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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 19 — Sep. 14, 2009
  • pp: 16927–16932
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Beam control and multi-color routing with spatial photonic defect modes

Xiaosheng Wang and Zhigang Chen  »View Author Affiliations


Optics Express, Vol. 17, Issue 19, pp. 16927-16932 (2009)
http://dx.doi.org/10.1364/OE.17.016927


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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

One of the fascinating features of photonic band-gap structures is a fundamentally different way of guiding light by defects in otherwise uniformly periodic structures as opposed to guidance by total internal reflection [1

1. 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).

]. In photonic crystals (PCs), for instance, splitting and routing of light along pre-designed paths has been highly touted and tested for optical communications, as lossless transmission of light around sharp bends is difficult to achieve in conventional optical fibers. Thus far, a variety of schemes have been proposed to achieve efficient switching and splitting based on linear time-domain frequency modes in PCs and cavity resonance waveguides [1

1. 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).

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]

]. On the other hand, bandgap guidance based on 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

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]

].

In this paper, we demonstrate by numerical simulation that, along 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

Let us begin our analysis by considering a probe beam propagating through 2D PLs containing defects (see Fig. 1
Fig. 1 (a) Schematic drawing of a 2D photonic lattice containing a single-site defect; (b-d) Input of a Gaussian probe beam, its diffraction output in a uniform lattice, and localized output through the defect channel, respectively. (e) A line defect superimposed with an elliptical input beam tilting towards left; (f) output of the probe beam through the line defect in (e).
). To make the discussion more relevant to the experimental setting [25

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]

], we assume that the lattices are optically induced in a nonlinear photorefractive SBN crystal with unperturbed refractive index 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]

,29

29. 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).

]:
iUz+Uxx+UyyE01+ILU=0
(1)
where 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 IL=I 0cos2(x)cos2(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 4.5×105 V/m in real units.

3. Results and discussion

By removing or decreasing the refractive index modulation in a lattice site, a negative single-site defect is introduced into the 2D lattice [Fig. 1(a)]. Such a defect can support a localized defect mode [21

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

] in a photonic bandgap originating from repeated Bragg reflection, as demonstrated in our earlier work [25

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]

]. As a starting point, we illustrate such defect guidance in Figs. 1(a-d). Instead of undertaking discrete diffraction due to coupling between the evanescent waveguides as in uniform lattices [Fig. 1(c)], a focused 2D Gaussian beam [Fig. 1(b)] aimed into the defect can be confined in the defect channel [Fig. 1(d)] throughout the lattices under appropriate conditions, forming a defect mode. Our focus here is to show guiding and steering of a light beam along a line defect as illustrated in Fig. 1(e). With a line defect, light can be confined in the direction perpendicular to the defect path due to Bragg reflection, but can be routed along the defect path due to coupling/resonance of adjacent defect modes akin to that in resonance cavity waveguide [5

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]

]. As an example, we launch the 2D Gaussian probe beam into the line defect with an initial tilting angle (transverse momentum) toward left [Fig. 1(e)]. After propagating through the lattice, we can see clearly that the beam is guided and translated by the line defect [Fig. 1(f)]. For these results, the refractive index in the defect sites is decreased by 70% as compared with that in the surrounding lattice sites. The incident angle of the probe beam with respect to the longitudinal propagation direction z is tan−1(0.5π/kΛ) 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..

We point out that such guidance is neither induced by nonlinear self-focusing since no self-action is taken into account here, nor by total internal reflection since the defect sites (guided region) has lower refractive index than the surrounding lattice sites. In fact, it is established by spatial bandgap guidance due to periodic refractive index modulation in the lattice. This also leads to the possibility of bending of light akin to that in PCs [2

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]

]. Some typical results for the guiding and steering of a light beam in L-shaped line defect with different designs of the corner defects are shown in Fig. 2
Fig. 2 Re-directing of light in L-shaped line defects with different corner structures. Top panels show the lattice structures superimposed with a left-tilted probe beam at input (zoom-in pictures of the corner are shown in the insets for better visibility); Bottom panels show the output of the probe beam guided and steered by the line defect (Media 1).
. The top row shows three lattices with different structured defects superimposed with the probe beam at input of the lattices, where the inserts are zoom-in pictures of different corner structures. For these three cases, the input beam has the same input tilt (as in Fig. 1) towards left. The bottom row shows the output profiles of the probe beam exiting the lattices after 6 cm of propagation. We can see clearly that, in each case, the input beam changes its direction of propagation around the corner of the L-shaped defect (Animation of the beam propagation can be seen in media file, bend.gif). Thus, the probe beam traveling to the left now ends up traveling in upward direction. It is noticeable that, at the output, there is a small portion of light turning backwards. If we consider the portion going upward is the “transmission”, then the portion going back will be the “reflection”. Clearly, different corner defect structures lead to different rate of transmission [estimated “transmission” is 90%, 82%, and 86% for Figs. 2(a-c), respectively].

In the present scheme, as the probe beam travels mainly along 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)
Fig. 3 Blocking and splitting of light with different designs of line defects. Top panels show lattice structures superimposed with a left-tilted probe beam at input; bottom panels show the probe beam exiting the lattice. (a) and (b) show examples of blocking (Media 2) and 50/50 splitting (Media 3) by adjusting the refractive index of the corner waveguide in L-defect to be 100% and 32.5% with respect to that in the uniform waveguide arrays, respectively. (c) and (d) show splitting of a light beam by T and + shaped line defects in the lattices.
, 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).

Next, we show that light routing around the boundary of a finite waveguide arrays based on linear surface defect modes is also possible provided that the surface line defects are properly designed. Nonlinear Tamm-like surface states and surface solitons [30

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]

] in waveguide arrays have been studies extensively, but demonstration of linear optical surface modes [31

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

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]

] requires specially designed surface defects. If a 2D PL is bounded by defects and a probe beam can evolve into a linear localized surface defect mode, then the probe beam can be routed anywhere in the lattice boundary with appropriate transverse momentum. Figures 4(a, b)
Fig. 4 Routing of a light beam around the surface of finite waveguide arrays. Top panels show the lattice structures superimposed with a left-tilted probe beam at input; and bottom panels show the output of the probe beam. (a) Steering of the probe beam around a corner along surface line defects, (b) blocking when the defect at the corner is missing, and (c) spiraling around the surface of a finite waveguide arrays bounded by surface line defects (Media 4).
show two results of proposed light routing along the surface of a semi-infinite square lattice. With appropriate design of the surface and corner defects, the probe beam can make a turn around surface corner [Fig. 4(a)], reverse its transverse travelling direction at the corner [Fig. 4(b)]. If the 2D waveguide lattice has a limited size or long enough propagation distance for the probe beam, then the probe beam can circle around the surface and make a round trip [see Fig. 4(c), Media 4 for routing around a 5x5 square lattice].

Finally, we propose multi-color routing in the same setting of a L-shaped defect structure. Since bandgap guidance in PLs is based on spatial defect modes (different from that in PCs), it is possible to form defect modes in a defect channel with different wavelengths of light [25

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]

]. Typical results are shown in Fig. 5
Fig. 5 Routing of a light beam of different wavelengths in the same setting of L-shaped defect channel in lattice structure shown in (a). (b-d) show the output of the probe beam exiting the lattice. From (b) to (d), the wavelengths used are 532 nm, 488 nm, and 633 nm, respectively.
, where in the same L-shaped defect structure [Fig. 5(a)], routing of a probe beam at 532nm [Fig. 5(b)], 488nm [Fig. 5(c)] and 633nm [Fig. 5(d)] is realized. We emphasize that these results were obtained under the same conditions (i.e. same lattice spacing, lattice index modulation, and same input tilt of the probe beam) as those in Figs. 2-4. Although the probe beam ended at different locations at the lattice output and the spatial broadening along the defect line is somewhat different due to different propagation velocities and diffraction along transverse 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

We demonstrated the possibility for re-directing, blocking, and tunable splitting of a light beam in 2D photonic lattices with structured defects. We show it is possible to route polychromatic as well as monochromatic light along predesigned paths inside or surrounding the lattices based on photonic bandgap guidance. These results might be useful for the development and implementation of microstructured devices where multi-color routing with low-index-contrast photonic structures is desirable. Our results might also be relevant to the Fano Resonance studied in different lattice systems [33

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

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]

].

This work was supported by NSF, AFOSR, and the 973 Program. We thank P. Zhang and J. Yang for assistance and discussion.

References and links

1.

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).

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]

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 282(5387), 274–276 (1998). [CrossRef] [PubMed]

4.

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]

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]

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]

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]

10.

Y. S. Kivshar, and G. P. Agrawal, Optical solitons: From fibers to photonic crystals (Academic Press, San Diego, 2003).

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.

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]

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 422(6928), 147–150 (2003). [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]

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]

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. 81, 3383 (1998). [CrossRef]

19.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Beam steering in waveguide arrays,” Appl. Phys. Lett. 80(18), 3247 (2002). [CrossRef]

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]

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]

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]

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 14(16), 7362 (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]

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]

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. 34(6), 797–799 (2009). [CrossRef] [PubMed]

29.

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).

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]

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]

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

  1. 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).
  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]
  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 282(5387), 274–276 (1998). [CrossRef] [PubMed]
  4. 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]
  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]
  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]
  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]
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