Abstract

We study nonlinear propagation of light in diffraction-managed photonic lattices created by periodically-curved arrays of optical waveguides. We identify different regimes of the nonlinear propagation of light in such structures depending on the input power. We start from the regime of self-collimation at low powers and demonstrate that, as the beam power increases, nonlinearity destroys the beam self-imaging and leads to nonlinear diffusion. At higher powers, we observe a sharp transition to the self-trapping and the formation of discrete diffraction-managed solitons.

© 2007 Optical Society of America

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  1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
    [CrossRef] [PubMed]
  2. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
    [CrossRef] [PubMed]
  3. T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901-4 (2002).
    [CrossRef] [PubMed]
  4. P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature Mater. 5, 93-96 (2006).
    [CrossRef] [PubMed]
  5. S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, and P. Laporta, "Observation of Dynamic Localization in Periodically Curved Waveguide Arrays," Phys. Rev. Lett. 96, 243901-4 (2006).
    [CrossRef] [PubMed]
  6. S. Longhi, "Self-imaging and modulational instability in an array of periodically curved waveguides," Opt. Lett. 30, 2137-2139 (2005).
    [CrossRef] [PubMed]
  7. R. Iyer, J. S. Aitchison, J. Wan, M. M. Dignam, C. M. de Sterke, "Exact dynamic localization in curved AlGaAs optical waveguide arrays," Opt. Express 15, 3212-3223 (2007).
    [CrossRef] [PubMed]
  8. I. L. Garanovich, A. A. Sukhorukov, and Yu. S. Kivshar, "Broadband diffraction management and selfcollimation of white light in photonic lattices," Phys. Rev. E 74, 066609 (2006).
    [CrossRef]
  9. D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled wave-guides," Opt. Lett. 13, 794-796 (1988).
    [CrossRef] [PubMed]
  10. 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]
  11. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).
  12. M. J. Ablowitz and Z. H. Musslimani, "Discrete diffraction managed spatial solitons," Phys. Rev. Lett. 87, 254102-4 (2001).
    [CrossRef] [PubMed]
  13. K. Staliunas, R. Herrero, and G. J. Valcarcel, de, "Arresting soliton collapse in two-dimensional nonlinear Schrodinger systems via spatiotemporal modulation of the external potential," Phys. Rev. A 75, 011604 (2007).
    [CrossRef]
  14. S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, "Channel optical waveguide directional couplers," Appl. Phys. Lett. 22, 46-47 (1973).
    [CrossRef]
  15. Y. V. Kartashov, L. Torner, and D. N. Christodoulides, "Soliton dragging by dynamic optical lattices," Opt. Lett. 30, 1378-1380 (2005).
    [CrossRef] [PubMed]
  16. I. L. Garanovich, A. A. Sukhorukov, and Yu. S. Kivshar, "Soliton control in modulated optically-induced photonic lattices," Opt. Express 13, 5704-5710 (2005).
    [CrossRef] [PubMed]
  17. C. R. Rosberg, I. L. Garanovich, A. A. Sukhorukov, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, "Demonstration of all-optical beam steering in modulated photonic lattices," Opt. Lett. 31, 1498-1500 (2006).
    [CrossRef] [PubMed]
  18. Y. Kominis and K. Hizanidis, "Continuous-wave-controlled steering of spatial solitons," J. Opt. Soc. Am. B 21, 562-567 (2004).
    [CrossRef]
  19. I. Tsopelas, Y. Kominis, and K. Hizanidis, "Soliton dynamics and interactions in dynamically photoinduced lattices," Phys. Rev. E 74, 036613 (2006).
    [CrossRef]
  20. A. C. Scott and L. Macneil, "Binding energy versus nonlinearity for a "small" stationary soliton," Phys. Lett. A 98, 87-88 (1983).
    [CrossRef]

2007 (2)

K. Staliunas, R. Herrero, and G. J. Valcarcel, de, "Arresting soliton collapse in two-dimensional nonlinear Schrodinger systems via spatiotemporal modulation of the external potential," Phys. Rev. A 75, 011604 (2007).
[CrossRef]

R. Iyer, J. S. Aitchison, J. Wan, M. M. Dignam, C. M. de Sterke, "Exact dynamic localization in curved AlGaAs optical waveguide arrays," Opt. Express 15, 3212-3223 (2007).
[CrossRef] [PubMed]

2006 (5)

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature Mater. 5, 93-96 (2006).
[CrossRef] [PubMed]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, and P. Laporta, "Observation of Dynamic Localization in Periodically Curved Waveguide Arrays," Phys. Rev. Lett. 96, 243901-4 (2006).
[CrossRef] [PubMed]

I. L. Garanovich, A. A. Sukhorukov, and Yu. S. Kivshar, "Broadband diffraction management and selfcollimation of white light in photonic lattices," Phys. Rev. E 74, 066609 (2006).
[CrossRef]

I. Tsopelas, Y. Kominis, and K. Hizanidis, "Soliton dynamics and interactions in dynamically photoinduced lattices," Phys. Rev. E 74, 036613 (2006).
[CrossRef]

C. R. Rosberg, I. L. Garanovich, A. A. Sukhorukov, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, "Demonstration of all-optical beam steering in modulated photonic lattices," Opt. Lett. 31, 1498-1500 (2006).
[CrossRef] [PubMed]

2005 (3)

2004 (1)

Y. Kominis and K. Hizanidis, "Continuous-wave-controlled steering of spatial solitons," J. Opt. Soc. Am. B 21, 562-567 (2004).
[CrossRef]

2003 (1)

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

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, 093901-4 (2002).
[CrossRef] [PubMed]

2001 (1)

M. J. Ablowitz and Z. H. Musslimani, "Discrete diffraction managed spatial solitons," Phys. Rev. Lett. 87, 254102-4 (2001).
[CrossRef] [PubMed]

2000 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

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]

1988 (1)

1983 (1)

A. C. Scott and L. Macneil, "Binding energy versus nonlinearity for a "small" stationary soliton," Phys. Lett. A 98, 87-88 (1983).
[CrossRef]

1973 (1)

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, "Channel optical waveguide directional couplers," Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz and Z. H. Musslimani, "Discrete diffraction managed spatial solitons," Phys. Rev. Lett. 87, 254102-4 (2001).
[CrossRef] [PubMed]

Aitchison, J. S.

R. Iyer, J. S. Aitchison, J. Wan, M. M. Dignam, C. M. de Sterke, "Exact dynamic localization in curved AlGaAs optical waveguide arrays," Opt. Express 15, 3212-3223 (2007).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[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]

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, 093901-4 (2002).
[CrossRef] [PubMed]

Christodoulides, D. N.

Dahlem, M. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature Mater. 5, 93-96 (2006).
[CrossRef] [PubMed]

de Sterke, C. M.

Dignam, M. M.

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[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]

Garanovich, I. L.

Garmire, E.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, "Channel optical waveguide directional couplers," Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

Garvin, H. L.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, "Channel optical waveguide directional couplers," Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

Herrero, R.

K. Staliunas, R. Herrero, and G. J. Valcarcel, de, "Arresting soliton collapse in two-dimensional nonlinear Schrodinger systems via spatiotemporal modulation of the external potential," Phys. Rev. A 75, 011604 (2007).
[CrossRef]

Hizanidis, K.

I. Tsopelas, Y. Kominis, and K. Hizanidis, "Soliton dynamics and interactions in dynamically photoinduced lattices," Phys. Rev. E 74, 036613 (2006).
[CrossRef]

Y. Kominis and K. Hizanidis, "Continuous-wave-controlled steering of spatial solitons," J. Opt. Soc. Am. B 21, 562-567 (2004).
[CrossRef]

Hunsperger, R. G.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, "Channel optical waveguide directional couplers," Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

Ibanescu, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature Mater. 5, 93-96 (2006).
[CrossRef] [PubMed]

Ippen, E. P.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature Mater. 5, 93-96 (2006).
[CrossRef] [PubMed]

Iyer, R.

Joannopoulos, J. D.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature Mater. 5, 93-96 (2006).
[CrossRef] [PubMed]

Joseph, R. I.

Kartashov, Y. V.

Kivshar, Yu. S.

Kolodziejski, L. A.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature Mater. 5, 93-96 (2006).
[CrossRef] [PubMed]

Kominis, Y.

I. Tsopelas, Y. Kominis, and K. Hizanidis, "Soliton dynamics and interactions in dynamically photoinduced lattices," Phys. Rev. E 74, 036613 (2006).
[CrossRef]

Y. Kominis and K. Hizanidis, "Continuous-wave-controlled steering of spatial solitons," J. Opt. Soc. Am. B 21, 562-567 (2004).
[CrossRef]

Krolikowski, W.

Laporta, P.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, and P. Laporta, "Observation of Dynamic Localization in Periodically Curved Waveguide Arrays," Phys. Rev. Lett. 96, 243901-4 (2006).
[CrossRef] [PubMed]

Lederer, F.

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

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901-4 (2002).
[CrossRef] [PubMed]

Lobino, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, and P. Laporta, "Observation of Dynamic Localization in Periodically Curved Waveguide Arrays," Phys. Rev. Lett. 96, 243901-4 (2006).
[CrossRef] [PubMed]

Longhi, S.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, and P. Laporta, "Observation of Dynamic Localization in Periodically Curved Waveguide Arrays," Phys. Rev. Lett. 96, 243901-4 (2006).
[CrossRef] [PubMed]

S. Longhi, "Self-imaging and modulational instability in an array of periodically curved waveguides," Opt. Lett. 30, 2137-2139 (2005).
[CrossRef] [PubMed]

Macneil, L.

A. C. Scott and L. Macneil, "Binding energy versus nonlinearity for a "small" stationary soliton," Phys. Lett. A 98, 87-88 (1983).
[CrossRef]

Marangoni, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, and P. Laporta, "Observation of Dynamic Localization in Periodically Curved Waveguide Arrays," Phys. Rev. Lett. 96, 243901-4 (2006).
[CrossRef] [PubMed]

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[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]

Musslimani, Z. H.

M. J. Ablowitz and Z. H. Musslimani, "Discrete diffraction managed spatial solitons," Phys. Rev. Lett. 87, 254102-4 (2001).
[CrossRef] [PubMed]

Neshev, D. N.

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, 093901-4 (2002).
[CrossRef] [PubMed]

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, 093901-4 (2002).
[CrossRef] [PubMed]

Petrich, G. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature Mater. 5, 93-96 (2006).
[CrossRef] [PubMed]

Rakich, P. T.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature Mater. 5, 93-96 (2006).
[CrossRef] [PubMed]

Ramponi, R.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, and P. Laporta, "Observation of Dynamic Localization in Periodically Curved Waveguide Arrays," Phys. Rev. Lett. 96, 243901-4 (2006).
[CrossRef] [PubMed]

Rosberg, C. R.

Scott, A. C.

A. C. Scott and L. Macneil, "Binding energy versus nonlinearity for a "small" stationary soliton," Phys. Lett. A 98, 87-88 (1983).
[CrossRef]

Silberberg, Y.

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

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[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]

Soljacic, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature Mater. 5, 93-96 (2006).
[CrossRef] [PubMed]

Somekh, S.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, "Channel optical waveguide directional couplers," Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

Staliunas, K.

K. Staliunas, R. Herrero, and G. J. Valcarcel, de, "Arresting soliton collapse in two-dimensional nonlinear Schrodinger systems via spatiotemporal modulation of the external potential," Phys. Rev. A 75, 011604 (2007).
[CrossRef]

Sukhorukov, A. A.

Tandon, S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature Mater. 5, 93-96 (2006).
[CrossRef] [PubMed]

Torner, L.

Tsopelas, I.

I. Tsopelas, Y. Kominis, and K. Hizanidis, "Soliton dynamics and interactions in dynamically photoinduced lattices," Phys. Rev. E 74, 036613 (2006).
[CrossRef]

Valcarcel, G. J.

K. Staliunas, R. Herrero, and G. J. Valcarcel, de, "Arresting soliton collapse in two-dimensional nonlinear Schrodinger systems via spatiotemporal modulation of the external potential," Phys. Rev. A 75, 011604 (2007).
[CrossRef]

Wan, J.

Yariv, A.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, "Channel optical waveguide directional couplers," Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

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, 093901-4 (2002).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, "Channel optical waveguide directional couplers," Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

J.Opt. Soc. Am. B (1)

Y. Kominis and K. Hizanidis, "Continuous-wave-controlled steering of spatial solitons," J. Opt. Soc. Am. B 21, 562-567 (2004).
[CrossRef]

Nature (1)

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

Nature Mater. (1)

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature Mater. 5, 93-96 (2006).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (4)

Phys. Lett. A (1)

A. C. Scott and L. Macneil, "Binding energy versus nonlinearity for a "small" stationary soliton," Phys. Lett. A 98, 87-88 (1983).
[CrossRef]

Phys. Rev. A (1)

K. Staliunas, R. Herrero, and G. J. Valcarcel, de, "Arresting soliton collapse in two-dimensional nonlinear Schrodinger systems via spatiotemporal modulation of the external potential," Phys. Rev. A 75, 011604 (2007).
[CrossRef]

Phys. Rev. E (2)

I. L. Garanovich, A. A. Sukhorukov, and Yu. S. Kivshar, "Broadband diffraction management and selfcollimation of white light in photonic lattices," Phys. Rev. E 74, 066609 (2006).
[CrossRef]

I. Tsopelas, Y. Kominis, and K. Hizanidis, "Soliton dynamics and interactions in dynamically photoinduced lattices," Phys. Rev. E 74, 036613 (2006).
[CrossRef]

Phys. Rev. Lett. (5)

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, and P. Laporta, "Observation of Dynamic Localization in Periodically Curved Waveguide Arrays," Phys. Rev. Lett. 96, 243901-4 (2006).
[CrossRef] [PubMed]

M. J. Ablowitz and Z. H. Musslimani, "Discrete diffraction managed spatial solitons," Phys. Rev. Lett. 87, 254102-4 (2001).
[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]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[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, 093901-4 (2002).
[CrossRef] [PubMed]

Other (1)

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).

Supplementary Material (2)

» Media 1: GIF (1537 KB)     
» Media 2: GIF (1537 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic of an array of periodically curved waveguides. (b) Effective coupling C eff in the curved waveguide array normalized to the coupling C 0 in the straight array, as a function of the bending amplitude A normalized to the amplitude A sc which corresponds to the self-collimation condition. Point ‘a’ corresponds to the self-collimation, when the bending amplitude is A=A sc, while for the point ‘b’ we take A=1/2A sc.

Fig. 2.
Fig. 2.

Linear propagation of light in a curved waveguide array. Shown are the absolute values of the amplitudes of the modes of individual waveguides (left) and corresponding optical field distribution (center). Right: beam width w [normalized to the input width] as a function of the propagation distance. (a) Bending amplitude corresponds to the self-collimation condition [point ‘a’ in Fig. 1(b)]. (b) Bending amplitude is half of that in (a) [point ‘b’ in Fig. 1(b)]. Bending period is L=15 mm. Waveguide array length is 150 mm.

Fig. 3.
Fig. 3.

(1.5MB) Nonlinear propagation of light in an array of periodically curved waveguides. Shown are the absolute values of the amplitudes of the modes of individual waveguides (left) and corresponding optical field patterns (center). Right: beam width w [normalized to the input width] as a function of the propagation distance. Waveguide array is the same as in Fig. 2(a). The input power is (a) P/P 0=0.70, (b) P/P 0=1.7, (c) P/P 0=2.7, and (d) P/P 0=3.4, where P 0 is the power required for the formation of one-site discrete soliton in the straight array. The animation shows the beam propagation dynamics and the output beam width as the input power increases from P/P 0=0.00029 to P/P 0=3.4. [Media 1, Media 2]

Fig. 4.
Fig. 4.

(a, b) Output beam width vs. the input power. Waveguide arrays are the same as in Figs. 2(a) and 2(b), respectively. (c) Critical power P cr/P 0 required for the formation of a one-site lattice soliton in an array of periodically curved waveguides as a function of the bending amplitude A. Bending period and waveguide array length is the same as in (a) and (b). Points ‘a’ and ‘b’ correspond to the bending amplitudes in (a) and (b), respectively.

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