Abstract

We experimentally observe the formation of spatial dark gap solitons in higher bands in one-dimensional waveguide arrays possessing a saturable defocusing nonlinearity. By using the prism-coupler scheme, pure Floquet-Bloch modes of higher bands are excited and dark gap solitons are formed due to the counteraction of normal diffraction and the defocusing nature of the photovoltaic nonlinearity. The modulation of refractive index induced by the soliton formation is demonstrated by the guidance of a low-power probe beam in the waveguide array sample. Additionally, the phase structure of dark solitons formed in the second band is discussed.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. E. Bjorkholm and A. A. Ashkin, “CW self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32(4), 129–132 (1974).
    [CrossRef]
  2. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992).
    [CrossRef] [PubMed]
  3. G. Assanto and G. I. Stegeman, “Simple physics of quadratic spatial solitons,” Opt. Express 10(9), 388–396 (2002).
    [PubMed]
  4. A. S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Lett. 21(1), 24–26 (1996).
    [CrossRef] [PubMed]
  5. O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78(1), 179–215 (2006).
    [CrossRef]
  6. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
    [CrossRef] [PubMed]
  7. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
    [CrossRef] [PubMed]
  8. H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
    [CrossRef]
  9. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
    [CrossRef] [PubMed]
  10. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90(25), 253902 (2003).
    [CrossRef] [PubMed]
  11. F. Chen, M. Stepić, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13(11), 4314–4324 (2005).
    [CrossRef] [PubMed]
  12. D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92(9), 093904 (2004).
    [CrossRef] [PubMed]
  13. Y. Zhang, Z. Liang, and B. Wu, “Gap solitons and Bloch waves in nonlinear periodic systems,” Phys. Rev. A 80(6), 063815 (2009).
    [CrossRef]
  14. M. Matuszewski, C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, A. Mitchell, M. Trippenbach, M. W. Austin, W. Królikowski, and Y. S. Kivshar, “Crossover from self-defocusing to discrete trapping in nonlinear waveguide arrays,” Opt. Express 14(1), 254–259 (2006).
    [CrossRef] [PubMed]
  15. D. Kip, C. E. Rüter, R. Dong, Z. Wang, and J. Xu, “Higher-band gap soliton formation in defocusing photonic lattices,” Opt. Lett. 33(18), 2056–2058 (2008).
    [CrossRef] [PubMed]
  16. D. Kip, “Photorefractive waveguides in oxide crystals: fabrication, properties, and applications,” Appl. Phys. B 67(2), 131–150 (1998).
    [CrossRef]
  17. M. Stepić, C. Wirth, C. E. Rüter, and D. Kip, “Observation of modulational instability in discrete media with self-defocusing nonlinearity,” Opt. Lett. 31(2), 247–249 (2006).
    [CrossRef] [PubMed]
  18. C. E. Rüter, J. Wisniewski, and D. Kip, “Prism coupling method to excite and analyze Floquet-Bloch modes in linear and nonlinear waveguide arrays,” Opt. Lett. 31(18), 2768–2770 (2006).
    [CrossRef] [PubMed]
  19. E. Smirnov, C. E. Rüter, M. Stepić, D. Kip, and V. Shandarov, “Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(6), 065601 (2006).
    [CrossRef]

2009 (1)

Y. Zhang, Z. Liang, and B. Wu, “Gap solitons and Bloch waves in nonlinear periodic systems,” Phys. Rev. A 80(6), 063815 (2009).
[CrossRef]

2008 (1)

2006 (5)

2005 (1)

2004 (1)

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92(9), 093904 (2004).
[CrossRef] [PubMed]

2003 (3)

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90(25), 253902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[CrossRef] [PubMed]

1998 (2)

D. Kip, “Photorefractive waveguides in oxide crystals: fabrication, properties, and applications,” Appl. Phys. B 67(2), 131–150 (1998).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

1996 (1)

1992 (1)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992).
[CrossRef] [PubMed]

1974 (1)

J. E. Bjorkholm and A. A. Ashkin, “CW self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32(4), 129–132 (1974).
[CrossRef]

Aitchison, J. S.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92(9), 093904 (2004).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90(25), 253902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

Ashkin, A. A.

J. E. Bjorkholm and A. A. Ashkin, “CW self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32(4), 129–132 (1974).
[CrossRef]

Assanto, G.

Austin, M. W.

Bjorkholm, J. E.

J. E. Bjorkholm and A. A. Ashkin, “CW self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32(4), 129–132 (1974).
[CrossRef]

Boyd, R.

H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

Chen, F.

Christodoulides, D. N.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[CrossRef] [PubMed]

Crosignani, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992).
[CrossRef] [PubMed]

Dong, R.

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[CrossRef] [PubMed]

Eisenberg, H. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90(25), 253902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992).
[CrossRef] [PubMed]

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[CrossRef] [PubMed]

Kewitsch, A. S.

Kip, D.

Kivshar, Y. S.

Królikowski, W.

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[CrossRef] [PubMed]

Liang, Z.

Y. Zhang, Z. Liang, and B. Wu, “Gap solitons and Bloch waves in nonlinear periodic systems,” Phys. Rev. A 80(6), 063815 (2009).
[CrossRef]

Mandelik, D.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92(9), 093904 (2004).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90(25), 253902 (2003).
[CrossRef] [PubMed]

Manela, O.

Matuszewski, M.

Mitchell, A.

Morandotti, R.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92(9), 093904 (2004).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90(25), 253902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[CrossRef] [PubMed]

Morandotti, Y.

H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

Morsch, O.

O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78(1), 179–215 (2006).
[CrossRef]

Neshev, D. N.

Oberthaler, M.

O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78(1), 179–215 (2006).
[CrossRef]

Rosberg, C. R.

Runde, D.

Rüter, C. E.

Segev, M.

F. Chen, M. Stepić, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13(11), 4314–4324 (2005).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992).
[CrossRef] [PubMed]

Shandarov, V.

E. Smirnov, C. E. Rüter, M. Stepić, D. Kip, and V. Shandarov, “Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(6), 065601 (2006).
[CrossRef]

F. Chen, M. Stepić, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13(11), 4314–4324 (2005).
[CrossRef] [PubMed]

Silberberg, Y.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92(9), 093904 (2004).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90(25), 253902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

Smirnov, E.

E. Smirnov, C. E. Rüter, M. Stepić, D. Kip, and V. Shandarov, “Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(6), 065601 (2006).
[CrossRef]

Sorel, M.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[CrossRef] [PubMed]

Stegeman, G. I.

Stepic, M.

Sukhorukov, A. A.

Trippenbach, M.

Wang, Z.

Wirth, C.

Wisniewski, J.

Wu, B.

Y. Zhang, Z. Liang, and B. Wu, “Gap solitons and Bloch waves in nonlinear periodic systems,” Phys. Rev. A 80(6), 063815 (2009).
[CrossRef]

Xu, J.

Yariv, A.

A. S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Lett. 21(1), 24–26 (1996).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992).
[CrossRef] [PubMed]

Zhang, Y.

Y. Zhang, Z. Liang, and B. Wu, “Gap solitons and Bloch waves in nonlinear periodic systems,” Phys. Rev. A 80(6), 063815 (2009).
[CrossRef]

Appl. Phys. B (1)

D. Kip, “Photorefractive waveguides in oxide crystals: fabrication, properties, and applications,” Appl. Phys. B 67(2), 131–150 (1998).
[CrossRef]

Nature (2)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. A (1)

Y. Zhang, Z. Liang, and B. Wu, “Gap solitons and Bloch waves in nonlinear periodic systems,” Phys. Rev. A 80(6), 063815 (2009).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

E. Smirnov, C. E. Rüter, M. Stepić, D. Kip, and V. Shandarov, “Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(6), 065601 (2006).
[CrossRef]

Phys. Rev. Lett. (6)

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92(9), 093904 (2004).
[CrossRef] [PubMed]

J. E. Bjorkholm and A. A. Ashkin, “CW self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32(4), 129–132 (1974).
[CrossRef]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90(25), 253902 (2003).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78(1), 179–215 (2006).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Scheme of the experimental setup: HW, half-wave plate; P, polarizer; BE, beam expander; M’s, mirrors; BS’s, beam splitters; PM, phase mask; S, screen; L, lens; MO’s, microscopic objectives; CCD’s, CCD cameras; PD, photodiode; WA, waveguide array. Inset: layout of the phase mask.

Fig. 2
Fig. 2

Measured band structure of the waveguide array used here. The left panel shows the relation of the effective refractive index neff (relative to the substrate index nsub ) of the linear FB modes as a function of transverse wave vector kz . The right panel monitors a schematic drawing of the refractive index profile (a) and experimental images of the intensity profiles of FB modes in the first (b) and third band (d) at the center of the BZ, and in the second band (c) at the edge of the BZ.

Fig. 3
Fig. 3

Numerical simulation (bottom) and experimental observation of a dark gap soliton originating from the second band (middle row), and guiding of a weak probe beam (top row) under the conditions of linear (a) and nonlinear excitation (b), respectively.

Fig. 4
Fig. 4

Numerical simulation (bottom) and experimental observation of a dark soliton originating from the third band (middle row), and guiding of a weak probe beam (top row) under the conditions of linear (a) and nonlinear excitation (b), respectively.

Fig. 5
Fig. 5

Intensity and phase profile of a dark soliton formed in the second band. (a) Numerical simulation of the soliton’s amplitude (blue line) and refractive index profile of the WA (green line), (b) output intensity profile of the formed dark soliton, and (c) corresponding phase profile measured by interfering the output signal light with a plane wave. The horizontal dotted line in (c) demonstrates the symmetric phase profile (equal/symmetric phase of channels ± 1).

Equations (1)

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

                                           i E x + 1 2 k 2 E z 2 + k ( Δ n ( z ) + Δ n n l n s u b ) E = 0   .                                  (1)

Metrics