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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 10 — May. 20, 2013
  • pp: 12443–12450
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Design of large-bandwidth single-mode operation waveguides in silicon three-dimensional photonic crystals using two guided modes

Jiapeng Fu, Aniwat Tandaechanurat, Satoshi Iwamoto, and Yasuhiko Arakawa  »View Author Affiliations


Optics Express, Vol. 21, Issue 10, pp. 12443-12450 (2013)
http://dx.doi.org/10.1364/OE.21.012443


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Abstract

We report on the design of silicon three-dimensional (3D) photonic crystal (PC) waveguides with a combination of acceptor-type and donor-type line defects. Tuning the width of the acceptor-type line defect allows the waveguide to support two guided modes, which enable single-mode propagation over 98.7% of the complete photonic bandgap (cPBG). In addition, we demonstrate that the frequency ranges for single-mode propagation can be extended to the entire range of the cPBG by further tuning the thickness of the layers in which the donor-type line defects are located. The wide ranges of available frequencies for single mode propagation enable flexible design of 3D PC components and will provide a route towards future 3D photonic circuits.

© 2013 OSA

1. Introduction

There has been great interest in the properties of photonic crystals (PCs), which prohibit the propagation of light with frequencies that lie within a photonic band gap (PBG) [1

1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987). [CrossRef] [PubMed]

,2

2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987). [CrossRef] [PubMed]

]. In the last twenty years many studies had been reported on the fundamental properties and potential applications of two-dimensional (2D) PCs [3

3. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999). [CrossRef] [PubMed]

8

8. K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012). [CrossRef]

], in which light is confined in the plane direction by means of the PBG, and in the perpendicular direction by means of total internal reflection. Meanwhile, three-dimensional (3D) PCs, possessing a complete PBG (cPBG), have also been receiving growing attention for their ability to control light of all polarizations in all directions [1

1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987). [CrossRef] [PubMed]

,2

2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987). [CrossRef] [PubMed]

]. 3D photonic crystal waveguides (PCWs) are a key optical component for the implementation of highly-integrated 3D optical circuits due to their capability of creating sharp bends with high transmission efficiencies [9

9. A. Chutinan and S. Noda, “Highly confined waveguides and waveguide bends in three-dimensional photonic crystal,” Appl. Phys. Lett. 75(24), 3739–3741 (1999). [CrossRef]

,10

10. A. Chutinan, S. John, and O. Toader, “Diffractionless flow of light in all-optical Microchips,” Phys. Rev. Lett. 90(12), 123901 (2003). [CrossRef] [PubMed]

]. In principle, thanks to the cPBG, 3D PCWs do not suffer from losses due to inter-mode coupling between TE and TM modes [11

11. Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes,” Appl. Phys. Lett. 82(11), 1661–1663 (2003). [CrossRef]

], nor do they experience leaky-mode region problems that are unavoidable in 2D PC slab waveguides. 3D PCs also offer new possibilities for directly funneling the light output from the 3D PC laser cavity [12

12. A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011). [CrossRef]

,13

13. D. Cao, A. Tandaechanurat, S. Nakayama, S. Ishida, S. Iwamoto, and Y. Arakawa, “Silicon-based three-dimensional photonic crystal nanocavity laser with InAs quantum-dot gain,” Appl. Phys. Lett. 101(19), 191107 (2012). [CrossRef]

] and subsequently guiding it through 3D waveguides to other optical components on the same chip with low losses [14

14. M. Okano, S. Kako, and S. Noda, “Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal,” Phys. Rev. B 68(23), 235110 (2003). [CrossRef]

16

16. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000). [CrossRef] [PubMed]

]. In addition, they are also an important element for incorporating other functionalities such as channel dropping [17

17. D. Stieler, A. Barsic, R. Biswas, G. Tuttle, and K.-M. Ho, “A planar four-port channel drop filter in the three-dimensional woodpile photonic crystal,” Opt. Express 17(8), 6128–6133 (2009). [CrossRef] [PubMed]

] in 3D optical circuits.

Here, we report on the design of silicon 3D PCWs with an enlarged BW for single-mode operation within the cPBG by utilizing two single guided modes. In an optimized structure, the BW covers the entire range of the cPBG. The paper is organized as follows: First we briefly describe the simulation method and calculation conditions in section 2. Then, we report the waveguide design which exhibits an ultra large BW by controlling the separation of modes in section 3. In section 4, several issues on the operation of the designed waveguide will be discussed.

2. Simulation method and calculation conditions

3. Design of single mode waveguides and results

Figure 1(a) shows our starting structure. The waveguide in a 3D woodpile PC is composed of three defect layers and an outer 3D PC cladding. The middle-defect layer has an acceptor-type line defect created by narrowing an original rod to the width Wmid. The upper-defect and lower-defect layers have donor-type line defects created by adding a cross rod just above and below the narrowed rod in the middle-defect layer. The additional-dielectric line defects have the same width and height as the original rods. These three defect rods work as a waveguide along the y direction.

The width of the middle line defect Wmid was varied from 0.24a (the original rod width) to 0a (the mid-rod is completely removed). We note that the cases of Wmid = 0.24a and 0a have already been discussed in [24

24. S. Kawashima, L. H. Lee, M. Okano, M. Imada, and S. Noda, “Design of donor-type line-defect waveguides in three-dimensional photonic crystals,” Opt. Express 13(24), 9774–9781 (2005). [CrossRef] [PubMed]

] and [25

25. S. Kawashima, M. Okano, M. Imada, and S. Noda, “Design of compound-defect waveguides in three-dimensional photonic crystals,” Opt. Express 14(13), 6303–6307 (2006). [CrossRef] [PubMed]

], respectively, using GaAs as a constituting material. From the dispersion relation when Wmid = 0.24a shown in Fig. 1(b), the PBG is mainly filled with two guided modes designated as modes A and B. In this case, mode B does not contribute to the single-mode operation of the waveguide, but instead diminishes the BW due to the crossing of the two modes. In order to circumvent this issue, the width of the central rod, Wmid, was reduced. As Wmid is decreased, all the guided modes move upward to higher frequencies due to a decrease in the effective refractive index of the waveguide. However, modes A and B move differently as Wmid changes. This difference can be understood by looking at the electric field distribution of these two modes (shown in Fig. 2
Fig. 2 Vertical cross-section, orthogonal to the guided direction, of Ez of modes A and B when Wmid = 0.08a.
when Wmid = 0.08a as an example). As mode A is more confined in the mid-rod region, it is more sensitive to the rod width than mode B. Consequently, these two modes tend to separate gradually with decreasing Wmid, while always being connected at wave vector k = π/a. This behavior can be observed in Fig. 3(a)
Fig. 3 (a) Dispersion relation of the waveguide modes when Wmid = 0.12a. (b) Relation between single-mode operation occupancy of PBG and the width of the mid-rod. (c) Dispersion relation of the waveguide modes when Wmid = 0.08a (optimized structure). (d) Dispersion relation of the waveguide modes when Wmid = 0.02a.
. When Wmid = 0.12a, the overlapping frequency region of these two modes is much smaller than the case Wmid = 0.24a. This enables one to use a part of mode B for expanding the frequency range of single-mode propagation.

In order to quantitatively discuss the effect of changing Wmid, we introduce the total BW for single-mode propagation, which is the summation of the BWs for mode A and B (BWA + BWB). BWA and BWB are defined as shown in Fig. 3(a). The PBG occupancy ratio of the total BW for single-mode propagation (BWA + BWB)/PBG as a function of Wmid is shown in Fig. 3(b). As Wmid is decreased from 0.24a, the PBG occupancy ratio is increased due to the separation of the two modes, reaching the highest value of 98.7% when Wmid = 0.06a and 0.08a. The dispersion diagram for Wmid = 0.08a is shown in Fig. 3(c). This result suggests that almost full frequency region of PBG can be utilized for efficient light propagation usingtwo guided modes A and B. The optimized Wmid corresponds to ~50 nm for optical-communication wavelengths (1.55 μm). This could be realized by typical planar processes and by layer-stacking techniques [12

12. A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011). [CrossRef]

,16

16. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000). [CrossRef] [PubMed]

,27

27. K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photon. 7, 133–137 (2013) and their supplementary information.

29

29. S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998). [CrossRef]

].

This wide total BW for single-mode propagation is attributed to a large mode separation between A and B as Wmid was reduced from 0.24a. On the other hand, with further decrease of Wmid, BWA gets much smaller as part of it moves out of the PBG. Although BWB gets larger and partly compensates for the diminished BWA, the total BW for single-mode propagation is reduced by the emergence of additional modes entering the PBG from the low frequency region as denoted with red arrow in Fig. 3(d). Note that adopting the same design conception of [24

24. S. Kawashima, L. H. Lee, M. Okano, M. Imada, and S. Noda, “Design of donor-type line-defect waveguides in three-dimensional photonic crystals,” Opt. Express 13(24), 9774–9781 (2005). [CrossRef] [PubMed]

] and [25

25. S. Kawashima, M. Okano, M. Imada, and S. Noda, “Design of compound-defect waveguides in three-dimensional photonic crystals,” Opt. Express 14(13), 6303–6307 (2006). [CrossRef] [PubMed]

] in our Si 3D PC only gives PBG occupancy of 76.9% and 87.2%, respectively (these correspond to the cases with Wmid = 0.24a and Wmid = 0a, respectively).

4. Discussion

We demonstrated wide frequency ranges in the PBG available for single mode propagation based on the combination of two guided modes A and B. Here we will discuss several issues regarding the use of proposed WGs.

The first issue is the effect of difference in coupling efficiencies for the two modes, especially at around the Brillouin zone edge (k = π/a), where the two modes have the same frequency. When an optical pulse is injected at the frequency corresponding to that at the Brillouin zone edge, strong distortion of the pulse might occur due to the difference. Supposing an optical pulse at 1.55 μm with a pulse duration of one to a few picoseconds which is a typical optical pulse used in various experiments, the spectral width is ~0.1-1% of the center frequency. In this small frequency range, the change of mode distributions is not significant. In addition, both modes have relatively similar field distributions at k = π/a except for the inversion with respect to the center line (see in Fig. 5
Fig. 5 Vertical cross-section, orthogonal to the guided direction, of Ez of modes A and B at the transition point k = π/a for the optimized structure with Wmid = 0.08a and Tnl = 0.2925a.
). Therefore, the distortion due to the difference in coupling efficiencies is expected not to be significant for these pulses. Even on the same band, the coupling efficiency will change in frequency [27

27. K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photon. 7, 133–137 (2013) and their supplementary information.

]. Design of efficient coupler for 3D PCWs will be needed.

Secondly, the frequency range for single mode propagation contains slow light regions. Small group velocities make the efficient external coupling difficult. Injector structures efficient for slow lights in 2D PCWs have been reported [30

30. J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, “Coupling into slow-mode photonic crystal waveguides,” Opt. Lett. 32(18), 2638–2640 (2007). [CrossRef] [PubMed]

,31

31. C. Martijn de Sterke, K. B. Dossou, T. P. White, L. C. Botten, and R. C. McPhedran, “Efficient coupling into slow light photonic crystal waveguide without transition region: role of evanescent modes,” Opt. Express 17(20), 17338–17343 (2009). [CrossRef] [PubMed]

]. The knowledge will be available for designing an efficient injector even for 3D PCWs. Once efficient couplers and injectors for 3D PCWs are invented, a multi-port configuration with add-drop functions [17

17. D. Stieler, A. Barsic, R. Biswas, G. Tuttle, and K.-M. Ho, “A planar four-port channel drop filter in the three-dimensional woodpile photonic crystal,” Opt. Express 17(8), 6128–6133 (2009). [CrossRef] [PubMed]

] as illustrated in Fig. 6
Fig. 6 Schematic illustration of a prospective configuration for an efficient use of the wide single-mode operation frequency range in the 3D PCW discussed in this report.
will enable to utilize the wide single-mode BW more effectively.

Increased propagation loss [32

32. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94(3), 033903 (2005). [CrossRef] [PubMed]

,33

33. L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenović, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18(26), 27627–27638 (2010). [CrossRef] [PubMed]

] and enhanced optical nonlinear effects [34

34. C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009). [CrossRef] [PubMed]

] in the slow light region will be other concerns. These are important general issues for 3D PCWs. In other reports [21

21. R. J. Liu, Z. Y. Li, Z. F. Feng, B. Y. Cheng, and D. Z. Zhang, “Channel-drop filters in three-dimensional woodpile photonic crystals,” J. Appl. Phys. 103(9), 094514 (2008). [CrossRef]

,24

24. S. Kawashima, L. H. Lee, M. Okano, M. Imada, and S. Noda, “Design of donor-type line-defect waveguides in three-dimensional photonic crystals,” Opt. Express 13(24), 9774–9781 (2005). [CrossRef] [PubMed]

27

27. K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photon. 7, 133–137 (2013) and their supplementary information.

], slow light regions are also observed. Detail characteristics of propagation loss in 3D PCWs, especially at slow light regions, are expected to be revealed in the near future. Enhanced optical nonlinear effects are unwanted effect for signal transmission. However, these could be utilized to incorporate several functionalities in 3D PC circuits using the slow light region.

5. Conclusion

We have successfully designed waveguides possessing an ultra-large BW for single-mode operation in silicon 3D PCs. The waveguides support two main guided modes, and thus the combination of these two modes can provide an ultra-large BW for single-mode propagation. By finely tuning the width of the acceptor-type line defect and the thickness of the neighboring layers where the donor-type line defects are located, the two guided modes can be made to cover an extremely large single-mode BW that occupies the entire range of the cPBG of the 3D PC. These wide ranges of available frequencies for single mode propagation enable to flexibly design of 3D PC components and circuits. The designed 3D PCW with such a large BW for single-mode operation is CMOS-compatible and would provide a route towards future 3D photonic circuits. We also found that the modulation scheme of Wmid and Tnl are also effective for improving single mode BW of 3D PCWs using GaAs as the dielectric material.

Acknowledgments

The authors thank Y. Hsiao and M. Holmes for their technical support. This work was supported by the Project for Developing Innovation Systems of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan, and by the Japan Society for the Promotion of Science (JSPS) through its “Funding Program for world-leading Innovation R&D on Science and Technology (FIRST Program)”.

References and links

1.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987). [CrossRef] [PubMed]

2.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987). [CrossRef] [PubMed]

3.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999). [CrossRef] [PubMed]

4.

H. C. Nguyen, S. Hashimoto, M. Shinkawa, and T. Baba, “Compact and fast photonic crystal silicon optical modulators,” Opt. Express 20(20), 22465–22474 (2012). [CrossRef] [PubMed]

5.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003). [CrossRef] [PubMed]

6.

C. H. Chen, S. Matsuo, K. Nozaki, A. Shinya, T. Sato, Y. Kawaguchi, H. Sumikura, and M. Notomi, “All-optical memory based on injection-locking bistability in photonic crystal lasers,” Opt. Express 19(4), 3387–3395 (2011). [CrossRef] [PubMed]

7.

S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11(22), 2927–2939 (2003). [CrossRef] [PubMed]

8.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012). [CrossRef]

9.

A. Chutinan and S. Noda, “Highly confined waveguides and waveguide bends in three-dimensional photonic crystal,” Appl. Phys. Lett. 75(24), 3739–3741 (1999). [CrossRef]

10.

A. Chutinan, S. John, and O. Toader, “Diffractionless flow of light in all-optical Microchips,” Phys. Rev. Lett. 90(12), 123901 (2003). [CrossRef] [PubMed]

11.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes,” Appl. Phys. Lett. 82(11), 1661–1663 (2003). [CrossRef]

12.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011). [CrossRef]

13.

D. Cao, A. Tandaechanurat, S. Nakayama, S. Ishida, S. Iwamoto, and Y. Arakawa, “Silicon-based three-dimensional photonic crystal nanocavity laser with InAs quantum-dot gain,” Appl. Phys. Lett. 101(19), 191107 (2012). [CrossRef]

14.

M. Okano, S. Kako, and S. Noda, “Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal,” Phys. Rev. B 68(23), 235110 (2003). [CrossRef]

15.

S. A. Rinne, F. García-Santamaría, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2(1), 52–56 (2008). [CrossRef]

16.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000). [CrossRef] [PubMed]

17.

D. Stieler, A. Barsic, R. Biswas, G. Tuttle, and K.-M. Ho, “A planar four-port channel drop filter in the three-dimensional woodpile photonic crystal,” Opt. Express 17(8), 6128–6133 (2009). [CrossRef] [PubMed]

18.

M. Deubel, M. Wegener, S. Linden, G. von Freymann, and S. John, “3D-2D-3D photonic crystal heterostructures fabricated by direct laser writing,” Opt. Lett. 31(6), 805–807 (2006). [CrossRef] [PubMed]

19.

E. Lidorikis, M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Polarization-Independent Linear Waveguides in 3D Photonic Crystals,” Phys. Rev. Lett. 91(2), 023902 (2003). [CrossRef] [PubMed]

20.

C. Sell, C. Christensen, J. Muehlmeier, G. Tuttle, Z. Y. Li, and K. M. Ho, “Waveguide networks in three-dimensional layer-by-layer photonic crystals,” Appl. Phys. Lett. 84(23), 4605–4607 (2004). [CrossRef]

21.

R. J. Liu, Z. Y. Li, Z. F. Feng, B. Y. Cheng, and D. Z. Zhang, “Channel-drop filters in three-dimensional woodpile photonic crystals,” J. Appl. Phys. 103(9), 094514 (2008). [CrossRef]

22.

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88(17), 171107 (2006). [CrossRef]

23.

D. Roundy, E. Lidorikis, and J. D. Joannopoulos, “Polarization-selective waveguide bends in a photonic crystal structure with layered square symmetry,” J. Appl. Phys. 96(12), 7750–7752 (2004). [CrossRef]

24.

S. Kawashima, L. H. Lee, M. Okano, M. Imada, and S. Noda, “Design of donor-type line-defect waveguides in three-dimensional photonic crystals,” Opt. Express 13(24), 9774–9781 (2005). [CrossRef] [PubMed]

25.

S. Kawashima, M. Okano, M. Imada, and S. Noda, “Design of compound-defect waveguides in three-dimensional photonic crystals,” Opt. Express 14(13), 6303–6307 (2006). [CrossRef] [PubMed]

26.

I. Staude, G. von Freymann, S. Essig, K. Busch, and M. Wegener, “Waveguides in three-dimensional photonic-bandgap materials by direct laser writing and silicon double inversion,” Opt. Lett. 36(1), 67–69 (2011). [CrossRef] [PubMed]

27.

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photon. 7, 133–137 (2013) and their supplementary information.

28.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003). [CrossRef] [PubMed]

29.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998). [CrossRef]

30.

J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, “Coupling into slow-mode photonic crystal waveguides,” Opt. Lett. 32(18), 2638–2640 (2007). [CrossRef] [PubMed]

31.

C. Martijn de Sterke, K. B. Dossou, T. P. White, L. C. Botten, and R. C. McPhedran, “Efficient coupling into slow light photonic crystal waveguide without transition region: role of evanescent modes,” Opt. Express 17(20), 17338–17343 (2009). [CrossRef] [PubMed]

32.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94(3), 033903 (2005). [CrossRef] [PubMed]

33.

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenović, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18(26), 27627–27638 (2010). [CrossRef] [PubMed]

34.

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009). [CrossRef] [PubMed]

OCIS Codes
(230.7370) Optical devices : Waveguides
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(130.5296) Integrated optics : Photonic crystal waveguides

ToC Category:
Photonic Crystals

History
Original Manuscript: January 2, 2013
Revised Manuscript: March 20, 2013
Manuscript Accepted: March 28, 2013
Published: May 14, 2013

Citation
Jiapeng Fu, Aniwat Tandaechanurat, Satoshi Iwamoto, and Yasuhiko Arakawa, "Design of large-bandwidth single-mode operation waveguides in silicon three-dimensional photonic crystals using two guided modes," Opt. Express 21, 12443-12450 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-12443


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References

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