Abstract

We introduce stripe-like quasi-nondiffracting lattices that can be generated via spatial spectrum engineering. The complexity of the spatial shapes of such lattices and the distance of their almost diffractionless propagation depend on the width of their ring-like spatial spectrum. Stripe-like lattices are extended in one direction and are localized in the orthogonal one, thereby creating either straight or curved in any desired fashion optically-induced channels that may be used for optical trapping, optical manipulation, or optical lattices for quantum and nonlinear optics applications. As an illustrative example, here we show their potential for spatial soliton control. Complex networks consisting of several intersecting or joining stripe-like lattices suited to a particular application may also be constructed.

© 2011 OSA

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  1. M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, ““Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
    [CrossRef]
  2. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
    [CrossRef] [PubMed]
  3. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195(1–4), 35–40 (2001).
    [CrossRef]
  4. C. López-Mariscal, M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Observation of parabolic nondiffracting optical fields,” Opt. Express 13(7), 2364–2369 (2005).
    [CrossRef] [PubMed]
  5. S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. 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]
  9. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28(9), 710–712 (2003).
    [CrossRef] [PubMed]
  10. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92(12), 123902 (2004).
    [CrossRef] [PubMed]
  11. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
    [CrossRef]
  12. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009).
    [CrossRef]
  13. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
    [CrossRef] [PubMed]
  14. X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96(8), 083904 (2006).
    [CrossRef] [PubMed]
  15. R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Observation of light localization in modulated Bessel optical lattices,” Opt. Express 14(7), 2825–2830 (2006).
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    [CrossRef] [PubMed]
  17. F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A 79(5), 053852 (2009).
    [CrossRef]
  18. Y. V. Kartashov, V. V. Vysloukh, and L. Torner, “Highly asymmetric soliton complexes in parabolic optical lattices,” Opt. Lett. 33(2), 141–143 (2008).
    [CrossRef] [PubMed]

2010 (2)

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, ““Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[CrossRef]

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
[CrossRef] [PubMed]

2009 (2)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009).
[CrossRef]

F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A 79(5), 053852 (2009).
[CrossRef]

2008 (2)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[CrossRef]

Y. V. Kartashov, V. V. Vysloukh, and L. Torner, “Highly asymmetric soliton complexes in parabolic optical lattices,” Opt. Lett. 33(2), 141–143 (2008).
[CrossRef] [PubMed]

2006 (3)

2005 (1)

2004 (2)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92(12), 123902 (2004).
[CrossRef] [PubMed]

2003 (3)

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (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. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28(9), 710–712 (2003).
[CrossRef] [PubMed]

2001 (1)

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195(1–4), 35–40 (2001).
[CrossRef]

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

1982 (1)

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[CrossRef]

Bandres, M. A.

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (2003).
[CrossRef] [PubMed]

Chavez-Cerda, S.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195(1–4), 35–40 (2001).
[CrossRef]

Chávez-Cerda, S.

Chen, Z.

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96(8), 083904 (2006).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92(12), 123902 (2004).
[CrossRef] [PubMed]

Christodoulides, D. N.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[CrossRef]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92(12), 123902 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (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]

Desyatnikov, A. S.

Dholakia, K.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, ““Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

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]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (2003).
[CrossRef] [PubMed]

Egorov, A. A.

Eugenieva, E. D.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92(12), 123902 (2004).
[CrossRef] [PubMed]

Fienup, J. R.

Fischer, R.

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]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (2003).
[CrossRef] [PubMed]

Gunn-Moore, F.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, ““Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[CrossRef]

Gutiérrez-Vega, J. C.

C. López-Mariscal, M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Observation of parabolic nondiffracting optical fields,” Opt. Express 13(7), 2364–2369 (2005).
[CrossRef] [PubMed]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195(1–4), 35–40 (2001).
[CrossRef]

Hu, B.

F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A 79(5), 053852 (2009).
[CrossRef]

Iturbe-Castillo, M. D.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195(1–4), 35–40 (2001).
[CrossRef]

Kartashov, Y. V.

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009).
[CrossRef]

Y. V. Kartashov, V. V. Vysloukh, and L. Torner, “Highly asymmetric soliton complexes in parabolic optical lattices,” Opt. Lett. 33(2), 141–143 (2008).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Shaping soliton properties in Mathieu lattices,” Opt. Lett. 31(2), 238–240 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
[CrossRef] [PubMed]

Kevrekidis, P. G.

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96(8), 083904 (2006).
[CrossRef] [PubMed]

Kivshar, Y.

Kivshar, Y. S.

Krolikowski, W.

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[CrossRef]

Lopez-Aguayo, S.

López-Aguayo, S.

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
[CrossRef] [PubMed]

López-Mariscal, C.

Martin, H.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92(12), 123902 (2004).
[CrossRef] [PubMed]

Mazilu, M.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, ““Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Mihalache, D.

F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A 79(5), 053852 (2009).
[CrossRef]

Neshev, D.

Neshev, D. N.

New, G. H. C.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195(1–4), 35–40 (2001).
[CrossRef]

Ostrovskaya, E.

Ramirez, G. A.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195(1–4), 35–40 (2001).
[CrossRef]

Rodriguez-Dagnino, R. M.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195(1–4), 35–40 (2001).
[CrossRef]

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[CrossRef]

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

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (2003).
[CrossRef] [PubMed]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[CrossRef]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[CrossRef]

Stevenson, D. J.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, ““Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[CrossRef]

Sukhorukov, A. A.

Tepichin, E.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195(1–4), 35–40 (2001).
[CrossRef]

Torner, L.

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009).
[CrossRef]

Y. V. Kartashov, V. V. Vysloukh, and L. Torner, “Highly asymmetric soliton complexes in parabolic optical lattices,” Opt. Lett. 33(2), 141–143 (2008).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Shaping soliton properties in Mathieu lattices,” Opt. Lett. 31(2), 238–240 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
[CrossRef] [PubMed]

Vysloukh, V. A.

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009).
[CrossRef]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Shaping soliton properties in Mathieu lattices,” Opt. Lett. 31(2), 238–240 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
[CrossRef] [PubMed]

Vysloukh, V. V.

Wang, X.

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96(8), 083904 (2006).
[CrossRef] [PubMed]

Ye, F.

F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A 79(5), 053852 (2009).
[CrossRef]

Appl. Opt. (1)

Laser Photonics Rev. (1)

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, ““Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[CrossRef]

Nature (1)

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]

Opt. Commun. (1)

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195(1–4), 35–40 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[CrossRef]

Phys. Rev. A (1)

F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A 79(5), 053852 (2009).
[CrossRef]

Phys. Rev. Lett. (6)

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92(12), 123902 (2004).
[CrossRef] [PubMed]

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (2003).
[CrossRef] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
[CrossRef] [PubMed]

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96(8), 083904 (2006).
[CrossRef] [PubMed]

Prog. Opt. (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Field modulus distributions and (b) spatial spectra for star-like quasi-nondiffracting beams with two, three, and four branches, respectively. Row (c) shows quasi-nondiffracting beams with gradually increasing amplitudes of vertical stripes and complex beam produced by the intersection of two vertical and two horizontal stripes. In all cases δ = 0.1 .

Fig. 2
Fig. 2

(a) Left and middle panels show fundamental solitons with U = 1 supported by star-like lattices where relative amplitudes of vertical stripes are 1.0 and 0.3 , respectively. Right panel shows field modulus distribution in tripole soliton with U = 27 in star-like lattice where relative amplitude of vertical stripe is 1.0 . All solitons in (a) are obtained at p = 4 . Row (b) illustrates a variety of routing scenarios available in star-like lattices. The initial velocities of out-of-phase solitons “ s 1 ”, “ s 2 ” are α 1 = 1.5 , α 2 = 1.5 (left), α 1 = 2.2 , α 2 = 2.2 (middle), and α 1 = 1.8 , α 2 = 2.0 (right). The input solitons correspond to U = 1.5 and p = 0.2 . (c) Snapshot images showing propagation of solitons at α = 1.6 , b = 4 , p = 0.5 in bent lattices where guiding channels are periodically curved or follow cubic parabola or tanh curves. Arrows in (b) and (c) show the direction of soliton motion.

Fig. 3
Fig. 3

Energy flow U (a) and width W (b) of fundamental soliton supported by the lattice with four branches versus propagation constant b. The point marked by circle corresponds to soliton in Fig. 2(a), left panel. (c) Upper and lower cutoffs versus lattice depth.

Fig. 4
Fig. 4

Field modulus distributions (top) and spatial spectra (bottom) in stripe-like quasi-nondiffracting beams that bent periodically (a), follow the shape of cubic parabola (b) or hyperbolic tangent (c) functions. The spectrum width is δ = 0.1 in all cases.

Equations (3)

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q nd ( η , ζ , ξ ) = exp ( i k t 2 ξ / 2 ) 0 2 π G ( φ ) exp [ i k t ( η cos φ + ζ sin φ ) ] d φ ,
i q ξ = 1 2 ( 2 q η 2 + 2 q ζ 2 ) E q | q | 2 + p R 1 + | q | 2 + p R ,
W = 2 U 1 ( η 2 + ζ 2 ) 1 / 2 | q | 2 d η d ζ , U = | q | 2 d η d ζ ,

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