Abstract

We investigate dynamic localization in curved femtosecond (fs) laser written waveguide arrays. The light propagation inside the array is directly observed by monitoring fluorescence of color centers induced during the fs writing process. In addition to monochromatic excitation the spectral response of the arrays is investigated by launching white light supercontinuum into the arrays.

© 2008 Optical Society of America

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  1. S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel optical waveguide directional coupler," Appl. Phys. Lett. 22, 46-48 (1973).
    [CrossRef]
  2. S. Jensen, "The nonlinear coherent coupler," IEEE J. Quantum Electron. 18, 1580-1583 (1982).
    [CrossRef]
  3. D. Christodoulides and R. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988).
    [CrossRef] [PubMed]
  4. H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
    [CrossRef]
  5. R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
    [CrossRef] [PubMed]
  6. R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, "Dynamics of discrete solitons in Optical Waveguide Arrays," Phys. Rev. Lett. 83, 2726-2729 (1999).
    [CrossRef]
  7. O. Bang, Y. Kivshar, A. Buryak, A. D. Rossi, and S. Trillo, "Two-dimensional solitary waves in media with quadratic and cubic nonlinearity," Phys. Rev. E 58, 5057-5069 (1998).
    [CrossRef]
  8. P. Kevrekidis, K. Rasmussen, and A. Bishop, "Localized excitations and their thresholds," Phys. Rev. E 61, 4652-4655 (2000).
    [CrossRef]
  9. D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  11. M. Kuznetsov, "Coupled wave analysis of multiple waveguide systems: The discrete harmonic oscillator," IEEE J. Quantum Electron. 21, 1893-1898 (1985).
    [CrossRef]
  12. H. Eisenberg, Y. Silberberg, R. Morandotti, and J. Aitchison, "Diffraction Management," Phys. Rev. Lett. 85, 1863-1866 (2000).
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  13. R. Gordon, "Harmonic oscillation in a spatially finite array waveguide," Opt. Lett. 29, 2752-2754 (2004).
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  14. K. Makris and D. Christodoulides, "Method of images in optical discrete systems," Phys. Rev. E 73, 036616 (2006).
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  15. A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, "Light evolution in arbitrary two-dimensional waveguide arrays," Phys. Rev. A 75, 053814 (2007).
    [CrossRef]
  16. H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Braeuer, and U. Peschel, "Visual observation of Zener Tunneling," Phys. Rev. Lett. 96, 023901 (2006).
    [CrossRef] [PubMed]
  17. R. Iwanow, D. May-Arrioja, D. Christodoulides, G. Stegeman, Y. Min, and W. Sohler, "Discrete Talbot effect in waveguide arrays," Phys. Rev. Lett. 95, 053902 (2005).
    [CrossRef] [PubMed]
  18. A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tuennermann, and F. Lederer, "Quasi-incoherent propagation in waveguide arrays," Appl. Phys. Lett. 90, 241113 (2007).
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  20. A. Szameit, T. Pertsch, S. Nolte, A. Tunnermann, U. Peschel, and F. Lederer, "Optical Bloch oscillations in general waveguide lattices," J. Opt. Soc. Am. B 24, 2632-2639 (2007).
    [CrossRef]
  21. T. Pertsch, P. Dannberg, W. Elflein, A. Braeuer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4753-4755 (2004).
  22. R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, "Experimental observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
    [CrossRef]
  23. 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, 053903 (2006).
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  24. D. Dunlap and V. Kenkre, "Dynamic localization of a charged particle moving under the influence of an electric field," Phys. Rev. B 34, 3625-3633 (1986).
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  25. M. Holthaus, "Collapse of minibands in far-infrared irradiated superlattices," Phys. Rev. Lett. 69, 351-354 (1992).
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  26. S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
    [CrossRef] [PubMed]
  27. R. Iyer, J. Aitchison, J. Wan, M. Dignam, and M. de Sterke, "Exact dynamic localization in curved AlGaAs optical waveguide arrays," Opt. Express 15, 3212-3223 (2007).
    [CrossRef] [PubMed]
  28. K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, "Ultrafast processes for bulk Mmdification of transparent materials," MRS Bulletin 31, 620-625 (2006).
    [CrossRef]
  29. S. Longhi, "Self-imaging and modulational instability in an array of periodically curved waveguides," Opt. Lett. 30, 2137-2139 (2005).
    [CrossRef] [PubMed]
  30. A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tuennermann, "Control of directional evanescent coupling in fs laser written waveguides," Opt. Express 15, 1579-1587 (2007).
    [CrossRef] [PubMed]
  31. I. Garanovich, A. Sukhorukov, and Y. Kivshar, "Broadband diffraction management and self-collimation of white light in photonic lattices," Phys. Rev. E 74, 066609 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
  34. A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
    [CrossRef]
  35. A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica," Opt. Express 14, 6055-6062 (2006).
    [CrossRef] [PubMed]
  36. A. Zoubir, M. Richardson, C. Rivero, A. Schulte, C. Lopez, K. Richardson, N. Ho, and R. Vallee, "Direct femtosecond laser writing of waveguides in As2S3 thin films," Opt. Lett. 29, 1840-1842 (2004).
    [CrossRef] [PubMed]
  37. J. Chan, T. Huser, S. Risbud, J. Hayden, and D. Krol, "Waveguide fabrication in phosphate glasses using femtosecond laser pulses," Appl. Phys. Lett. 82, 2371-2373 (2003).
    [CrossRef]
  38. R. Osellame, M. Lobini, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. Bookey, R. Thompson, N. Psaila, and A. Kar, "Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient," Appl. Phys. Lett. 90, 241107 (2007).
    [CrossRef]
  39. A. Zoubir, C. Lopez, M. Richardson, and K. Richardson, "Femtosecond laser fabrication of tubular waveguides in PMMA," Opt. Lett. 29, 1840-1842 (2004).
    [CrossRef] [PubMed]
  40. D. Bloemer, A. Szameit, F. Dreisow, T. Schreiber, S. Nolte, and A. Tuennermann, "Measurement of the nonlinear refractive index of fs-laser-written waveguides in fused silica," Opt. Express 14, 2151-2157 (2006).
    [CrossRef]
  41. S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Ultrafast laser processing: new options for three- dimensional photonic structures," J. Mod. Opt. 51, 2533-2542 (2004).
    [CrossRef]
  42. K. Kajihara, L. Skuja, M. Hirano, and H. Hosono, "Formation and decay of nonbridging oxygen hole centers in SiO2 glasses induced by F2 laser irradiation: In situ observation using a pump and probe technique," Appl. Phys. Lett. 79, 1757-1759 (2001).
    [CrossRef]
  43. L. Skuja, T. Suzuki, and K. Tanimura, "Site-selective laser-spectroscopy studies of the intrinsic 1.9-eV luminescence center in glassy SiO2," Phys. Rev. B 52(21), 15208-15216 (1995).
    [CrossRef]
  44. M. Stevens-Kalceff, A. Stesmans, and J. Wong, "Defects induced in fused silica by high fluence ultraviolet laser pulses at 355 nm," Appl. Phys. Lett. 80, 758-760 (2002).
    [CrossRef]
  45. T. Fukuda, S. Ishikawa, T. Fujii, K. Sakuma, and H. Hosoya, "Low-loss optical waveguides written by femtosecond laser pulses for three-dimensional photonic devices," Proc. SPIE 5339, 524-538 (2004).
    [CrossRef]
  46. J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical waveguides," Opt. Commun. 247, 353-365 (2005).
    [CrossRef]
  47. M. M. Dignam and C. M. de Sterke, "Conditions for dynamic localization in geralized ac electric fields," Phys. Rev. Lett. 88, 046806 (2002).
    [CrossRef] [PubMed]
  48. A. Sukhorukov, D. Neshev, A. Dreischuh, R. Fischer, S. Ha,W. Krolikowski, J. Bolger, A. Mitchell, B. Eggleton, and Y. Kivshar, "Polychromatic nonlinear surface modes generated by supercontinuum light," Opt. Express 14, 11265-11270 (2006).
    [CrossRef] [PubMed]
  49. A. Sukhorukov, D. Neshev, and Y. Kivshar, "Shaping and control of polychromatic light in nonlinear photonic lattices," Opt. Express 15, 13058 (2007).
    [CrossRef] [PubMed]

2007 (8)

D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (2007).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, "Light evolution in arbitrary two-dimensional waveguide arrays," Phys. Rev. A 75, 053814 (2007).
[CrossRef]

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tuennermann, and F. Lederer, "Quasi-incoherent propagation in waveguide arrays," Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

A. Szameit, T. Pertsch, S. Nolte, A. Tunnermann, U. Peschel, and F. Lederer, "Optical Bloch oscillations in general waveguide lattices," J. Opt. Soc. Am. B 24, 2632-2639 (2007).
[CrossRef]

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

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tuennermann, "Control of directional evanescent coupling in fs laser written waveguides," Opt. Express 15, 1579-1587 (2007).
[CrossRef] [PubMed]

R. Osellame, M. Lobini, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. Bookey, R. Thompson, N. Psaila, and A. Kar, "Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient," Appl. Phys. Lett. 90, 241107 (2007).
[CrossRef]

A. Sukhorukov, D. Neshev, and Y. Kivshar, "Shaping and control of polychromatic light in nonlinear photonic lattices," Opt. Express 15, 13058 (2007).
[CrossRef] [PubMed]

2006 (10)

A. Sukhorukov, D. Neshev, A. Dreischuh, R. Fischer, S. Ha,W. Krolikowski, J. Bolger, A. Mitchell, B. Eggleton, and Y. Kivshar, "Polychromatic nonlinear surface modes generated by supercontinuum light," Opt. Express 14, 11265-11270 (2006).
[CrossRef] [PubMed]

D. Bloemer, A. Szameit, F. Dreisow, T. Schreiber, S. Nolte, and A. Tuennermann, "Measurement of the nonlinear refractive index of fs-laser-written waveguides in fused silica," Opt. Express 14, 2151-2157 (2006).
[CrossRef]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

I. Garanovich, A. Sukhorukov, and Y. Kivshar, "Broadband diffraction management and self-collimation of white light in photonic lattices," Phys. Rev. E 74, 066609 (2006).
[CrossRef]

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
[CrossRef]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica," Opt. Express 14, 6055-6062 (2006).
[CrossRef] [PubMed]

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, "Ultrafast processes for bulk Mmdification of transparent materials," MRS Bulletin 31, 620-625 (2006).
[CrossRef]

K. Makris and D. Christodoulides, "Method of images in optical discrete systems," Phys. Rev. E 73, 036616 (2006).
[CrossRef]

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, 053903 (2006).
[CrossRef] [PubMed]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Braeuer, and U. Peschel, "Visual observation of Zener Tunneling," Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

2005 (4)

R. Iwanow, D. May-Arrioja, D. Christodoulides, G. Stegeman, Y. Min, and W. Sohler, "Discrete Talbot effect in waveguide arrays," Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

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

A. Szameit, D. Bloemer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Discrete nonlinear localization in femtosecond laser written waveguides in fused silica," Opt. Express 13, 10552- 10557 (2005).
[CrossRef] [PubMed]

J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical waveguides," Opt. Commun. 247, 353-365 (2005).
[CrossRef]

2004 (7)

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Ultrafast laser processing: new options for three- dimensional photonic structures," J. Mod. Opt. 51, 2533-2542 (2004).
[CrossRef]

T. Fukuda, S. Ishikawa, T. Fujii, K. Sakuma, and H. Hosoya, "Low-loss optical waveguides written by femtosecond laser pulses for three-dimensional photonic devices," Proc. SPIE 5339, 524-538 (2004).
[CrossRef]

A. Zoubir, C. Lopez, M. Richardson, and K. Richardson, "Femtosecond laser fabrication of tubular waveguides in PMMA," Opt. Lett. 29, 1840-1842 (2004).
[CrossRef] [PubMed]

A. Zoubir, M. Richardson, C. Rivero, A. Schulte, C. Lopez, K. Richardson, N. Ho, and R. Vallee, "Direct femtosecond laser writing of waveguides in As2S3 thin films," Opt. Lett. 29, 1840-1842 (2004).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Braeuer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4753-4755 (2004).

R. Gordon, "Harmonic oscillation in a spatially finite array waveguide," Opt. Lett. 29, 2752-2754 (2004).
[CrossRef] [PubMed]

R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

2003 (1)

J. Chan, T. Huser, S. Risbud, J. Hayden, and D. Krol, "Waveguide fabrication in phosphate glasses using femtosecond laser pulses," Appl. Phys. Lett. 82, 2371-2373 (2003).
[CrossRef]

2002 (2)

M. M. Dignam and C. M. de Sterke, "Conditions for dynamic localization in geralized ac electric fields," Phys. Rev. Lett. 88, 046806 (2002).
[CrossRef] [PubMed]

M. Stevens-Kalceff, A. Stesmans, and J. Wong, "Defects induced in fused silica by high fluence ultraviolet laser pulses at 355 nm," Appl. Phys. Lett. 80, 758-760 (2002).
[CrossRef]

2001 (1)

K. Kajihara, L. Skuja, M. Hirano, and H. Hosono, "Formation and decay of nonbridging oxygen hole centers in SiO2 glasses induced by F2 laser irradiation: In situ observation using a pump and probe technique," Appl. Phys. Lett. 79, 1757-1759 (2001).
[CrossRef]

2000 (2)

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

P. Kevrekidis, K. Rasmussen, and A. Bishop, "Localized excitations and their thresholds," Phys. Rev. E 61, 4652-4655 (2000).
[CrossRef]

1999 (2)

R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, "Dynamics of discrete solitons in Optical Waveguide Arrays," Phys. Rev. Lett. 83, 2726-2729 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, "Experimental observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

1998 (3)

O. Bang, Y. Kivshar, A. Buryak, A. D. Rossi, and S. Trillo, "Two-dimensional solitary waves in media with quadratic and cubic nonlinearity," Phys. Rev. E 58, 5057-5069 (1998).
[CrossRef]

H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, "Optical Bloch oscillations in waveguide arrays," Opt. Lett. 23, 1701-1703 (1998).
[CrossRef]

1995 (1)

L. Skuja, T. Suzuki, and K. Tanimura, "Site-selective laser-spectroscopy studies of the intrinsic 1.9-eV luminescence center in glassy SiO2," Phys. Rev. B 52(21), 15208-15216 (1995).
[CrossRef]

1992 (1)

M. Holthaus, "Collapse of minibands in far-infrared irradiated superlattices," Phys. Rev. Lett. 69, 351-354 (1992).
[CrossRef] [PubMed]

1988 (1)

1986 (1)

D. Dunlap and V. Kenkre, "Dynamic localization of a charged particle moving under the influence of an electric field," Phys. Rev. B 34, 3625-3633 (1986).
[CrossRef]

1985 (1)

M. Kuznetsov, "Coupled wave analysis of multiple waveguide systems: The discrete harmonic oscillator," IEEE J. Quantum Electron. 21, 1893-1898 (1985).
[CrossRef]

1983 (1)

H. Haus and L. Molter-Orr, "Coupled multiple waveguide systems," IEEE J. Quantum Electron. 19, 840-844 (1983).
[CrossRef]

1982 (1)

S. Jensen, "The nonlinear coherent coupler," IEEE J. Quantum Electron. 18, 1580-1583 (1982).
[CrossRef]

1973 (1)

S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel optical waveguide directional coupler," Appl. Phys. Lett. 22, 46-48 (1973).
[CrossRef]

Aitchinson, J.

R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, "Experimental observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

Aitchison, J.

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

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

R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, "Dynamics of discrete solitons in Optical Waveguide Arrays," Phys. Rev. Lett. 83, 2726-2729 (1999).
[CrossRef]

H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Austin, M. W.

D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (2007).
[CrossRef] [PubMed]

Bang, O.

O. Bang, Y. Kivshar, A. Buryak, A. D. Rossi, and S. Trillo, "Two-dimensional solitary waves in media with quadratic and cubic nonlinearity," Phys. Rev. E 58, 5057-5069 (1998).
[CrossRef]

Bishop, A.

P. Kevrekidis, K. Rasmussen, and A. Bishop, "Localized excitations and their thresholds," Phys. Rev. E 61, 4652-4655 (2000).
[CrossRef]

Bloemer, D.

Bolger, J.

D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (2007).
[CrossRef] [PubMed]

A. Sukhorukov, D. Neshev, A. Dreischuh, R. Fischer, S. Ha,W. Krolikowski, J. Bolger, A. Mitchell, B. Eggleton, and Y. Kivshar, "Polychromatic nonlinear surface modes generated by supercontinuum light," Opt. Express 14, 11265-11270 (2006).
[CrossRef] [PubMed]

Bookey, H.

R. Osellame, M. Lobini, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. Bookey, R. Thompson, N. Psaila, and A. Kar, "Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient," Appl. Phys. Lett. 90, 241107 (2007).
[CrossRef]

Boyd, A.

H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Braeuer, A.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Braeuer, and U. Peschel, "Visual observation of Zener Tunneling," Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Braeuer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4753-4755 (2004).

Bui, L.

D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (2007).
[CrossRef] [PubMed]

Burghoff, J.

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
[CrossRef]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica," Opt. Express 14, 6055-6062 (2006).
[CrossRef] [PubMed]

A. Szameit, D. Bloemer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Discrete nonlinear localization in femtosecond laser written waveguides in fused silica," Opt. Express 13, 10552- 10557 (2005).
[CrossRef] [PubMed]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Ultrafast laser processing: new options for three- dimensional photonic structures," J. Mod. Opt. 51, 2533-2542 (2004).
[CrossRef]

Buryak, A.

O. Bang, Y. Kivshar, A. Buryak, A. D. Rossi, and S. Trillo, "Two-dimensional solitary waves in media with quadratic and cubic nonlinearity," Phys. Rev. E 58, 5057-5069 (1998).
[CrossRef]

Cerullo, G.

R. Osellame, M. Lobini, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. Bookey, R. Thompson, N. Psaila, and A. Kar, "Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient," Appl. Phys. Lett. 90, 241107 (2007).
[CrossRef]

Chan, J.

J. Chan, T. Huser, S. Risbud, J. Hayden, and D. Krol, "Waveguide fabrication in phosphate glasses using femtosecond laser pulses," Appl. Phys. Lett. 82, 2371-2373 (2003).
[CrossRef]

Chiodo, N.

R. Osellame, M. Lobini, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. Bookey, R. Thompson, N. Psaila, and A. Kar, "Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient," Appl. Phys. Lett. 90, 241107 (2007).
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K. Makris and D. Christodoulides, "Method of images in optical discrete systems," Phys. Rev. E 73, 036616 (2006).
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R. Iwanow, D. May-Arrioja, D. Christodoulides, G. Stegeman, Y. Min, and W. Sohler, "Discrete Talbot effect in waveguide arrays," Phys. Rev. Lett. 95, 053902 (2005).
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D. Christodoulides and R. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988).
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Cianci, E.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Braeuer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4753-4755 (2004).

de Sterke, C. M.

J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical waveguides," Opt. Commun. 247, 353-365 (2005).
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M. M. Dignam and C. M. de Sterke, "Conditions for dynamic localization in geralized ac electric fields," Phys. Rev. Lett. 88, 046806 (2002).
[CrossRef] [PubMed]

de Sterke, M.

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, 053903 (2006).
[CrossRef] [PubMed]

Dignam, M.

Dignam, M. M.

J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical waveguides," Opt. Commun. 247, 353-365 (2005).
[CrossRef]

M. M. Dignam and C. M. de Sterke, "Conditions for dynamic localization in geralized ac electric fields," Phys. Rev. Lett. 88, 046806 (2002).
[CrossRef] [PubMed]

Dreischuh, A.

D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (2007).
[CrossRef] [PubMed]

A. Sukhorukov, D. Neshev, A. Dreischuh, R. Fischer, S. Ha,W. Krolikowski, J. Bolger, A. Mitchell, B. Eggleton, and Y. Kivshar, "Polychromatic nonlinear surface modes generated by supercontinuum light," Opt. Express 14, 11265-11270 (2006).
[CrossRef] [PubMed]

Dreisow, F.

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tuennermann, "Control of directional evanescent coupling in fs laser written waveguides," Opt. Express 15, 1579-1587 (2007).
[CrossRef] [PubMed]

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tuennermann, and F. Lederer, "Quasi-incoherent propagation in waveguide arrays," Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, "Light evolution in arbitrary two-dimensional waveguide arrays," Phys. Rev. A 75, 053814 (2007).
[CrossRef]

D. Bloemer, A. Szameit, F. Dreisow, T. Schreiber, S. Nolte, and A. Tuennermann, "Measurement of the nonlinear refractive index of fs-laser-written waveguides in fused silica," Opt. Express 14, 2151-2157 (2006).
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Dunlap, D.

D. Dunlap and V. Kenkre, "Dynamic localization of a charged particle moving under the influence of an electric field," Phys. Rev. B 34, 3625-3633 (1986).
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Eggleton, B. J.

D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (2007).
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R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, "Dynamics of discrete solitons in Optical Waveguide Arrays," Phys. Rev. Lett. 83, 2726-2729 (1999).
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R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, "Experimental observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
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H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, A. Braeuer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4753-4755 (2004).

Fischer, R.

D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (2007).
[CrossRef] [PubMed]

A. Sukhorukov, D. Neshev, A. Dreischuh, R. Fischer, S. Ha,W. Krolikowski, J. Bolger, A. Mitchell, B. Eggleton, and Y. Kivshar, "Polychromatic nonlinear surface modes generated by supercontinuum light," Opt. Express 14, 11265-11270 (2006).
[CrossRef] [PubMed]

Foglietti, V.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Fujii, T.

T. Fukuda, S. Ishikawa, T. Fujii, K. Sakuma, and H. Hosoya, "Low-loss optical waveguides written by femtosecond laser pulses for three-dimensional photonic devices," Proc. SPIE 5339, 524-538 (2004).
[CrossRef]

Fukuda, T.

T. Fukuda, S. Ishikawa, T. Fujii, K. Sakuma, and H. Hosoya, "Low-loss optical waveguides written by femtosecond laser pulses for three-dimensional photonic devices," Proc. SPIE 5339, 524-538 (2004).
[CrossRef]

Garanovich, I.

I. Garanovich, A. Sukhorukov, and Y. Kivshar, "Broadband diffraction management and self-collimation of white light in photonic lattices," Phys. Rev. E 74, 066609 (2006).
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Garvin, H.

S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel optical waveguide directional coupler," Appl. Phys. Lett. 22, 46-48 (1973).
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Ha, S.

D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (2007).
[CrossRef] [PubMed]

A. Sukhorukov, D. Neshev, A. Dreischuh, R. Fischer, S. Ha,W. Krolikowski, J. Bolger, A. Mitchell, B. Eggleton, and Y. Kivshar, "Polychromatic nonlinear surface modes generated by supercontinuum light," Opt. Express 14, 11265-11270 (2006).
[CrossRef] [PubMed]

Hartung, H.

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tuennermann, and F. Lederer, "Quasi-incoherent propagation in waveguide arrays," Appl. Phys. Lett. 90, 241113 (2007).
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H. Haus and L. Molter-Orr, "Coupled multiple waveguide systems," IEEE J. Quantum Electron. 19, 840-844 (1983).
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J. Chan, T. Huser, S. Risbud, J. Hayden, and D. Krol, "Waveguide fabrication in phosphate glasses using femtosecond laser pulses," Appl. Phys. Lett. 82, 2371-2373 (2003).
[CrossRef]

Hirano, M.

K. Kajihara, L. Skuja, M. Hirano, and H. Hosono, "Formation and decay of nonbridging oxygen hole centers in SiO2 glasses induced by F2 laser irradiation: In situ observation using a pump and probe technique," Appl. Phys. Lett. 79, 1757-1759 (2001).
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Holthaus, M.

M. Holthaus, "Collapse of minibands in far-infrared irradiated superlattices," Phys. Rev. Lett. 69, 351-354 (1992).
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Hosono, H.

K. Kajihara, L. Skuja, M. Hirano, and H. Hosono, "Formation and decay of nonbridging oxygen hole centers in SiO2 glasses induced by F2 laser irradiation: In situ observation using a pump and probe technique," Appl. Phys. Lett. 79, 1757-1759 (2001).
[CrossRef]

Hosoya, H.

T. Fukuda, S. Ishikawa, T. Fujii, K. Sakuma, and H. Hosoya, "Low-loss optical waveguides written by femtosecond laser pulses for three-dimensional photonic devices," Proc. SPIE 5339, 524-538 (2004).
[CrossRef]

Hunsperger, R.

S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel optical waveguide directional coupler," Appl. Phys. Lett. 22, 46-48 (1973).
[CrossRef]

Huser, T.

J. Chan, T. Huser, S. Risbud, J. Hayden, and D. Krol, "Waveguide fabrication in phosphate glasses using femtosecond laser pulses," Appl. Phys. Lett. 82, 2371-2373 (2003).
[CrossRef]

Ishikawa, S.

T. Fukuda, S. Ishikawa, T. Fujii, K. Sakuma, and H. Hosoya, "Low-loss optical waveguides written by femtosecond laser pulses for three-dimensional photonic devices," Proc. SPIE 5339, 524-538 (2004).
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K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, "Ultrafast processes for bulk Mmdification of transparent materials," MRS Bulletin 31, 620-625 (2006).
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R. Iwanow, D. May-Arrioja, D. Christodoulides, G. Stegeman, Y. Min, and W. Sohler, "Discrete Talbot effect in waveguide arrays," Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
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S. Jensen, "The nonlinear coherent coupler," IEEE J. Quantum Electron. 18, 1580-1583 (1982).
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Kajihara, K.

K. Kajihara, L. Skuja, M. Hirano, and H. Hosono, "Formation and decay of nonbridging oxygen hole centers in SiO2 glasses induced by F2 laser irradiation: In situ observation using a pump and probe technique," Appl. Phys. Lett. 79, 1757-1759 (2001).
[CrossRef]

Kar, A.

R. Osellame, M. Lobini, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. Bookey, R. Thompson, N. Psaila, and A. Kar, "Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient," Appl. Phys. Lett. 90, 241107 (2007).
[CrossRef]

Kenkre, V.

D. Dunlap and V. Kenkre, "Dynamic localization of a charged particle moving under the influence of an electric field," Phys. Rev. B 34, 3625-3633 (1986).
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P. Kevrekidis, K. Rasmussen, and A. Bishop, "Localized excitations and their thresholds," Phys. Rev. E 61, 4652-4655 (2000).
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Kivshar, Y.

A. Sukhorukov, D. Neshev, and Y. Kivshar, "Shaping and control of polychromatic light in nonlinear photonic lattices," Opt. Express 15, 13058 (2007).
[CrossRef] [PubMed]

A. Sukhorukov, D. Neshev, A. Dreischuh, R. Fischer, S. Ha,W. Krolikowski, J. Bolger, A. Mitchell, B. Eggleton, and Y. Kivshar, "Polychromatic nonlinear surface modes generated by supercontinuum light," Opt. Express 14, 11265-11270 (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, 053903 (2006).
[CrossRef] [PubMed]

I. Garanovich, A. Sukhorukov, and Y. Kivshar, "Broadband diffraction management and self-collimation of white light in photonic lattices," Phys. Rev. E 74, 066609 (2006).
[CrossRef]

O. Bang, Y. Kivshar, A. Buryak, A. D. Rossi, and S. Trillo, "Two-dimensional solitary waves in media with quadratic and cubic nonlinearity," Phys. Rev. E 58, 5057-5069 (1998).
[CrossRef]

Kivshar, Y. S.

D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (2007).
[CrossRef] [PubMed]

Krol, D.

J. Chan, T. Huser, S. Risbud, J. Hayden, and D. Krol, "Waveguide fabrication in phosphate glasses using femtosecond laser pulses," Appl. Phys. Lett. 82, 2371-2373 (2003).
[CrossRef]

Krolikowski, W.

D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (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, 053903 (2006).
[CrossRef] [PubMed]

A. Sukhorukov, D. Neshev, A. Dreischuh, R. Fischer, S. Ha,W. Krolikowski, J. Bolger, A. Mitchell, B. Eggleton, and Y. Kivshar, "Polychromatic nonlinear surface modes generated by supercontinuum light," Opt. Express 14, 11265-11270 (2006).
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Kuznetsov, M.

M. Kuznetsov, "Coupled wave analysis of multiple waveguide systems: The discrete harmonic oscillator," IEEE J. Quantum Electron. 21, 1893-1898 (1985).
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Laforest, M.

J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical waveguides," Opt. Commun. 247, 353-365 (2005).
[CrossRef]

Laporta, P.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Lederer, F.

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, "Light evolution in arbitrary two-dimensional waveguide arrays," Phys. Rev. A 75, 053814 (2007).
[CrossRef]

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tuennermann, and F. Lederer, "Quasi-incoherent propagation in waveguide arrays," Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

A. Szameit, T. Pertsch, S. Nolte, A. Tunnermann, U. Peschel, and F. Lederer, "Optical Bloch oscillations in general waveguide lattices," J. Opt. Soc. Am. B 24, 2632-2639 (2007).
[CrossRef]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica," Opt. Express 14, 6055-6062 (2006).
[CrossRef] [PubMed]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Braeuer, and U. Peschel, "Visual observation of Zener Tunneling," Phys. Rev. Lett. 96, 023901 (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, 053903 (2006).
[CrossRef] [PubMed]

A. Szameit, D. Bloemer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Discrete nonlinear localization in femtosecond laser written waveguides in fused silica," Opt. Express 13, 10552- 10557 (2005).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Braeuer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4753-4755 (2004).

R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

U. Peschel, T. Pertsch, and F. Lederer, "Optical Bloch oscillations in waveguide arrays," Opt. Lett. 23, 1701-1703 (1998).
[CrossRef]

Lobini, M.

R. Osellame, M. Lobini, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. Bookey, R. Thompson, N. Psaila, and A. Kar, "Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient," Appl. Phys. Lett. 90, 241107 (2007).
[CrossRef]

Lobino, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Longhi, S.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
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S. Longhi, "Self-imaging and modulational instability in an array of periodically curved waveguides," Opt. Lett. 30, 2137-2139 (2005).
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K. Makris and D. Christodoulides, "Method of images in optical discrete systems," Phys. Rev. E 73, 036616 (2006).
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R. Osellame, M. Lobini, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. Bookey, R. Thompson, N. Psaila, and A. Kar, "Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient," Appl. Phys. Lett. 90, 241107 (2007).
[CrossRef]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

May-Arrioja, D.

R. Iwanow, D. May-Arrioja, D. Christodoulides, G. Stegeman, Y. Min, and W. Sohler, "Discrete Talbot effect in waveguide arrays," Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Michaelis, D.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Braeuer, and U. Peschel, "Visual observation of Zener Tunneling," Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

Min, Y.

R. Iwanow, D. May-Arrioja, D. Christodoulides, G. Stegeman, Y. Min, and W. Sohler, "Discrete Talbot effect in waveguide arrays," Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

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D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (2007).
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A. Sukhorukov, D. Neshev, A. Dreischuh, R. Fischer, S. Ha,W. Krolikowski, J. Bolger, A. Mitchell, B. Eggleton, and Y. Kivshar, "Polychromatic nonlinear surface modes generated by supercontinuum light," Opt. Express 14, 11265-11270 (2006).
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H. Eisenberg, Y. Silberberg, R. Morandotti, and J. Aitchison, "Diffraction Management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, "Dynamics of discrete solitons in Optical Waveguide Arrays," Phys. Rev. Lett. 83, 2726-2729 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, "Experimental observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
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H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
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Neshev, D.

Neshev, D. N.

D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (2007).
[CrossRef] [PubMed]

Nolte, S.

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, "Light evolution in arbitrary two-dimensional waveguide arrays," Phys. Rev. A 75, 053814 (2007).
[CrossRef]

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tuennermann, and F. Lederer, "Quasi-incoherent propagation in waveguide arrays," Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tuennermann, "Control of directional evanescent coupling in fs laser written waveguides," Opt. Express 15, 1579-1587 (2007).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, S. Nolte, A. Tunnermann, U. Peschel, and F. Lederer, "Optical Bloch oscillations in general waveguide lattices," J. Opt. Soc. Am. B 24, 2632-2639 (2007).
[CrossRef]

D. Bloemer, A. Szameit, F. Dreisow, T. Schreiber, S. Nolte, and A. Tuennermann, "Measurement of the nonlinear refractive index of fs-laser-written waveguides in fused silica," Opt. Express 14, 2151-2157 (2006).
[CrossRef]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica," Opt. Express 14, 6055-6062 (2006).
[CrossRef] [PubMed]

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, "Ultrafast processes for bulk Mmdification of transparent materials," MRS Bulletin 31, 620-625 (2006).
[CrossRef]

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
[CrossRef]

A. Szameit, D. Bloemer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Discrete nonlinear localization in femtosecond laser written waveguides in fused silica," Opt. Express 13, 10552- 10557 (2005).
[CrossRef] [PubMed]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Ultrafast laser processing: new options for three- dimensional photonic structures," J. Mod. Opt. 51, 2533-2542 (2004).
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R. Osellame, M. Lobini, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. Bookey, R. Thompson, N. Psaila, and A. Kar, "Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient," Appl. Phys. Lett. 90, 241107 (2007).
[CrossRef]

Pertsch, T.

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tuennermann, "Control of directional evanescent coupling in fs laser written waveguides," Opt. Express 15, 1579-1587 (2007).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, S. Nolte, A. Tunnermann, U. Peschel, and F. Lederer, "Optical Bloch oscillations in general waveguide lattices," J. Opt. Soc. Am. B 24, 2632-2639 (2007).
[CrossRef]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, "Light evolution in arbitrary two-dimensional waveguide arrays," Phys. Rev. A 75, 053814 (2007).
[CrossRef]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Braeuer, and U. Peschel, "Visual observation of Zener Tunneling," Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
[CrossRef]

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, 053903 (2006).
[CrossRef] [PubMed]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica," Opt. Express 14, 6055-6062 (2006).
[CrossRef] [PubMed]

A. Szameit, D. Bloemer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Discrete nonlinear localization in femtosecond laser written waveguides in fused silica," Opt. Express 13, 10552- 10557 (2005).
[CrossRef] [PubMed]

R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
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T. Pertsch, P. Dannberg, W. Elflein, A. Braeuer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4753-4755 (2004).

U. Peschel, T. Pertsch, and F. Lederer, "Optical Bloch oscillations in waveguide arrays," Opt. Lett. 23, 1701-1703 (1998).
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A. Szameit, T. Pertsch, S. Nolte, A. Tunnermann, U. Peschel, and F. Lederer, "Optical Bloch oscillations in general waveguide lattices," J. Opt. Soc. Am. B 24, 2632-2639 (2007).
[CrossRef]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, "Light evolution in arbitrary two-dimensional waveguide arrays," Phys. Rev. A 75, 053814 (2007).
[CrossRef]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Braeuer, and U. Peschel, "Visual observation of Zener Tunneling," Phys. Rev. Lett. 96, 023901 (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, 053903 (2006).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, "Experimental observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, "Dynamics of discrete solitons in Optical Waveguide Arrays," Phys. Rev. Lett. 83, 2726-2729 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, "Optical Bloch oscillations in waveguide arrays," Opt. Lett. 23, 1701-1703 (1998).
[CrossRef]

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R. Osellame, M. Lobini, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. Bookey, R. Thompson, N. Psaila, and A. Kar, "Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient," Appl. Phys. Lett. 90, 241107 (2007).
[CrossRef]

Ramponi, R.

R. Osellame, M. Lobini, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. Bookey, R. Thompson, N. Psaila, and A. Kar, "Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient," Appl. Phys. Lett. 90, 241107 (2007).
[CrossRef]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901 (2006).
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P. Kevrekidis, K. Rasmussen, and A. Bishop, "Localized excitations and their thresholds," Phys. Rev. E 61, 4652-4655 (2000).
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Richardson, M.

Risbud, S.

J. Chan, T. Huser, S. Risbud, J. Hayden, and D. Krol, "Waveguide fabrication in phosphate glasses using femtosecond laser pulses," Appl. Phys. Lett. 82, 2371-2373 (2003).
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Rossi, A. D.

O. Bang, Y. Kivshar, A. Buryak, A. D. Rossi, and S. Trillo, "Two-dimensional solitary waves in media with quadratic and cubic nonlinearity," Phys. Rev. E 58, 5057-5069 (1998).
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T. Fukuda, S. Ishikawa, T. Fujii, K. Sakuma, and H. Hosoya, "Low-loss optical waveguides written by femtosecond laser pulses for three-dimensional photonic devices," Proc. SPIE 5339, 524-538 (2004).
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Schaffer, C. B.

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, "Ultrafast processes for bulk Mmdification of transparent materials," MRS Bulletin 31, 620-625 (2006).
[CrossRef]

Schieck, R.

R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

Schreiber, T.

Schulte, A.

Silberberg, Y.

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

R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, "Dynamics of discrete solitons in Optical Waveguide Arrays," Phys. Rev. Lett. 83, 2726-2729 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, "Experimental observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
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Skuja, L.

K. Kajihara, L. Skuja, M. Hirano, and H. Hosono, "Formation and decay of nonbridging oxygen hole centers in SiO2 glasses induced by F2 laser irradiation: In situ observation using a pump and probe technique," Appl. Phys. Lett. 79, 1757-1759 (2001).
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L. Skuja, T. Suzuki, and K. Tanimura, "Site-selective laser-spectroscopy studies of the intrinsic 1.9-eV luminescence center in glassy SiO2," Phys. Rev. B 52(21), 15208-15216 (1995).
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Sohler, W.

R. Iwanow, D. May-Arrioja, D. Christodoulides, G. Stegeman, Y. Min, and W. Sohler, "Discrete Talbot effect in waveguide arrays," Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
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Stegeman, G.

R. Iwanow, D. May-Arrioja, D. Christodoulides, G. Stegeman, Y. Min, and W. Sohler, "Discrete Talbot effect in waveguide arrays," Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

Stesmans, A.

M. Stevens-Kalceff, A. Stesmans, and J. Wong, "Defects induced in fused silica by high fluence ultraviolet laser pulses at 355 nm," Appl. Phys. Lett. 80, 758-760 (2002).
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Stevens-Kalceff, M.

M. Stevens-Kalceff, A. Stesmans, and J. Wong, "Defects induced in fused silica by high fluence ultraviolet laser pulses at 355 nm," Appl. Phys. Lett. 80, 758-760 (2002).
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Streppel, U.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Braeuer, and U. Peschel, "Visual observation of Zener Tunneling," Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

Sukhorukov, A.

A. Sukhorukov, D. Neshev, and Y. Kivshar, "Shaping and control of polychromatic light in nonlinear photonic lattices," Opt. Express 15, 13058 (2007).
[CrossRef] [PubMed]

A. Sukhorukov, D. Neshev, A. Dreischuh, R. Fischer, S. Ha,W. Krolikowski, J. Bolger, A. Mitchell, B. Eggleton, and Y. Kivshar, "Polychromatic nonlinear surface modes generated by supercontinuum light," Opt. Express 14, 11265-11270 (2006).
[CrossRef] [PubMed]

I. Garanovich, A. Sukhorukov, and Y. Kivshar, "Broadband diffraction management and self-collimation of white light in photonic lattices," Phys. Rev. E 74, 066609 (2006).
[CrossRef]

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, 053903 (2006).
[CrossRef] [PubMed]

Sukhorukov, A. A.

D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (2007).
[CrossRef] [PubMed]

Suzuki, T.

L. Skuja, T. Suzuki, and K. Tanimura, "Site-selective laser-spectroscopy studies of the intrinsic 1.9-eV luminescence center in glassy SiO2," Phys. Rev. B 52(21), 15208-15216 (1995).
[CrossRef]

Szameit, A.

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tuennermann, and F. Lederer, "Quasi-incoherent propagation in waveguide arrays," Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, "Light evolution in arbitrary two-dimensional waveguide arrays," Phys. Rev. A 75, 053814 (2007).
[CrossRef]

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tuennermann, "Control of directional evanescent coupling in fs laser written waveguides," Opt. Express 15, 1579-1587 (2007).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, S. Nolte, A. Tunnermann, U. Peschel, and F. Lederer, "Optical Bloch oscillations in general waveguide lattices," J. Opt. Soc. Am. B 24, 2632-2639 (2007).
[CrossRef]

D. Bloemer, A. Szameit, F. Dreisow, T. Schreiber, S. Nolte, and A. Tuennermann, "Measurement of the nonlinear refractive index of fs-laser-written waveguides in fused silica," Opt. Express 14, 2151-2157 (2006).
[CrossRef]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica," Opt. Express 14, 6055-6062 (2006).
[CrossRef] [PubMed]

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
[CrossRef]

A. Szameit, D. Bloemer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Discrete nonlinear localization in femtosecond laser written waveguides in fused silica," Opt. Express 13, 10552- 10557 (2005).
[CrossRef] [PubMed]

Tanimura, K.

L. Skuja, T. Suzuki, and K. Tanimura, "Site-selective laser-spectroscopy studies of the intrinsic 1.9-eV luminescence center in glassy SiO2," Phys. Rev. B 52(21), 15208-15216 (1995).
[CrossRef]

Thompson, R.

R. Osellame, M. Lobini, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. Bookey, R. Thompson, N. Psaila, and A. Kar, "Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient," Appl. Phys. Lett. 90, 241107 (2007).
[CrossRef]

Trillo, S.

O. Bang, Y. Kivshar, A. Buryak, A. D. Rossi, and S. Trillo, "Two-dimensional solitary waves in media with quadratic and cubic nonlinearity," Phys. Rev. E 58, 5057-5069 (1998).
[CrossRef]

Trompeter, H.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Braeuer, and U. Peschel, "Visual observation of Zener Tunneling," Phys. Rev. Lett. 96, 023901 (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, 053903 (2006).
[CrossRef] [PubMed]

Tuennermann, A.

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, "Light evolution in arbitrary two-dimensional waveguide arrays," Phys. Rev. A 75, 053814 (2007).
[CrossRef]

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tuennermann, and F. Lederer, "Quasi-incoherent propagation in waveguide arrays," Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tuennermann, "Control of directional evanescent coupling in fs laser written waveguides," Opt. Express 15, 1579-1587 (2007).
[CrossRef] [PubMed]

D. Bloemer, A. Szameit, F. Dreisow, T. Schreiber, S. Nolte, and A. Tuennermann, "Measurement of the nonlinear refractive index of fs-laser-written waveguides in fused silica," Opt. Express 14, 2151-2157 (2006).
[CrossRef]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica," Opt. Express 14, 6055-6062 (2006).
[CrossRef] [PubMed]

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
[CrossRef]

A. Szameit, D. Bloemer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Discrete nonlinear localization in femtosecond laser written waveguides in fused silica," Opt. Express 13, 10552- 10557 (2005).
[CrossRef] [PubMed]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Ultrafast laser processing: new options for three- dimensional photonic structures," J. Mod. Opt. 51, 2533-2542 (2004).
[CrossRef]

Tunnermann, A.

Vallee, R.

Wan, J.

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

J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical waveguides," Opt. Commun. 247, 353-365 (2005).
[CrossRef]

Watanabe, W.

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, "Ultrafast processes for bulk Mmdification of transparent materials," MRS Bulletin 31, 620-625 (2006).
[CrossRef]

Will, M.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Ultrafast laser processing: new options for three- dimensional photonic structures," J. Mod. Opt. 51, 2533-2542 (2004).
[CrossRef]

Wong, J.

M. Stevens-Kalceff, A. Stesmans, and J. Wong, "Defects induced in fused silica by high fluence ultraviolet laser pulses at 355 nm," Appl. Phys. Lett. 80, 758-760 (2002).
[CrossRef]

Yariv, A.

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Zoubir, A.

Appl. Phys. B. (1)

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
[CrossRef]

Appl. Phys. Lett. (6)

J. Chan, T. Huser, S. Risbud, J. Hayden, and D. Krol, "Waveguide fabrication in phosphate glasses using femtosecond laser pulses," Appl. Phys. Lett. 82, 2371-2373 (2003).
[CrossRef]

R. Osellame, M. Lobini, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. Bookey, R. Thompson, N. Psaila, and A. Kar, "Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient," Appl. Phys. Lett. 90, 241107 (2007).
[CrossRef]

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tuennermann, and F. Lederer, "Quasi-incoherent propagation in waveguide arrays," Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel optical waveguide directional coupler," Appl. Phys. Lett. 22, 46-48 (1973).
[CrossRef]

K. Kajihara, L. Skuja, M. Hirano, and H. Hosono, "Formation and decay of nonbridging oxygen hole centers in SiO2 glasses induced by F2 laser irradiation: In situ observation using a pump and probe technique," Appl. Phys. Lett. 79, 1757-1759 (2001).
[CrossRef]

M. Stevens-Kalceff, A. Stesmans, and J. Wong, "Defects induced in fused silica by high fluence ultraviolet laser pulses at 355 nm," Appl. Phys. Lett. 80, 758-760 (2002).
[CrossRef]

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S. Jensen, "The nonlinear coherent coupler," IEEE J. Quantum Electron. 18, 1580-1583 (1982).
[CrossRef]

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[CrossRef]

J. Mod. Opt. (1)

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Ultrafast laser processing: new options for three- dimensional photonic structures," J. Mod. Opt. 51, 2533-2542 (2004).
[CrossRef]

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

MRS Bulletin (1)

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, "Ultrafast processes for bulk Mmdification of transparent materials," MRS Bulletin 31, 620-625 (2006).
[CrossRef]

Opt. Commun. (1)

J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical waveguides," Opt. Commun. 247, 353-365 (2005).
[CrossRef]

Opt. Express (7)

A. Sukhorukov, D. Neshev, A. Dreischuh, R. Fischer, S. Ha,W. Krolikowski, J. Bolger, A. Mitchell, B. Eggleton, and Y. Kivshar, "Polychromatic nonlinear surface modes generated by supercontinuum light," Opt. Express 14, 11265-11270 (2006).
[CrossRef] [PubMed]

A. Sukhorukov, D. Neshev, and Y. Kivshar, "Shaping and control of polychromatic light in nonlinear photonic lattices," Opt. Express 15, 13058 (2007).
[CrossRef] [PubMed]

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tuennermann, "Control of directional evanescent coupling in fs laser written waveguides," Opt. Express 15, 1579-1587 (2007).
[CrossRef] [PubMed]

D. Bloemer, A. Szameit, F. Dreisow, T. Schreiber, S. Nolte, and A. Tuennermann, "Measurement of the nonlinear refractive index of fs-laser-written waveguides in fused silica," Opt. Express 14, 2151-2157 (2006).
[CrossRef]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica," Opt. Express 14, 6055-6062 (2006).
[CrossRef] [PubMed]

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

A. Szameit, D. Bloemer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Discrete nonlinear localization in femtosecond laser written waveguides in fused silica," Opt. Express 13, 10552- 10557 (2005).
[CrossRef] [PubMed]

Opt. Lett. (6)

Phys. Rev. A (1)

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, and F. Lederer, "Light evolution in arbitrary two-dimensional waveguide arrays," Phys. Rev. A 75, 053814 (2007).
[CrossRef]

Phys. Rev. B (2)

D. Dunlap and V. Kenkre, "Dynamic localization of a charged particle moving under the influence of an electric field," Phys. Rev. B 34, 3625-3633 (1986).
[CrossRef]

L. Skuja, T. Suzuki, and K. Tanimura, "Site-selective laser-spectroscopy studies of the intrinsic 1.9-eV luminescence center in glassy SiO2," Phys. Rev. B 52(21), 15208-15216 (1995).
[CrossRef]

Phys. Rev. E (4)

I. Garanovich, A. Sukhorukov, and Y. Kivshar, "Broadband diffraction management and self-collimation of white light in photonic lattices," Phys. Rev. E 74, 066609 (2006).
[CrossRef]

K. Makris and D. Christodoulides, "Method of images in optical discrete systems," Phys. Rev. E 73, 036616 (2006).
[CrossRef]

O. Bang, Y. Kivshar, A. Buryak, A. D. Rossi, and S. Trillo, "Two-dimensional solitary waves in media with quadratic and cubic nonlinearity," Phys. Rev. E 58, 5057-5069 (1998).
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[CrossRef]

Phys. Rev. Lett. (13)

D. N. Neshev, A. A. Sukhorukov, A. Dreischuh, R. Fischer, S. Ha, J. Bolger, L. Bui, W. Krolikowski, B. J. Eggleton, A. Mitchell, M. W. Austin, and Y. S. Kivshar, "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901 (2007).
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H. Eisenberg, Y. Silberberg, R. Morandotti, and J. Aitchison, "Diffraction Management," Phys. Rev. Lett. 85, 1863-1866 (2000).
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H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
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R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 113902 (2004).
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R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, "Dynamics of discrete solitons in Optical Waveguide Arrays," Phys. Rev. Lett. 83, 2726-2729 (1999).
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H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Braeuer, and U. Peschel, "Visual observation of Zener Tunneling," Phys. Rev. Lett. 96, 023901 (2006).
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R. Iwanow, D. May-Arrioja, D. Christodoulides, G. Stegeman, Y. Min, and W. Sohler, "Discrete Talbot effect in waveguide arrays," Phys. Rev. Lett. 95, 053902 (2005).
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T. Pertsch, P. Dannberg, W. Elflein, A. Braeuer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4753-4755 (2004).

R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, and Y. Silberberg, "Experimental observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
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Proc. SPIE (1)

T. Fukuda, S. Ishikawa, T. Fujii, K. Sakuma, and H. Hosoya, "Low-loss optical waveguides written by femtosecond laser pulses for three-dimensional photonic devices," Proc. SPIE 5339, 524-538 (2004).
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Other (1)

M. Abramowitz and I. Stegun, Pocketbook of Mathematical Functions (Verlag Harry Deutsch, 1984).

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Figures (7)

Fig. 1.
Fig. 1.

Scheme of the writing procedure. Inset: Exemplary microscope images of a curved waveguide lattice.

Fig. 2.
Fig. 2.

(a) Fluorescence setup for visualization of the light evolution (b) Straight waveguide array, separation 14 µm, with normalized intensity inside the excited waveguide. The coupling constant is fitted to c=0.185mm-1

Fig. 3.
Fig. 3.

Propagation losses of curved waveguides with near-field and fluorescence measurements: red P 0=28 mW, Δn=4·10-4; green P 0=22 mW, Δn=2·10-4

Fig. 4.
Fig. 4.

Fluorescence pattern of dynamic localization and corresponding experimental (red curves) and theoretical (black curves) cross-sections. The waveguide spacing is 14 µm resulting in a coupling constant between adjacent waveguides c=0.185 mm-1

Fig. 5.
Fig. 5.

(a) Setup for the investigation of the coupling between the single guides. The generation of the supercontinuum light was achieved by coupling picosecond laser pulses into a PCF. (b) Spectrum of the generated supercontinuum.

Fig. 6.
Fig. 6.

(a) Polychromatic discrete diffraction in a straight lattice after z=25 mm and a waveguide spacing of 16 µm. (b) Simulation of the output pattern. Wavelength scale in nanometer

Fig. 7.
Fig. 7.

(a) Curved waveguide array with a bending amplitude of A 633nm=42 µm for a longitudinal period of z 0=25 mm. In this case, self-collimation occurs at λ=633 nm. (b) For a bending amplitude of A 543nm=36 µm the self-collimation wavelength is 543 nm. The wavelengths are given in nanometers.

Equations (11)

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i Ψ ( x x 0 , z ) z + λ 4 π n 0 2 Ψ ( x x 0 , z ) x 2 + 2 π λ ν ( x x 0 ( z ) ) Ψ ( x x 0 , z ) = 0 .
i Ψ ( x ̂ , z ̂ ) z ̂ i x ˙ 0 Ψ ( x ̂ , z ̂ ) x ̂ + λ 4 πn 0 2 Ψ ( x ̂ , z ̂ ) x ̂ 2 + 2 π λ ν ( x ̂ ) Ψ ( x ̂ , z ̂ ) = 0 .
Ψ ( x ̂ , z ̂ ) = Φ ( x ̂ , z ̂ ) exp { i πn 0 λ ( 2 x ˙ 0 ( z ̂ ) x ̂ ( z ̂ ) + 0 z ̂ x ˙ 0 2 ( ξ ) ) } ,
i Φ ( x ̂ , z ̂ ) z ̂ + λ 4 πn 0 2 Φ ( x ̂ , z ̂ ) x ̂ 2 + 2 π λ ν ( x ̂ ) Φ ( x ̂ , z ̂ ) = 2 πn 0 λ x ̈ 0 x ̂ Φ ( x ̂ , z ̂ ) .
i d φ n d z ̂ + c ( φ n + 1 + φ n 1 ) = ω x ̈ 0 n φ n
φ n = exp { i ( κ n ω x ˙ 0 ( z ̂ ) n ) } exp { i 2 c 0 z ̂ cos [ κ ω x ˙ 0 ( ξ ) ] }
c eff = c z 0 0 z 0 cos { ω x ˙ 0 ( ξ ) } .
x 0 ( z ) = A 0 ( cos { 2 πz z 0 } 1 )
J α ( x ) = 1 π 0 π cos { α τ x sin τ } d τ ,
c eff = c J 0 ( 2 π ω A 0 z 0 ) .
2 π ω A 0 z 0 = η ,

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