## Stripe-like quasi-nondiffracting optical lattices |

Optics Express, Vol. 19, Issue 10, pp. 9505-9511 (2011)

http://dx.doi.org/10.1364/OE.19.009505

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### 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

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 Jr, 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]

6. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. **21**(15), 2758–2769 (1982). [CrossRef] [PubMed]

7. 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]

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]

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]

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]

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]

*ξ*axis may be written in terms of the Whittaker integral:where

*φ*is the azimuthal angle in the frequency space,

7. 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]

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]

*E*is proportional to the external biasing field, the lattice shape is described by the function

*p*determines the lattice depth. Further we set

*b*is the propagation constant. Representative examples of solitons supported by lattices consisting of two intersecting stripe-like beams are shown in Fig. 2(a) . The shapes of the solitons are strongly affected by the details of the interference pattern in the crossing region. In a single-stripe lattice [like the one shown in Fig. 1(a), left] that does not feature any refractive index modulation in the horizontal direction, low intensity solitons are strongly elongated along such direction (note that this is due to the fact that single-stripe lattices does not support any localized linear modes and this is in contrast to solitons in parabolic lattices addressed in [18

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]

*U*[see Eq. (3) for definition] is a monotonically increasing function of the propagation constant [Fig. 3(a) ], while the integral soliton width

*W*, defined asdiverges in the high-intensity limit and approaches a constant value for low-intensity solitons [Fig. 3(b)]. Solitons in such lattices exist between the lower

*p*[Fig. 3(c)]. Both fundamental and multipole solitons are stable inside most of their existence domain.

## References and links

1. | M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, ““Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. |

2. | J. Durnin, J. J. Miceli Jr, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. |

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. |

4. | C. López-Mariscal, M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Observation of parabolic nondiffracting optical fields,” Opt. Express |

5. | S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. |

6. | J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. |

7. | 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. |

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 |

9. | D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. |

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. |

11. | F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. |

12. | Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. |

13. | Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett. |

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. |

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 |

16. | Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Shaping soliton properties in Mathieu lattices,” Opt. Lett. |

17. | F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A |

18. | Y. V. Kartashov, V. V. Vysloukh, and L. Torner, “Highly asymmetric soliton complexes in parabolic optical lattices,” Opt. Lett. |

**OCIS Codes**

(260.1960) Physical optics : Diffraction theory

(190.6135) Nonlinear optics : Spatial solitons

**ToC Category:**

Physical Optics

**History**

Original Manuscript: April 4, 2011

Revised Manuscript: April 27, 2011

Manuscript Accepted: April 27, 2011

Published: April 29, 2011

**Citation**

Yaroslav V. Kartashov, Servando López-Aguayo, Victor A. Vysloukh, and Lluis Torner, "Stripe-like quasi-nondiffracting optical lattices," Opt. Express **19**, 9505-9511 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9505

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### References

- 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]
- J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987). [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]
- 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]
- 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. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982). [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]
- D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28(9), 710–712 (2003). [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]
- 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. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009). [CrossRef]
- 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]
- 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). [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]
- F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A 79(5), 053852 (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]

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