## Beam control and multi-color routing with spatial photonic defect modes

Optics Express, Vol. 17, Issue 19, pp. 16927-16932 (2009)

http://dx.doi.org/10.1364/OE.17.016927

Acrobat PDF (204 KB)

### Abstract

We demonstrate tunable re-directing, blocking, and splitting of a light beam along defect channels based on spatial bandgap guidance in two-dimensional photonic lattices. We show the possibility for linear control of beam propagation and multicolor routing with specially designed junctions and surface structures embedded in otherwise uniform square lattices.

© 2009 OSA

## 1. Introduction

*time-domain frequency modes*in PCs and cavity resonance waveguides [1–6

6. M. Bayindir, B. Temelkuran, and E. Ozbay, “Propagation of photons by hopping: A waveguiding mechanism through localized coupled cavities in three-dimensional photonic crystals,” Phys. Rev. B **61**(18), R11855–R11858 (2000). [CrossRef]

*spatial frequency modes*in closely-spaced waveguide arrays, or photonic lattices (PLs), represents another possibility for unconventional guidance of light. It has been proposed that blocking and routing of light can be achieved with discrete solitons in two-dimensional (2D) networks of nonlinear waveguide arrays [7

7. D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. **87**(23), 233901 (2001). [CrossRef] [PubMed]

8. J. Meier, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, G. Salamo, H. Yang, M. Sorel, Y. Silberberg, and J. S. Aitchison, “Incoherent blocker soliton interactions in Kerr waveguide arrays,” Opt. Lett. **30**(23), 3174–3176 (2005). [CrossRef] [PubMed]

9. 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]

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]

^{−3}or less, as achieved with different techniques from optical induction in nonlinear crystals [13

13. 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 Stat. Nonlin. Soft Matter Phys. **66**(4), 046602 (2002). [CrossRef] [PubMed]

15. Z. Chen and K. McCarthy, “Spatial soliton pixels from partially incoherent light,” Opt. Lett. **27**(22), 2019–2021 (2002). [CrossRef]

16. K. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. **21**(21), 1729 (1996). [CrossRef] [PubMed]

20. Y. Tan, F. Chen, M. Stepić, V. Shandarov, and D. Kip, “Reconfigurable optical channel waveguides in lithium niobate crystals,” Opt. Express **16**(14), 10465 (2008). [CrossRef] [PubMed]

21. F. Fedele, J. Yang, and Z. Chen, “Defect modes in one-dimensional photonic lattices,” Opt. Lett. **30**(12), 1506–1508 (2005). [CrossRef] [PubMed]

26. G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. **94**(16), 163902 (2005). [CrossRef] [PubMed]

27. U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. **75**(10), 1348 (1999). [CrossRef]

23. X. Wang, Z. Chen, and J. Yang, “Guiding light in optically induced ring lattices with a low-refractive-index core,” Opt. Lett. **31**(12), 1887–1889 (2006). [CrossRef] [PubMed]

25. I. Makasyuk, Z. Chen, and J. Yang, “Band-gap guidance in optically induced photonic lattices with a negative defect,” Phys. Rev. Lett. **96**(22), 223903 (2006). [CrossRef] [PubMed]

30. S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Arès, M. Sorel, Y. Min, W. Sohler, X. I. A. O. S. H. E. N. G. Wang, A. N. N. A. Bezryadina, and Z. H. I. G. A. N. G. Chen, “Observation of one-and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. **16**(04), 401 (2007). [CrossRef]

32. N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, “Observation of optical Shockley-like surface states in photonic superlattices,” Opt. Lett. **34**(11), 1633–1635 (2009). [CrossRef] [PubMed]

*line defects*(trains of missing or heterogeneous waveguides), a light beam with an initial input tilt (transverse momentum) can be guided and steered through the defect channel. By fine-tuning the defect strength at the intersection of appropriately designed “L”, “T” and “+” shaped defect channels, it is possible to achieve re-directing, blocking, and controllable power splitting of a light beam in the transverse directions while the beam propagates primarily along the longitudinal direction. Moreover, we propose light routing around the boundary of a finite waveguide arrays based on linear surface defect modes as well as multi-color routing around the corner of L-shaped defect channels.

## 2. Numerical model

25. I. Makasyuk, Z. Chen, and J. Yang, “Band-gap guidance in optically induced photonic lattices with a negative defect,” Phys. Rev. Lett. **96**(22), 223903 (2006). [CrossRef] [PubMed]

*n*

_{0}=2.3. The induced index lattices have a spatial period of 13 μm and a refractive index modulation on the order of 10

^{−4}. The probe beam propagating in the lattices has a wavelength of 532 nm. Linear propagation of the probe beam in the PLs can be described by the following normalized equation [22

22. F. Fedele, J. Yang, and Z. Chen, “Properties of defect modes in one-dimensional optically-induced photonic lattices,” Stud. Appl. Math. **115**(2), 279–301 (2005). [CrossRef]

*U*is the envelope of the optical field,

*z*sets the propagation direction and (

*x*,

*y*) are the transverse coordinates,

*E*

_{0}is the applied dc field, and

*I*

_{L}=I_{0}cos

^{2}(

*x*)cos

^{2}(

*y*)

*D*(

*x,y*) is the normalized lattice intensity pattern with a peak intensity

*I*

_{0}.

*D*(

*x,y*) is used to structure the defects, and for the line defect shown in Fig. 1(e),

*D*(

*x,y*)={0.3, if −1/2≤

*x*≤1/2; 1, if otherwise}. For all calculations,

*I*

_{0}=4, and

*E*

_{0}=8.4 corresponding to 4.5×10

^{5}V/m in real units.

## 3. Results and discussion

21. F. Fedele, J. Yang, and Z. Chen, “Defect modes in one-dimensional photonic lattices,” Opt. Lett. **30**(12), 1506–1508 (2005). [CrossRef] [PubMed]

25. I. Makasyuk, Z. Chen, and J. Yang, “Band-gap guidance in optically induced photonic lattices with a negative defect,” Phys. Rev. Lett. **96**(22), 223903 (2006). [CrossRef] [PubMed]

5. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. **24**(11), 711–713 (1999). [CrossRef]

*z*is tan

^{−1}(0.5π/

*k*Λ) towards left (this angle is 0.25 degree with current parameters, which can be adjusted by changing the lattice spacing Λ). With such an incident angle, the probe beam aims to the zero diffraction direction initially, thus it is expected to experience less diffraction in the transverse

*y*-direction..

2. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. **77**(18), 3787–3790 (1996). [CrossRef] [PubMed]

*z*-direction with an input tilt, the term “reflection” or “transmission” here refers merely to routing the probe beam to the lower or upper branch of the L-defect after propagating through the lattice. In fact, by properly design the defect structure at the corner, we can achieve blocking and controllable splitting of a light beam in the

*transverse directions*while propagating through the lattices along

*z*-direction. Some examples for blocking and splitting of a probe beam in L-shaped defects are shown in Figs. 3(a, b) , simply by fine-tuning the defect strength (index modulation) at the corner. In Fig. 3(a) the corner waveguide (indicated by the red arrow) has the same refractive index as in a normal lattice site. In this case, the traverse velocity of the probe beam reversed its direction (from –

*y*to +

*y*) at the corner [see Fig. 3(a), Media 2]. This means during its propagation the probe beam is “blocked” by the corner and “reflected” to opposite transverse direction. Intuitively, this results from the “anti-defect” at the corner that breaks the coupling of defect modes along two (vertical and horizontal) branches of the “L” shaped defects, so the probe beam traveling along the horizontal branch cannot be coupled into the vertical branch when hitting the corner. If we make the refractive index of the corner waveguide to be only 32.5% of that in a non-defect lattice site but still 2.5% more than that in the line defects, then the probe beam can split into two equal portions moving upward and backward [see Fig. 3(b), Media 3]. In such a case, the corner defect adjusts the coupling between horizontal and vertical branches, resulting in partial transmission and reflection. The ratio of beam power splitting can be changed by fine-tuning the refractive index of the corner waveguide. In addition to the L-shaped defect structure, splitting of a light beam by “T” and “+” shaped defect structures can also be realized, and some examples are shown in Figs. 3(c, d) obtained with same parameters as used for Fig. 2 and in Figs. 3(a, b).

30. S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Arès, M. Sorel, Y. Min, W. Sohler, X. I. A. O. S. H. E. N. G. Wang, A. N. N. A. Bezryadina, and Z. H. I. G. A. N. G. Chen, “Observation of one-and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. **16**(04), 401 (2007). [CrossRef]

31. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, M. Volatier, V. Aimez, R. Arès, C. E. Rüter, and D. Kip, “Optical modes at the interface between two dissimilar discrete meta-materials,” Opt. Express **15**(8), 4663 (2007). [CrossRef] [PubMed]

32. N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, “Observation of optical Shockley-like surface states in photonic superlattices,” Opt. Lett. **34**(11), 1633–1635 (2009). [CrossRef] [PubMed]

**96**(22), 223903 (2006). [CrossRef] [PubMed]

*x*-direction for different wavelengths, routing along the defect channel is achieved simultaneously for all three colors. This could be promising for applications where switching and routing of white light or ultra-short pulses is desirable. Multi-color routing and polychromatic dynamic localization of light beams are also of fundamental interest, as has been demonstrated recently in curved photonic lattices [17

17. A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. **5**(4), 271–275 (2009). [CrossRef]

## 4. Summary

33. R. A. Vicencio, J. Brand, and S. Flach, “Fano blockade by a bose-einstein condensate in an optical lattice,” Phys. Rev. Lett. **98**(18), 184102 (2007). [CrossRef] [PubMed]

34. A. E. Miroshnichenko and Y. S. Kivshar, “Engineering Fano resonances in discrete arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **72**(5), 056611 (2005). [CrossRef] [PubMed]

## References and links

1. | J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, |

2. | A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. |

3. | S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science |

4. | T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. |

5. | A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. |

6. | M. Bayindir, B. Temelkuran, and E. Ozbay, “Propagation of photons by hopping: A waveguiding mechanism through localized coupled cavities in three-dimensional photonic crystals,” Phys. Rev. B |

7. | D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. |

8. | J. Meier, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, G. Salamo, H. Yang, M. Sorel, Y. Silberberg, and J. S. Aitchison, “Incoherent blocker soliton interactions in Kerr waveguide arrays,” Opt. Lett. |

9. | D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature |

10. | Y. S. Kivshar, and G. P. Agrawal, |

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. | 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 Stat. Nonlin. Soft Matter Phys. |

14. | 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 |

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

16. | K. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. |

17. | A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. |

18. | H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Observation of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. |

19. | T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Beam steering in waveguide arrays,” Appl. Phys. Lett. |

20. | Y. Tan, F. Chen, M. Stepić, V. Shandarov, and D. Kip, “Reconfigurable optical channel waveguides in lithium niobate crystals,” Opt. Express |

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

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

23. | X. Wang, Z. Chen, and J. Yang, “Guiding light in optically induced ring lattices with a low-refractive-index core,” Opt. Lett. |

24. | X. Wang, J. Young, Z. Chen, D. Weinstein, and J. Yang, “Observation of lower to higher bandgap transition of one-dimensional defect modes,” Opt. Express |

25. | I. Makasyuk, Z. Chen, and J. Yang, “Band-gap guidance in optically induced photonic lattices with a negative defect,” Phys. Rev. Lett. |

26. | G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. |

27. | U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. |

28. | A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. |

29. | J. Yang, X. Wang, J. Wang, and Z. Chen, “Light localization by defects in optically induced photonic structures” in |

30. | S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Arès, M. Sorel, Y. Min, W. Sohler, X. I. A. O. S. H. E. N. G. Wang, A. N. N. A. Bezryadina, and Z. H. I. G. A. N. G. Chen, “Observation of one-and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. |

31. | S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, M. Volatier, V. Aimez, R. Arès, C. E. Rüter, and D. Kip, “Optical modes at the interface between two dissimilar discrete meta-materials,” Opt. Express |

32. | N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, “Observation of optical Shockley-like surface states in photonic superlattices,” Opt. Lett. |

33. | R. A. Vicencio, J. Brand, and S. Flach, “Fano blockade by a bose-einstein condensate in an optical lattice,” Phys. Rev. Lett. |

34. | A. E. Miroshnichenko and Y. S. Kivshar, “Engineering Fano resonances in discrete arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

**OCIS Codes**

(050.1940) Diffraction and gratings : Diffraction

(230.7370) Optical devices : Waveguides

(160.5293) Materials : Photonic bandgap materials

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: July 28, 2009

Revised Manuscript: August 27, 2009

Manuscript Accepted: August 28, 2009

Published: September 8, 2009

**Citation**

Xiaosheng Wang and Zhigang Chen, "Beam control and multi-color routing with spatial photonic defect modes," Opt. Express **17**, 16927-16932 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-19-16927

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### References

- J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystal: Molding the Flow of Light (second edition) (Princeton U. Press, 2008).
- A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996). [CrossRef] [PubMed]
- S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282(5387), 274–276 (1998). [CrossRef] [PubMed]
- T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35(8), 654 (1999). [CrossRef]
- A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999). [CrossRef]
- M. Bayindir, B. Temelkuran, and E. Ozbay, “Propagation of photons by hopping: A waveguiding mechanism through localized coupled cavities in three-dimensional photonic crystals,” Phys. Rev. B 61(18), R11855–R11858 (2000). [CrossRef]
- D. N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001). [CrossRef] [PubMed]
- J. Meier, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, G. Salamo, H. Yang, M. Sorel, Y. Silberberg, and J. S. Aitchison, “Incoherent blocker soliton interactions in Kerr waveguide arrays,” Opt. Lett. 30(23), 3174–3176 (2005). [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]
- Y. S. Kivshar, and G. P. Agrawal, Optical solitons: From fibers to photonic crystals (Academic Press, San Diego, 2003).
- 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]
- 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 Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002). [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]
- Z. Chen and K. McCarthy, “Spatial soliton pixels from partially incoherent light,” Opt. Lett. 27(22), 2019–2021 (2002). [CrossRef]
- K. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729 (1996). [CrossRef] [PubMed]
- A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. 5(4), 271–275 (2009). [CrossRef]
- H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Observation of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 81, 3383 (1998). [CrossRef]
- T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Beam steering in waveguide arrays,” Appl. Phys. Lett. 80(18), 3247 (2002). [CrossRef]
- Y. Tan, F. Chen, M. Stepić, V. Shandarov, and D. Kip, “Reconfigurable optical channel waveguides in lithium niobate crystals,” Opt. Express 16(14), 10465 (2008). [CrossRef] [PubMed]
- F. Fedele, J. Yang, and Z. Chen, “Defect modes in one-dimensional photonic lattices,” Opt. Lett. 30(12), 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(2), 279–301 (2005). [CrossRef]
- X. Wang, Z. Chen, and J. Yang, “Guiding light in optically induced ring lattices with a low-refractive-index core,” Opt. Lett. 31(12), 1887–1889 (2006). [CrossRef] [PubMed]
- X. Wang, J. Young, Z. Chen, D. Weinstein, and J. Yang, “Observation of lower to higher bandgap transition of one-dimensional defect modes,” Opt. Express 14(16), 7362 (2006). [CrossRef] [PubMed]
- I. Makasyuk, Z. Chen, and J. Yang, “Band-gap guidance in optically induced photonic lattices with a negative defect,” Phys. Rev. Lett. 96(22), 223903 (2006). [CrossRef] [PubMed]
- G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94(16), 163902 (2005). [CrossRef] [PubMed]
- U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75(10), 1348 (1999). [CrossRef]
- A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34(6), 797–799 (2009). [CrossRef] [PubMed]
- J. Yang, X. Wang, J. Wang, and Z. Chen, “Light localization by defects in optically induced photonic structures” in Nonlinearities in Periodic Structures and Metamaterials, C. Denz, S. Flach, Y. S. Kivshar eds. (Springer, 2009).
- S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Arès, M. Sorel, Y. Min, W. Sohler, X. I. A. O. S. H. E. N. G. Wang, A. N. N. A. Bezryadina, and Z. H. I. G. A. N. G. Chen, “Observation of one-and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(04), 401 (2007). [CrossRef]
- S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, M. Volatier, V. Aimez, R. Arès, C. E. Rüter, and D. Kip, “Optical modes at the interface between two dissimilar discrete meta-materials,” Opt. Express 15(8), 4663 (2007). [CrossRef] [PubMed]
- N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, “Observation of optical Shockley-like surface states in photonic superlattices,” Opt. Lett. 34(11), 1633–1635 (2009). [CrossRef] [PubMed]
- R. A. Vicencio, J. Brand, and S. Flach, “Fano blockade by a bose-einstein condensate in an optical lattice,” Phys. Rev. Lett. 98(18), 184102 (2007). [CrossRef] [PubMed]
- A. E. Miroshnichenko and Y. S. Kivshar, “Engineering Fano resonances in discrete arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 056611 (2005). [CrossRef] [PubMed]

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