Abstract

The observation of a two-dimensional discrete soliton in a cubic 5×5 fs laser written waveguide array in fused silica is reported for the first time. In addition to the localization the sharp edges of the array allow to study the influence of the array’s boundaries. The results are in excellent agreement with theoretical predictions and provide the basis for a variety of future applications for nonlinear two-dimensional integrated optical devices.

© 2006 Optical Society of America

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  1. D. Christodoulides and R. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988).
    [CrossRef] [PubMed]
  2. 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]
  3. J. Meier, G. Stegeman, D. Christodoulides, R. Morandotti, M. Sorel, H. Yang, G. Salamo, J. Aitchison, and Y. Silberberg, "Nonlinear beam interactions in 1D discrete Kerr systems," Opt. Exp. 13, 1797-1807 (2005).
    [CrossRef]
  4. R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 1139021-4 (2004).
    [CrossRef]
  5. A. Fratalocchi, G. Assanto, K. Brzdakiewicz, and M. Karpierz, "Discrete propagation and spatial solitons in nematic liquid crystals," Opt. Lett. 29, 1530-1532 (2004).
    [CrossRef] [PubMed]
  6. N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete Solitons in photorefractive optically induced nonlinear photonic lattices," Phys. Rev. E 66, 04660211-5 (2002).
    [CrossRef]
  7. D. Christodoulides and E. Eugenieva, "Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays," Phys. Rev. Lett. 87, 2339011-4 (2001).
    [CrossRef]
  8. E. Eugenieva, N. Efremidis, and D. Christodoulides, "Design of switching junctions for two-dimensional discrete soliton networks," Opt. Lett. 26, 1978-1980 (2001).
    [CrossRef]
  9. J. Fleischer, M. Segev, N. Efremidis, and D. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
    [CrossRef] [PubMed]
  10. J. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Exp. 13, 1780-1796 (2005).
    [CrossRef]
  11. T. Pertsch, U. Peschel, S. Nolte, A. Tuennermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, "Nonlinearity and disorder in two-dimensional fiber arrays," Phys. Rev. Lett. 39, 468-470 (2004).
  12. S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A. 77, 109-111 (2003).
    [CrossRef]
  13. W. Watanabe, T. Asano, K. Yamada, and K. Itoh, "Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses," Opt. Lett. 28, 2491-2493 (2003).
    [CrossRef] [PubMed]
  14. K. Davies, K. Miura, N. Sugimoto, and K. Hirao, "Writing waveguides in glass with a fs-laser," Opt. Lett. 21, 1729-1731 (1996).
    [CrossRef]
  15. D. Bloemer, A. Szameit, F. Dreisow, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, F. Lederer, and A. Tuennermann, "Measurement of the nonlinear refractive index of fs-laser-written waveguides in fused silica," Opt. Exp. 14, 2151-2157 (2006).
    [CrossRef]
  16. T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tuennermann, "Discrete diffraction in two-dimensional arrays of coupled waveguides in silica," Opt. Lett. 29, 468-470 (2004).
    [CrossRef] [PubMed]
  17. A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, F. Lederer, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
    [CrossRef]
  18. A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Discrete Nonlinear Localization in Femtosecond Laser Written Waveguides in Fused Silica," Opt. Exp. 13, 10552-10557 (2005).
    [CrossRef]
  19. I. Mansour and F. Caccavale, "An improved procedure to calculate the refractive index profile from the measured near-field intensity," J. Lightwave Technol. 14, 423-428 (1996).
    [CrossRef]
  20. M. Ams, G. Marshall, D. Spence, and M. Withford, "Slit-beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses," Opt. Express 13, 5676-5681 (2005).
    [CrossRef] [PubMed]

2006 (2)

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

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

2005 (4)

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Discrete Nonlinear Localization in Femtosecond Laser Written Waveguides in Fused Silica," Opt. Exp. 13, 10552-10557 (2005).
[CrossRef]

J. Meier, G. Stegeman, D. Christodoulides, R. Morandotti, M. Sorel, H. Yang, G. Salamo, J. Aitchison, and Y. Silberberg, "Nonlinear beam interactions in 1D discrete Kerr systems," Opt. Exp. 13, 1797-1807 (2005).
[CrossRef]

J. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Exp. 13, 1780-1796 (2005).
[CrossRef]

M. Ams, G. Marshall, D. Spence, and M. Withford, "Slit-beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses," Opt. Express 13, 5676-5681 (2005).
[CrossRef] [PubMed]

2004 (4)

T. Pertsch, U. Peschel, S. Nolte, A. Tuennermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, "Nonlinearity and disorder in two-dimensional fiber arrays," Phys. Rev. Lett. 39, 468-470 (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, 1139021-4 (2004).
[CrossRef]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tuennermann, "Discrete diffraction in two-dimensional arrays of coupled waveguides in silica," Opt. Lett. 29, 468-470 (2004).
[CrossRef] [PubMed]

A. Fratalocchi, G. Assanto, K. Brzdakiewicz, and M. Karpierz, "Discrete propagation and spatial solitons in nematic liquid crystals," Opt. Lett. 29, 1530-1532 (2004).
[CrossRef] [PubMed]

2003 (3)

W. Watanabe, T. Asano, K. Yamada, and K. Itoh, "Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses," Opt. Lett. 28, 2491-2493 (2003).
[CrossRef] [PubMed]

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

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A. 77, 109-111 (2003).
[CrossRef]

2002 (1)

N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete Solitons in photorefractive optically induced nonlinear photonic lattices," Phys. Rev. E 66, 04660211-5 (2002).
[CrossRef]

2001 (2)

D. Christodoulides and E. Eugenieva, "Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays," Phys. Rev. Lett. 87, 2339011-4 (2001).
[CrossRef]

E. Eugenieva, N. Efremidis, and D. Christodoulides, "Design of switching junctions for two-dimensional discrete soliton networks," Opt. Lett. 26, 1978-1980 (2001).
[CrossRef]

1998 (1)

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]

1996 (2)

K. Davies, K. Miura, N. Sugimoto, and K. Hirao, "Writing waveguides in glass with a fs-laser," Opt. Lett. 21, 1729-1731 (1996).
[CrossRef]

I. Mansour and F. Caccavale, "An improved procedure to calculate the refractive index profile from the measured near-field intensity," J. Lightwave Technol. 14, 423-428 (1996).
[CrossRef]

1988 (1)

Aitchison, J.

J. Meier, G. Stegeman, D. Christodoulides, R. Morandotti, M. Sorel, H. Yang, G. Salamo, J. Aitchison, and Y. Silberberg, "Nonlinear beam interactions in 1D discrete Kerr systems," Opt. Exp. 13, 1797-1807 (2005).
[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]

Ams, M.

Asano, T.

Assanto, G.

Bartal, G.

J. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Exp. 13, 1780-1796 (2005).
[CrossRef]

Bartelt, H.

T. Pertsch, U. Peschel, S. Nolte, A. Tuennermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, "Nonlinearity and disorder in two-dimensional fiber arrays," Phys. Rev. Lett. 39, 468-470 (2004).

Bloemer, D.

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

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

Brzdakiewicz, K.

Buljan, H.

J. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Exp. 13, 1780-1796 (2005).
[CrossRef]

Burghoff, J.

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

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

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Discrete Nonlinear Localization in Femtosecond Laser Written Waveguides in Fused Silica," Opt. Exp. 13, 10552-10557 (2005).
[CrossRef]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tuennermann, "Discrete diffraction in two-dimensional arrays of coupled waveguides in silica," Opt. Lett. 29, 468-470 (2004).
[CrossRef] [PubMed]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A. 77, 109-111 (2003).
[CrossRef]

Caccavale, F.

I. Mansour and F. Caccavale, "An improved procedure to calculate the refractive index profile from the measured near-field intensity," J. Lightwave Technol. 14, 423-428 (1996).
[CrossRef]

Christodoulides, D.

J. Meier, G. Stegeman, D. Christodoulides, R. Morandotti, M. Sorel, H. Yang, G. Salamo, J. Aitchison, and Y. Silberberg, "Nonlinear beam interactions in 1D discrete Kerr systems," Opt. Exp. 13, 1797-1807 (2005).
[CrossRef]

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

N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete Solitons in photorefractive optically induced nonlinear photonic lattices," Phys. Rev. E 66, 04660211-5 (2002).
[CrossRef]

D. Christodoulides and E. Eugenieva, "Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays," Phys. Rev. Lett. 87, 2339011-4 (2001).
[CrossRef]

E. Eugenieva, N. Efremidis, and D. Christodoulides, "Design of switching junctions for two-dimensional discrete soliton networks," Opt. Lett. 26, 1978-1980 (2001).
[CrossRef]

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

Cohen, O.

J. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Exp. 13, 1780-1796 (2005).
[CrossRef]

Davies, K.

Dreisow, F.

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

Efremidis, N.

J. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Exp. 13, 1780-1796 (2005).
[CrossRef]

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

N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete Solitons in photorefractive optically induced nonlinear photonic lattices," Phys. Rev. E 66, 04660211-5 (2002).
[CrossRef]

E. Eugenieva, N. Efremidis, and D. Christodoulides, "Design of switching junctions for two-dimensional discrete soliton networks," Opt. Lett. 26, 1978-1980 (2001).
[CrossRef]

Eisenberg, H.

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]

Eugenieva, E.

D. Christodoulides and E. Eugenieva, "Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays," Phys. Rev. Lett. 87, 2339011-4 (2001).
[CrossRef]

E. Eugenieva, N. Efremidis, and D. Christodoulides, "Design of switching junctions for two-dimensional discrete soliton networks," Opt. Lett. 26, 1978-1980 (2001).
[CrossRef]

Fleischer, J.

J. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Exp. 13, 1780-1796 (2005).
[CrossRef]

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

N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete Solitons in photorefractive optically induced nonlinear photonic lattices," Phys. Rev. E 66, 04660211-5 (2002).
[CrossRef]

Fratalocchi, A.

Freedman, B.

J. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Exp. 13, 1780-1796 (2005).
[CrossRef]

Hirao, K.

Itoh, K.

Iwanow, 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, 1139021-4 (2004).
[CrossRef]

Joseph, R.

Karpierz, M.

Kobelke, J.

T. Pertsch, U. Peschel, S. Nolte, A. Tuennermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, "Nonlinearity and disorder in two-dimensional fiber arrays," Phys. Rev. Lett. 39, 468-470 (2004).

Lederer, F.

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

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, F. Lederer, 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, "Discrete Nonlinear Localization in Femtosecond Laser Written Waveguides in Fused Silica," Opt. Exp. 13, 10552-10557 (2005).
[CrossRef]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tuennermann, "Discrete diffraction in two-dimensional arrays of coupled waveguides in silica," Opt. Lett. 29, 468-470 (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, 1139021-4 (2004).
[CrossRef]

T. Pertsch, U. Peschel, S. Nolte, A. Tuennermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, "Nonlinearity and disorder in two-dimensional fiber arrays," Phys. Rev. Lett. 39, 468-470 (2004).

Manela, O.

J. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Exp. 13, 1780-1796 (2005).
[CrossRef]

Mansour, I.

I. Mansour and F. Caccavale, "An improved procedure to calculate the refractive index profile from the measured near-field intensity," J. Lightwave Technol. 14, 423-428 (1996).
[CrossRef]

Marshall, G.

Meier, J.

J. Meier, G. Stegeman, D. Christodoulides, R. Morandotti, M. Sorel, H. Yang, G. Salamo, J. Aitchison, and Y. Silberberg, "Nonlinear beam interactions in 1D discrete Kerr systems," Opt. Exp. 13, 1797-1807 (2005).
[CrossRef]

Min, Y.

R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 1139021-4 (2004).
[CrossRef]

Miura, K.

Morandotti, R.

J. Meier, G. Stegeman, D. Christodoulides, R. Morandotti, M. Sorel, H. Yang, G. Salamo, J. Aitchison, and Y. Silberberg, "Nonlinear beam interactions in 1D discrete Kerr systems," Opt. Exp. 13, 1797-1807 (2005).
[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]

Nolte, S.

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

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

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Discrete Nonlinear Localization in Femtosecond Laser Written Waveguides in Fused Silica," Opt. Exp. 13, 10552-10557 (2005).
[CrossRef]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tuennermann, "Discrete diffraction in two-dimensional arrays of coupled waveguides in silica," Opt. Lett. 29, 468-470 (2004).
[CrossRef] [PubMed]

T. Pertsch, U. Peschel, S. Nolte, A. Tuennermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, "Nonlinearity and disorder in two-dimensional fiber arrays," Phys. Rev. Lett. 39, 468-470 (2004).

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A. 77, 109-111 (2003).
[CrossRef]

Pertsch, T.

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

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, F. Lederer, 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, "Discrete Nonlinear Localization in Femtosecond Laser Written Waveguides in Fused Silica," Opt. Exp. 13, 10552-10557 (2005).
[CrossRef]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tuennermann, "Discrete diffraction in two-dimensional arrays of coupled waveguides in silica," Opt. Lett. 29, 468-470 (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, 1139021-4 (2004).
[CrossRef]

T. Pertsch, U. Peschel, S. Nolte, A. Tuennermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, "Nonlinearity and disorder in two-dimensional fiber arrays," Phys. Rev. Lett. 39, 468-470 (2004).

Peschel, U.

T. Pertsch, U. Peschel, S. Nolte, A. Tuennermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, "Nonlinearity and disorder in two-dimensional fiber arrays," Phys. Rev. Lett. 39, 468-470 (2004).

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tuennermann, "Discrete diffraction in two-dimensional arrays of coupled waveguides in silica," Opt. Lett. 29, 468-470 (2004).
[CrossRef] [PubMed]

Salamo, G.

J. Meier, G. Stegeman, D. Christodoulides, R. Morandotti, M. Sorel, H. Yang, G. Salamo, J. Aitchison, and Y. Silberberg, "Nonlinear beam interactions in 1D discrete Kerr systems," Opt. Exp. 13, 1797-1807 (2005).
[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, 1139021-4 (2004).
[CrossRef]

Schreiber, T.

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

Schuster, K.

T. Pertsch, U. Peschel, S. Nolte, A. Tuennermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, "Nonlinearity and disorder in two-dimensional fiber arrays," Phys. Rev. Lett. 39, 468-470 (2004).

Schwartz, T.

J. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Exp. 13, 1780-1796 (2005).
[CrossRef]

Sears, S.

N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete Solitons in photorefractive optically induced nonlinear photonic lattices," Phys. Rev. E 66, 04660211-5 (2002).
[CrossRef]

Segev, M.

J. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Exp. 13, 1780-1796 (2005).
[CrossRef]

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

N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete Solitons in photorefractive optically induced nonlinear photonic lattices," Phys. Rev. E 66, 04660211-5 (2002).
[CrossRef]

Silberberg, Y.

J. Meier, G. Stegeman, D. Christodoulides, R. Morandotti, M. Sorel, H. Yang, G. Salamo, J. Aitchison, and Y. Silberberg, "Nonlinear beam interactions in 1D discrete Kerr systems," Opt. Exp. 13, 1797-1807 (2005).
[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]

Sohler, W.

R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 1139021-4 (2004).
[CrossRef]

Sorel, M.

J. Meier, G. Stegeman, D. Christodoulides, R. Morandotti, M. Sorel, H. Yang, G. Salamo, J. Aitchison, and Y. Silberberg, "Nonlinear beam interactions in 1D discrete Kerr systems," Opt. Exp. 13, 1797-1807 (2005).
[CrossRef]

Spence, D.

Stegeman, G.

J. Meier, G. Stegeman, D. Christodoulides, R. Morandotti, M. Sorel, H. Yang, G. Salamo, J. Aitchison, and Y. Silberberg, "Nonlinear beam interactions in 1D discrete Kerr systems," Opt. Exp. 13, 1797-1807 (2005).
[CrossRef]

R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 1139021-4 (2004).
[CrossRef]

Sugimoto, N.

Szameit, A.

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

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, F. Lederer, 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, "Discrete Nonlinear Localization in Femtosecond Laser Written Waveguides in Fused Silica," Opt. Exp. 13, 10552-10557 (2005).
[CrossRef]

Tuennermann, A.

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

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

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Discrete Nonlinear Localization in Femtosecond Laser Written Waveguides in Fused Silica," Opt. Exp. 13, 10552-10557 (2005).
[CrossRef]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tuennermann, "Discrete diffraction in two-dimensional arrays of coupled waveguides in silica," Opt. Lett. 29, 468-470 (2004).
[CrossRef] [PubMed]

T. Pertsch, U. Peschel, S. Nolte, A. Tuennermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, "Nonlinearity and disorder in two-dimensional fiber arrays," Phys. Rev. Lett. 39, 468-470 (2004).

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A. 77, 109-111 (2003).
[CrossRef]

Watanabe, W.

Will, M.

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tuennermann, "Discrete diffraction in two-dimensional arrays of coupled waveguides in silica," Opt. Lett. 29, 468-470 (2004).
[CrossRef] [PubMed]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A. 77, 109-111 (2003).
[CrossRef]

Withford, M.

Yamada, K.

Yang, H.

J. Meier, G. Stegeman, D. Christodoulides, R. Morandotti, M. Sorel, H. Yang, G. Salamo, J. Aitchison, and Y. Silberberg, "Nonlinear beam interactions in 1D discrete Kerr systems," Opt. Exp. 13, 1797-1807 (2005).
[CrossRef]

Appl. Phys. A. (1)

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A. 77, 109-111 (2003).
[CrossRef]

Appl. Phys. B. (1)

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

J. Lightwave Technol. (1)

I. Mansour and F. Caccavale, "An improved procedure to calculate the refractive index profile from the measured near-field intensity," J. Lightwave Technol. 14, 423-428 (1996).
[CrossRef]

Nature (1)

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

Opt. Exp. (4)

J. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Exp. 13, 1780-1796 (2005).
[CrossRef]

J. Meier, G. Stegeman, D. Christodoulides, R. Morandotti, M. Sorel, H. Yang, G. Salamo, J. Aitchison, and Y. Silberberg, "Nonlinear beam interactions in 1D discrete Kerr systems," Opt. Exp. 13, 1797-1807 (2005).
[CrossRef]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, and F. Lederer, "Discrete Nonlinear Localization in Femtosecond Laser Written Waveguides in Fused Silica," Opt. Exp. 13, 10552-10557 (2005).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. E (1)

N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete Solitons in photorefractive optically induced nonlinear photonic lattices," Phys. Rev. E 66, 04660211-5 (2002).
[CrossRef]

Phys. Rev. Lett. (4)

D. Christodoulides and E. Eugenieva, "Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays," Phys. Rev. Lett. 87, 2339011-4 (2001).
[CrossRef]

R. Iwanow, R. Schieck, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons," Phys. Rev. Lett. 93, 1139021-4 (2004).
[CrossRef]

T. Pertsch, U. Peschel, S. Nolte, A. Tuennermann, F. Lederer, J. Kobelke, K. Schuster, and H. Bartelt, "Nonlinearity and disorder in two-dimensional fiber arrays," Phys. Rev. Lett. 39, 468-470 (2004).

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]

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Figures (5)

Fig. 1.
Fig. 1.

Scheme of the writing process in a transparent bulk material by use of fs laser pulses. Inset: Microscope image of a cubic array (end view) with a waveguide separation of 40 µm.

Fig. 2.
Fig. 2.

(a) Measured mode profile at λ=800 nm and (b) corresponding refractive index profile.

Fig. 3.
Fig. 3.

Setup for the investigation of nonlinear propagation effects in the waveguide array.

Fig. 4.
Fig. 4.

Measured (a) and theoretical (b) intensity distributions at the exit of the array due to discrete diffraction in the linear case at low input peak power (Ppeak =40kW) with strong influence of the array’s boundaries. In comparison the theoretical output pattern without boundary effects (c) and isotropic coupling and boundary effects (d). The red circle marks the excited waveguide.

Fig. 5.
Fig. 5.

Comparison of measured and theoretical array output intensity patterns as a function of the input peak power. The red circle marks the excited waveguide.

Equations (9)

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

n 2 ( x , y ) = n eff 2 λ 2 4 π 2 Δ A ( x , y ) A ( x , y ) ,
i d dz E m , n = β E m , n + c h ( E m + 1 , n + E m 1 , n ) +
c ν ( E m , n + 1 + E m , n 1 ) + κ E m , n 2 E m , n ,
κ = ω ν A eff n 2
E m , n = 1 κ a m , n e i β z ,
i d dz a m , n = c h ( a m + 1 , n + a m 1 , n ) +
c ν ( a m , n + 1 + a m , n 1 ) + a m , n 2 a m , n .
a m , n 2 a m , n c h ( a m + 1 , n + a m 1 , n ) + c ν ( a m , n + 1 + a m , n 1 ) 1
c h = 10.33 m 1 , c ν = 14.76 m 1 .

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