitz, “Stability analysis of nonlinear coherent coupling,” J. Appl. Phys. 58, 4512–4514 (1985).
[CrossRef]

Heeger, A. J.

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42, 1698–1701 (1979).
[CrossRef]

Heinrich, M.

R. Keil, M. Heinrich, F. Dreisow, Th. Pertsch, A. Tunnermann, 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, Y. V. Kartashov, M. Heinrich, F. Dreisow, R. Keil, S. Nolte, A. Tnnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Nonlinearity-induced broadening of resonances in dynamically modulated couplers,” Opt. Lett. 34, 2700–2702 (2009).
[CrossRef]

Hizaidis, K.

K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Localized modes in a circular array of coupled nonlinear optical waveguides,” Int. J. Bifurc. Chaos Appl. Sci. Eng. 16, 1739–1752 (2006).
[CrossRef]

Hizanidis, K.

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Centrally coupled circular array of optical waveguides: the existence of stable steady-state continuous waves and breathing modes,” Phys. Scr. T107, 13–19 (2004).
[CrossRef]

Hudgings, J.

J. Hudgings, L. Molter, and M. Dutta, “Design and modeling of passive optical switches and power dividers using non-planar coupled fiber arrays,” IEEE J. Quantum Electron. 36, 1438–1444 (2000).
[CrossRef]

Hunsmann, S.

Th. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).
[CrossRef]

Iwanow, R.

Jensen, S. M.

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

Jones, D. J.

D. J. Jones and L. A. Molter, “Generalized switching properties of three-guide circular fiber arrays using coupled-mode analysis,” IEEE J. Quantum Electron. 30, 119–125 (1994).
[CrossRef]

Joseph, R. I.

Kartashov, Y. V.

Keil, R.

R. Keil, M. Heinrich, F. Dreisow, Th. Pertsch, A. Tunnermann, 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, Y. V. Kartashov, M. Heinrich, F. Dreisow, R. Keil, S. Nolte, A. Tnnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Nonlinearity-induced broadening of resonances in dynamically modulated couplers,” Opt. Lett. 34, 2700–2702 (2009).
[CrossRef]

Kivshar, Y. S

Y. S Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

Kivshar, Y. S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[CrossRef]

Królikowski, W.

Laporta, P.

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

Lederer, F.

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, R. Keil, S. Nolte, A. Tnnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Nonlinearity-induced broadening of resonances in dynamically modulated couplers,” Opt. Lett. 34, 2700–2702 (2009).
[CrossRef]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assantoc, M. Segevd, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

T. Pertsch, R. Iwanow, R. Schiek, G. I. Stegeman, U. Peschel, F. Lederer, Y. H. Min, and W. Sohler, “Spatial ultrafast switching and frequency conversion in lithium niobate waveguide arrays,” Opt. Lett. 30, 177–179 (2005).
[CrossRef]

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

C. Schmidt-Hattenberger, R. Muschall, U. Trustschel, and F. Lederer, “A 1×7 fibre coupler with Kerr nonlinearity,” Opt. Quantum Electron. 25, 185–193 (1993).
[CrossRef]

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

Longhi, S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[CrossRef]

S. Longhi, “Light transfer control and diffraction management in circular fibre waveguide arrays,” J. Phys. B 40, 4477–4492 (2007).
[CrossRef]

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

Marqui, P.

P. Marqui, J. M. Bilbault, and M. Remoissenet, “Observation of nonlinear localized modes in an electrical lattice,” Phys. Rev. E 51, 6127–6133 (1995).
[CrossRef]

Miller, P. D.

Min, Y. H.

Molter, L.

J. Hudgings, L. Molter, and M. Dutta, “Design and modeling of passive optical switches and power dividers using non-planar coupled fiber arrays,” IEEE J. Quantum Electron. 36, 1438–1444 (2000).
[CrossRef]

Molter, L. A.

D. J. Jones and L. A. Molter, “Generalized switching properties of three-guide circular fiber arrays using coupled-mode analysis,” IEEE J. Quantum Electron. 30, 119–125 (1994).
[CrossRef]

Monberg, E. M.

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.

C. Schmidt-Hattenberger, R. Muschall, U. Trustschel, and F. Lederer, “A 1×7 fibre coupler with Kerr nonlinearity,” Opt. Quantum Electron. 25, 185–193 (1993).
[CrossRef]

Nolte, S.

R. Keil, M. Heinrich, F. Dreisow, Th. Pertsch, A. Tunnermann, 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, Y. V. Kartashov, M. Heinrich, F. Dreisow, R. Keil, S. Nolte, A. Tnnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Nonlinearity-induced broadening of resonances in dynamically modulated couplers,” Opt. Lett. 34, 2700–2702 (2009).
[CrossRef]

Oberthaler, M. K.

Th. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).
[CrossRef]

Ornigotti, M.

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

Pertsch, T.

Pertsch, Th.

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

Peschel, U.

Pierre, C.

M. P. Castanier and C. Pierre, “Individual and interactive mechanisms for localization and dissipation in a mono-coupled nearly-periodic structure,” J. Sound Vib. 168, 479–505 (1993).
[CrossRef]

Remoissenet, M.

P. Marqui, J. M. Bilbault, and M. Remoissenet, “Observation of nonlinear localized modes in an electrical lattice,” Phys. Rev. E 51, 6127–6133 (1995).
[CrossRef]

Schiek, R.

Schmidt-Hattenberger, C.

Schrieffer, J. R.

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42, 1698–1701 (1979).
[CrossRef]

Scott, A. C.

A. C. Scott and M. Tabor, “Davydov solitons in polypeptides,” Philos. Trans. R. Soc. London 315, 423–436 (1985).
[CrossRef]

Segev, M.

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

Segevd, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assantoc, M. Segevd, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assantoc, M. Segevd, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

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

A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose–Einstein condensates,” Phys. Rev. Lett. 86, 2353–2356 (2001).
[CrossRef]

Sohler, W.

Stegeman, G. I.

Su, W. P.

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42, 1698–1701 (1979).
[CrossRef]

Sukhorukov, A. A.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[CrossRef]

Szameit, A.

R. Keil, M. Heinrich, F. Dreisow, Th. Pertsch, A. Tunnermann, 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, Y. V. Kartashov, M. Heinrich, F. Dreisow, R. Keil, S. Nolte, A. Tnnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Nonlinearity-induced broadening of resonances in dynamically modulated couplers,” Opt. Lett. 34, 2700–2702 (2009).
[CrossRef]

Tabor, M.

A. C. Scott and M. Tabor, “Davydov solitons in polypeptides,” Philos. Trans. R. Soc. London 315, 423–436 (1985).
[CrossRef]

Taunay, T. F.

Tnnermann, A.

Torner, L.

Trombettoni, A.

Th. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).
[CrossRef]

A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose–Einstein condensates,” Phys. Rev. Lett. 86, 2353–2356 (2001).
[CrossRef]

Trustschel, U.

C. Schmidt-Hattenberger, R. Muschall, U. Trustschel, and F. Lederer, “A 1×7 fibre coupler with Kerr nonlinearity,” Opt. Quantum Electron. 25, 185–193 (1993).
[CrossRef]

Trutschel, U.

Tsopelas, I.

K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Localized modes in a circular array of coupled nonlinear optical waveguides,” Int. J. Bifurc. Chaos Appl. Sci. Eng. 16, 1739–1752 (2006).
[CrossRef]

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Centrally coupled circular array of optical waveguides: the existence of stable steady-state continuous waves and breathing modes,” Phys. Scr. T107, 13–19 (2004).
[CrossRef]

Tunnermann, A.

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

Vysloukh, V. A.

Wabnitz, S.

B. Daino, G. Gregori, and S. Wabnitz, “Stability analysis of nonlinear coherent coupling,” J. Appl. Phys. 58, 4512–4514 (1985).
[CrossRef]

Yan, M. F.

Zhu, B.

IEEE J. Quantum Electron.

D. J. Jones and L. A. Molter, “Generalized switching properties of three-guide circular fiber arrays using coupled-mode analysis,” IEEE J. Quantum Electron. 30, 119–125 (1994).
[CrossRef]

J. Hudgings, L. Molter, and M. Dutta, “Design and modeling of passive optical switches and power dividers using non-planar coupled fiber arrays,” IEEE J. Quantum Electron. 36, 1438–1444 (2000).
[CrossRef]

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

Int. J. Bifurc. Chaos Appl. Sci. Eng.

K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Localized modes in a circular array of coupled nonlinear optical waveguides,” Int. J. Bifurc. Chaos Appl. Sci. Eng. 16, 1739–1752 (2006).
[CrossRef]

J. Appl. Phys.

B. Daino, G. Gregori, and S. Wabnitz, “Stability analysis of nonlinear coherent coupling,” J. Appl. Phys. 58, 4512–4514 (1985).
[CrossRef]

J. Phys. B

S. Longhi, “Light transfer control and diffraction management in circular fibre waveguide arrays,” J. Phys. B 40, 4477–4492 (2007).
[CrossRef]

J. Sound Vib.

M. P. Castanier and C. Pierre, “Individual and interactive mechanisms for localization and dissipation in a mono-coupled nearly-periodic structure,” J. Sound Vib. 168, 479–505 (1993).
[CrossRef]

J. Theor. Biol.

A. S. Davydov, “The theory of contraction of proteins under their excitation,” J. Theor. Biol. 38, 559–569 (1973).
[CrossRef]

Nature

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

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

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

C. Schmidt-Hattenberger, R. Muschall, U. Trustschel, and F. Lederer, “A 1×7 fibre coupler with Kerr nonlinearity,” Opt. Quantum Electron. 25, 185–193 (1993).
[CrossRef]

Philos. Trans. R. Soc. London

A. C. Scott and M. Tabor, “Davydov solitons in polypeptides,” Philos. Trans. R. Soc. London 315, 423–436 (1985).
[CrossRef]

Phys. Rep.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assantoc, M. Segevd, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[CrossRef]

Phys. Rev. E

P. Marqui, J. M. Bilbault, and M. Remoissenet, “Observation of nonlinear localized modes in an electrical lattice,” Phys. Rev. E 51, 6127–6133 (1995).
[CrossRef]

Phys. Rev. Lett.

A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose–Einstein condensates,” Phys. Rev. Lett. 86, 2353–2356 (2001).
[CrossRef]

Th. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).
[CrossRef]

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

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42, 1698–1701 (1979).
[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]

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

Phys. Scr.

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Centrally coupled circular array of optical waveguides: the existence of stable steady-state continuous waves and breathing modes,” Phys. Scr. T107, 13–19 (2004).
[CrossRef]

Sci. Rep.

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

Other

Y. S Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

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Figures (8)

Fig. 1.
Fig. 1.

Schematic of centrally coupled circular array of optical fibers containing N identical optical fibers. C is the coupling strength of neighboring circular array elements and C0 is coupling coefficient of the central fiber to the circular array.

Fig. 2.
Fig. 2.

(a) Normalized power confined in the central and one of the peripheral fibers as a function of the propagation constants of the defected fibers ϵ and the normalized propagation distance ζ. In this system it is N=20, α=0.314, and un(0)=δn,0. (b) Variation of the signal power along the defected fibers for ϵ=10. The insets of the figure show the power distribution in the array at some specific normalized propagation length.

Fig. 3.
Fig. 3.

Maximum power transferred from the central fiber to the defected peripheral fiber as a function of the defect parameter difference δ. The insets show the power distribution in the elements of the centrally coupled circular array in the two extremes δ=±10. N=20 and α=0.314. At the lower extremes the power is localized in the central fiber along the propagation length. In contrast, at the upper extreme the distribution of power in the array elements is ζ dependent.

Fig. 4.
Fig. 4.

Normalized control power confined in the central and one of the peripheral fibers versus the normalized nonlinear coefficient χ and the normalized propagation distance ζ. In this system N=20, α=0.314, and Un(0)=δn,0+δn,1.

Fig. 5.
Fig. 5.

Duffing potential V(S1)=aS12/2+bS14/4 for positive and negative value of coefficient a.

Fig. 6.
Fig. 6.

Effect of noise on the variations of control powers in the initially excited fibers n=0, 1 when the system is initially prepared at its unstable equilibrium points S1=0 (left-hand column) and the corresponding motion in the Duffing potential (right-hand column). (a) Regular oscillations around the unstable equilibrium point S1=0. (b) and (c) Regular oscillations around the negative and positive stable equilibrium points. (d) Irregular oscillations are a combination of three regular oscillations.

Fig. 7.
Fig. 7.

Coupling of the weak signal power between defected fibers n=0, 1 in a centrally coupled circular array containing N=20 waveguides with a coupling ratio α=0.314 and a nonlinear parameter |χ|=20. (a) Self-focusing media and in-phase input control fields (χcos(ϕ)>0). (b) Self-defocusing media and in-phase input control fields (χcos(ϕ)0). (c) Self-defocusing media and out-of-phase input control fields (χcos(ϕ)>0). (d) Self-focusing media and out-of-phase input control fields χcos(ϕ)0. The insets of the subplots show the variation of the control power along the fibers n=0, 1.

Fig. 8.
Fig. 8.

Coupling of the weak signal power between the defected fibers n=0, 1. All the system parameters are similar to those in Fig. 7(b) except the phase difference of control fields injected to the fiber n=0, 1 which is ϕ=π/4.

Equations (12)

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

idqndz=βn(s)qn+C(qn1+qn+1)+C0q0+2κ|Qn|2qn,
idq0dz=βn(s)q0+C0n=0Nqn+2κ|Q0|2q0,
idQndz=βn(c)Qn+C(Qn1+Qn+1)+C0Q0+κ|Qn|2Qn,
idQ0dz=βn(c)Q0+C0n=0NQn+κ|Q0|2Q0,
idundζ=un1+un+1+αu0+γn(ζ)un,
idu0dζ=αn=0Nun+γ0(ζ)u0,
idUndζ=Un1+Un+1+αU0+χ|Un|2Un,
idU0dz=αn=0NUn+χ|U0|2U0,
idU0dζ=αU1+χ|U0|2U0,
idU1dζ=αU0+χ|U1|2U1.
S0=|U0|2+|U1|2;S1=|U0|2|U1|2;S2=2Re(U0U1*);S3=2Im(U0U1*).
S¨1+aS1+bS13=0,

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