Abstract

We have theoretically investigated the characteristics of three-dimensional (3D) photonic crystal (PC) waveguides formed by the introduction of dielectric line defects. We show that the guided modes in 3D PC waveguides strongly depend on the volume, position and number of dielectric defects introduced. We have succeeded in designing a waveguide structure with a large single-mode bandwidth of 178 nm (range = 1,466 to 1,644 nm) for wavelengths used in optical communications. Our study indicates that there is great flexibility in the design of 3D PC waveguides and that a variety of desirable properties can be obtained by altering the configuration of the line defects appropriately.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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Appl. Phys. Lett. (9)

D. Mori, and T. Baba, “Dispersion-controlled optical group delay device by chirped photonic crystal waveguides,” Appl. Phys. Lett. 85, 1101-1103 (2004).
[CrossRef]

H. Takano, B-S. Song, T. Asano, and S. Noda, “Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal,” Appl. Phys. Lett. 86, 241101 (2005).
[CrossRef]

G. Subramania, and S. Y. Lin, “Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography,” Appl. Phys. Lett. 85, 5037-5039 (2004).
[CrossRef]

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

D. Roundy, and J. Joannopoulos, “Photonic crystal structure with square symmetry within each layer and a three-dimensional band gap,” Appl. Phys. Lett. 82, 3835-3837 (2003).
[CrossRef]

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

M. Bayindir, and E. Ozbay, “Dropping of electromagnetic waves through localized modes in three-dimensional photonic band gap structures,” Appl. Phys. Lett. 81, 4514-4516 (2002).
[CrossRef]

E. Özbay, E. Michel, G. Tuttle, R. Biswas, M. Sigalas, and K-M. Ho, “Micromachined millimeter-wave photonic band-gap crystals,” Appl. Phys. Lett. 64, 2059-2061 (1994).
[CrossRef]

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, 1661-1663 (2003).
[CrossRef]

J. Appl. Phys. (1)

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, 7750-7752 (2004).
[CrossRef]

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

H. S. Sözüer, and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231-239 (1994).
[CrossRef]

Jpn. J. Appl. Phys. (1)

A. Chutinan, and S. Noda, “Design for waveguides in three-dimensional photonic crystals,” Jpn. J. Appl. Phys. 39, 2353-2356 (2000).
[CrossRef]

NATO Advanced Science Institutes Series (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Photonic band gaps and localization,” in Proceedings of the NATO Advanced Science Institutes Series, C. M. Soukoulis, ed. (Plenum, New York, 1993), pp. 235.

Nature (1)

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Nature Mater. (1)

M. Deubel, G. V. Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Mater. 3, 444-447 (2004).
[CrossRef]

Phy. Rev. B (1)

E. Özbay, G. Tuttle, M. Sigalas, C. M. Soukoulis, and K. M. Ho, “Defect structures in a layer-by-layer photonic band-gap crystal,” Phy. Rev. B 51, 13961-13965 (1995).
[CrossRef]

Phys. Rev. B (5)

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, 235110 (2003).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 075313 (2001).
[CrossRef]

M. Okano, and S. Noda, “Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains,” Phys. Rev. B 70, 125105 (2004).
[CrossRef]

M. Bayindir, and E. Ozbay, “Heavy photons at coupled-cavity waveguide band edges in a three-dimensional photonic crystal,” Phys. Rev. B 62, R2247-R2250 (2000).
[CrossRef]

Phys. Rev. Lett. (4)

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

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

K. M. Leung, and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646-2649 (1990).
[CrossRef] [PubMed]

Z. Zhang, and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650-2653 (1990).
[CrossRef] [PubMed]

Science (3)

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

B-S. Song, S. Noda, and T. Asano, “Photonic devices based on in-planehetero photonic crystals,” Science 300, 1537 (2003).
[CrossRef] [PubMed]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Solid State Commun. (1)

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

(a) Schematic representation of a 3D PC waveguide created by changing the width of the red rod. (b) Dispersion relations of guided modes for W A=0.7a (left) and W A=0.8a (right).

Fig. 2.
Fig. 2.

Vertical cross-section, orthogonal to the guided direction, of the magnetic-field component (Hz ) of mode A.

Fig. 3.
Fig. 3.

(a) Schematic representation of a 3D PC waveguide created by inserting an additional rod between two original rods. (b) The dispersion relation of the guided modes.

Fig. 4.
Fig. 4.

Vertical cross-section, orthogonal to the guided direction, of Hz of mode B.

Fig. 5.
Fig. 5.

(a) Schematic representation of a 3D PC waveguide created by introducing a dielectric rod that crosses the original rods. (b) Top view of the defect layer (left) and vertical cross-section of the waveguide structure (right).

Fig. 6.
Fig. 6.

(a) The dispersion relation of the guided modes. (b) Vertical cross-section, orthogonal to the guided direction, of Hx of mode C1.

Fig. 7.
Fig. 7.

(a) Schematic representation of the vertical cross-section of a 3D PC waveguide created by translation of the upper and lower neighboring rods of a single cross rod. (b) The dispersion relation of the guided modes. (c) Vertical cross-section, orthogonal to the guided direction, of Hx of mode C1.

Fig. 8.
Fig. 8.

(a) The layout of upper and lower layers with introduced cross-rod defects and the layout of the middle layer including the original rod. (b) Schematic representation of a 3D PC waveguide created by sandwiching the original rod between two cross rods. (c) Schematic vertical cross-section of the waveguide structure.

Fig. 9.
Fig. 9.

(a) The dispersion relation of the guided modes. (b) Vertical cross-section, orthogonal to the guided direction, of Hx of mode D.

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