## Observation of composite gap solitons in optically induced nonlinear lattices in LiNbO_{3}:Fe crystal

Optics Express, Vol. 14, Issue 5, pp. 1924-1932 (2006)

http://dx.doi.org/10.1364/OE.14.001924

Acrobat PDF (511 KB)

### Abstract

We observe experimentally, the first time to our knowledge, two types of composite gap solitons in optically induced one-dimensional nonlinear lattice in LiNbO_{3} crystal. We observe the staggered bright composite gap soliton when a single Gauss probe beam is incident at Bragg angle as well as a dipole probe beam is incident at normal incidence. When a single Gauss beam is at normal incidence, the in-phase bright composite gap solitons are observed.

© 2006 Optical Society of America

## 1. Introduction

1. E. Yablonovich, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. **58**, 2059–2062 (1987). [CrossRef]

2. A. S. Davydov and N. I. Kislukha, “Solitary excitation in one-dimensional molecular chains,” Phys. Status Solodi B **59**, 465–470 (1973). [CrossRef]

3. W. P. Su, J. R. Schieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. **42**, 1968–1701 (1979). [CrossRef]

4. A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose-Einstein condensates,” Phys. Rev. Lett. **86**, 2353–2356 (2001). [CrossRef] [PubMed]

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

6. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E. **66**, 046602 (2002). [CrossRef]

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**, 023902 (2003). [CrossRef] [PubMed]

_{3}crystal were used to form the spatial gap solitons [8

8. F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO_{3} waveguide arrays,” Opt. Express **13**, 4314–4324 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-11-4314 [CrossRef] [PubMed]

9. Z. Chen and K. MaCarthy, “Spatial soliton pixels from partially incoherent light,” Opt. Lett. **27**, 2019–2021 (2002). [CrossRef]

10. J. Petter, J. Schröder, D. Träger, and C. Denz, “Optical control of arrays of photorefractive screening solitons,” Opt. Lett. **28**, 438440 (2003). [CrossRef] [PubMed]

11. A. S. Desyatnikov, E. A. Ostrovskaya, Y. S. Kivshar, and C. Denz, “Composite band-gap solitons in nonlinear optically induced lattice,” Phys. Rev. Lett. **91**, 153902 (2003). [CrossRef] [PubMed]

12. D. Neshev, Y. S. Kivshar, H. Martin, and Z. Chen, “Soliton stripes in two-dimensional nonlinear photonic lattices,” Opt. Lett. **29**, 486488 (2004). [CrossRef] [PubMed]

_{3}: Fe crystal. The lattice is created by interfering a pair of extraordinary-polarized coherent plane waves in the sample, which possess the self-defocusing nonlinearity arising from the bulk photovoltaic effect. The nonlinear refractive index change is given by

*r*is the electro-optic coefficient,

*E*is the space charge field,

_{sc}*E*is the amplitude of the photovoltaic field,

_{p}*I*is the light intensity, and

*I*is the dark irradiance. The maximum nonlinear index change optically induced by the photovotic nonlinearity can be very high (about 0.003[13

_{d}13. S. Orlov, A. Yariv, and M. Segev, “Nonlinear self-phase matching of optical second harmonic generation in lithium niobate,” Appl. Phys. Lett. **68**, 16101612 (1996). [CrossRef]

*n*is approximate to 10

^{-4}. With sufficiently high nonlinearity, the staggered composite gap solitons are observed when a single Gauss probe beam is incident at Bragg angle (k

_{x}=π/

*D*,

*D*is the lattice period) as well as a dipole probe beam is at normal incident. The in-phase composite gap solitons are observed when a single Gauss probe beam is launched into the lattice at normal incidence (k

_{x}=0), with sufficiently high nonlinearity.

## 2. Experimental setup and methods

*λ*=632.8 nm) is split into two parts called lattice-forming beams which interfere in the sample to create the waveguide arrays. The lattice-forming beams which have the same power of 0.8 mw are extraordinarily polarized and create a grating with period

*D*= 14

*μ*m. The intensity of each lattice-forming beams is 0.84 mW/mm

^{2}. Extraordinarily polarized beam from another He-Ne laser is also split into two parts: one of which is focused onto the input face of the sample by a spherical lens L

_{1}(f=3.5 cm) to act as the probe beam; the other is used to interfere with the signal output beam to reveal the relative phase of solitonic components. The power of the probe beam is 1μw and the light intensity ratio of lattice-forming beam to probe beam is 1.1/1. The light distributions at the input and output faces of crystal are imaged onto a CCD camera by the lens L

_{2}(12× magnification) , respectively. The LiNbO

_{3}:Fe crystal employed in the experiment is doped with iron of 0.05wt% concentration and its dimensions are 9×9.5×10 mm

^{3}(x×y×z).

## 3. Experimental results and discussion

### 3.1 A single Gauss beam be incident at Bragg angle

*α*=0.59°), the staggered composite gap solitons are observed. Figure 2 shows the forming process of an even symmetry composite gap soliton. At the input face of sample, the probe beam is centered between two adjacent intensity maxima of lattice-forming beams’ interfering pattern [Fig. 2(a)]. At the time t=0, the intensity profile of probe beam at output face of sample has roughly 11 channels’ width [Fig. 2(b)]. As illumination time increasing, the pattern begins to narrow: at t=90 minutes it shrinks to 6 channels’ width [Fig. 2(c)], at t=130 minutes it concentrates at two channels accompanied by two slightly excited neighbor channels [Fig. 2(d)]. The two intensity peaks of the formed gap soliton reside on the input two adjacent intensity maxima of lattice-forming beams’ interfering pattern. Figure 3 shows the forming process of an odd symmetry composite gap soliton when the probe beam is centered on the intensity maximum of lattice-forming beams’ interfering pattern. At t=150 minutes, the odd symmetry composite gap soliton forms whose intensity peak resides on the input intensity maximum of the lattice-forming beams’ interfering pattern [Fig. 3(d)]. The patterns of lattice after the formation of the composite gap solitons are shown in Fig. 2(e) and Fig. 3(e).

_{3}: Fe crystal develops rather slowly, there is no nonlinearity caused by the probe beam at the time t=0. So Fig. 2(b) and Fig. 3(b) display the discrete diffraction, which is resulted from coupling between adjacent channels and multiple interference effects, fundamentally different from the linear diffraction in homogeneous media. The existence of gap solitons is closely linked to the structure of the linear wave spectrum. In linear regime, the wave propagating in a waveguide array is subjected to a periodic potential, so the dispersion relation (propagating constant

*β*to Bloch wave number

*K*) is divided into transmission bands, separated by gaps in which propagating mode is forbidden. In our experiment, the optically induced lattice (Δ

*n*≈ 10

^{-4}) belongs to the low index-step lattice, so the first band is primarily excited by the probe beam [14

14. D. Mandelik, H. S. Eeisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. **90**, 053902 (2003). [CrossRef] [PubMed]

### 3.2 A dipole probe beam be incident at normal incidence

*π*. The dipole probe beam is launched into the lattice at normal incidence with its two bright parts aligned at two adjacent intensity minima of lattice-forming beams’ interfering pattern at the input face of sample [Fig. 5(a)]. At the time t=0, the intensity profile of probe beam at the output face of sample has roughly 10 waveguide channels’ width [Fig. 5(b)]. As illumination time increasing, the pattern begins to narrow: At t=40 minutes, it has 8 waveguide channels’ width [Fig. 5(c)]; at t=90 minutes, it shrinks to 6 waveguide channels’ width [Fig. 5(d)]. Eventually, the pattern concentrate at two channels accompanied by two slightly excited neighbor channels at t=140 minutes [Fig. 5(e)]. In periodic lattice, gap solitons have the profile closing resembling modulated Bloch waves near the corresponding band edges [15]. So, if we shape the probe beam to match the profile of the modulated Bloch-wave properly, we can realize the spatial gap solitons’ formation. The gap solitons that arise from the edge of first band have the “phase signature” of the Bloch mode associated with the same transverse momentum [7

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**, 023902 (2003). [CrossRef] [PubMed]

8. F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO_{3} waveguide arrays,” Opt. Express **13**, 4314–4324 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-11-4314 [CrossRef] [PubMed]

_{3}sample. At the time t=0, we observed the discrete diffraction. With sufficiently high nonlinearity, the nonlinear self-action of probe beam as well as the strong interaction between the probe beam and the lattice-forming beams make the probe beam be localized in the lattice. So the dipole probe beam with the lattice-forming beams creates the composite gap solitons, which is in good agreement with the case of a single Gauss beam being incident at Bragg angle. But the excitation method of a single Gauss beam be incident at Bragg angle may lead to a nonpure excitation of gap solitons in the lattice whose index step is not very low [14

14. D. Mandelik, H. S. Eeisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. **90**, 053902 (2003). [CrossRef] [PubMed]

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

### 3.3 A single Gauss beam be at normal incidence

17. F. Fedele, J. Yang, and Z. Chen, “Defect modes in one-dimensional photonic lattices,” Opt. Lett. **30**, 1506–1508 (2005). [CrossRef] [PubMed]

18. F. Fedele, J. Yang, and Z. Chen, “Properties of defect modes in one-dimensional optically induced photonic lattices,” Stud. Appl. Math. **115**, 277–299 (2005). [CrossRef]

18. F. Fedele, J. Yang, and Z. Chen, “Properties of defect modes in one-dimensional optically induced photonic lattices,” Stud. Appl. Math. **115**, 277–299 (2005). [CrossRef]

18. F. Fedele, J. Yang, and Z. Chen, “Properties of defect modes in one-dimensional optically induced photonic lattices,” Stud. Appl. Math. **115**, 277–299 (2005). [CrossRef]

19. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. **28**, 710–712 (2003). [CrossRef] [PubMed]

20. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. **83**. 2726–2729 (1999). [CrossRef]

## 4. Conclusion

_{3}: Fe crystal. The staggered composite gap solitons are observed when a single Gauss beam is incident at Bragg angle as well as a dipole beam is incident at normal incidence. Being incident at normal incidence, the single Gauss beam forms the in-phase composite gap solitons with the lattice-forming beams. It is the first time to our knowledge to observe two types of composite gap solitons in optically induced one-dimensional lattice.

## Acknowledgments

## References and links

1. | E. Yablonovich, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. |

2. | A. S. Davydov and N. I. Kislukha, “Solitary excitation in one-dimensional molecular chains,” Phys. Status Solodi B |

3. | W. P. Su, J. R. Schieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. |

4. | A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose-Einstein condensates,” Phys. Rev. Lett. |

5. | H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. |

6. | N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E. |

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. | F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO |

9. | Z. Chen and K. MaCarthy, “Spatial soliton pixels from partially incoherent light,” Opt. Lett. |

10. | J. Petter, J. Schröder, D. Träger, and C. Denz, “Optical control of arrays of photorefractive screening solitons,” Opt. Lett. |

11. | A. S. Desyatnikov, E. A. Ostrovskaya, Y. S. Kivshar, and C. Denz, “Composite band-gap solitons in nonlinear optically induced lattice,” Phys. Rev. Lett. |

12. | D. Neshev, Y. S. Kivshar, H. Martin, and Z. Chen, “Soliton stripes in two-dimensional nonlinear photonic lattices,” Opt. Lett. |

13. | S. Orlov, A. Yariv, and M. Segev, “Nonlinear self-phase matching of optical second harmonic generation in lithium niobate,” Appl. Phys. Lett. |

14. | D. Mandelik, H. S. Eeisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. |

15. | D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, nlin-ps/0405019. |

16. | D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. |

17. | F. Fedele, J. Yang, and Z. Chen, “Defect modes in one-dimensional photonic lattices,” Opt. Lett. |

18. | F. Fedele, J. Yang, and Z. Chen, “Properties of defect modes in one-dimensional optically induced photonic lattices,” Stud. Appl. Math. |

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

20. | R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. |

**OCIS Codes**

(190.5330) Nonlinear optics : Photorefractive optics

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(230.7380) Optical devices : Waveguides, channeled

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: December 2, 2005

Revised Manuscript: February 25, 2006

Manuscript Accepted: February 26, 2006

Published: March 6, 2006

**Citation**

Tao Song, Si Min Liu, Ru Guo, Zhao Hong Liu, Nan Zhu, and Yuan Mei Gao, "Observation of composite gap solitons in optically induced nonlinear lattices in LiNbO3:Fe crystal," Opt. Express **14**, 1924-1932 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-5-1924

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### References

- E. Yablonovich, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef]
- A. S. Davydov, and N. I. Kislukha, "Solitary excitation in one-dimensional molecular chains," Phys. Status Solodi B 59, 465-470 (1973). [CrossRef]
- W. P. Su, J. R. Schieffer, and A. J. Heeger, "Solitons in polyacetylene," Phys. Rev. Lett. 42, 1968 (1979). [CrossRef]
- A. Trombettoni, and A. Smerzi, "Discrete solitons and breathers with dilute Bose-Einstein condensates," Phys. Rev. Lett. 86, 2353-2356 (2001). [CrossRef] [PubMed]
- H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998). [CrossRef]
- N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E. 66, 046602 (2002). [CrossRef]
- 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, 023902 (2003). [CrossRef] [PubMed]
- F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, M. Segev, "Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express 13, 4314-4324 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-11-4314 [CrossRef] [PubMed]
- Z. Chen and K. MaCarthy, "Spatial soliton pixels from partially incoherent light," Opt. Lett. 27, 2019-2021 (2002). [CrossRef]
- J. Petter, J. Schröder, D. Träger, and C. Denz, "Optical control of arrays of photorefractive screening solitons," Opt. Lett. 28, 438-440 (2003). [CrossRef] [PubMed]
- A. S. Desyatnikov, E. A. Ostrovskaya, Y. S. Kivshar, and C. Denz, "Composite band-gap solitons in nonlinear optically induced lattice," Phys. Rev. Lett. 91, 153902 (2003). [CrossRef] [PubMed]
- D. Neshev, Y. S. Kivshar, H. Martin and Z. Chen, "Soliton stripes in two-dimensional nonlinear photonic lattices," Opt. Lett. 29, 486-488 (2004). [CrossRef] [PubMed]
- S. Orlov, A. Yariv, and M. Segev, "Nonlinear self-phase matching of optical second harmonic generation in lithium niobate," Appl. Phys. Lett. 68, 1610-1612 (1996). [CrossRef]
- D. Mandelik, H. S. Eeisenberg, Y. Silberberg, R. Morandotti and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902 (2003). [CrossRef] [PubMed]
- D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, nlin-ps/0405019.
- D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, "Gap solitons in waveguide arrays," Phys. Rev. Lett. 92, 093904 (2004). [CrossRef] [PubMed]
- F. Fedele, J. Yang and Z. Chen, "Defect modes in one-dimensional photonic lattices," Opt. Lett. 30, 1506-1508 (2005). [CrossRef] [PubMed]
- F. Fedele, J. Yang, and Z. Chen, "Properties of defect modes in one-dimensional optically induced photonic lattices," Stud. Appl. Math. 115, 277-299 (2005). [CrossRef]
- D. Neshev, E. Ostrovskaya, Y. Kivshar, W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710-712 (2003). [CrossRef] [PubMed]
- R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Dynamics of discrete solitons in optical waveguide arrays,"Phys. Rev. Lett. 83. 2726-2729 (1999). [CrossRef]

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