Abstract

We systematically investigate and compare general methods of designing single mode photonic crystal waveguides in a two-dimensional hexagonal lattice of air holes in a dielectric material. We apply the rather general methods to dielectric-core hexagonal lattice photonic crystals since they have not been widely explored before. We show that it is possible to obtain single mode guiding in a limited portion of the photonic bandgap of hexagonal lattice structures. We also compare the potentials of different photonic crystal lattices for designing single-mode waveguides and conclude that triangular lattice structures are the best choice.

© 2003 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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  10. A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, and A. Scherer, ???Role of distributed Bragg reflection in photonic-crystal optical waveguides,??? Phys. Rev. B 64, 041102 (1-4) (2001).
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    [CrossRef]
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Appl. Phys. Lett. (1)

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, ???Lightwave propagation through a 120 degrees sharply bent single-line-defect photonic crystal waveguide,??? Appl. Phys. Lett. 76, 952-954 (2000).
[CrossRef]

Electron. Lett. (2)

T. Baba, N. Fukaya, and J. Yonekura, ???Observation of light propagation in photonic crystal optical waveguides with bends,??? Electron. Lett. 35, 654-655 (1999).
[CrossRef]

A. Adibi, R. K. Lee, Y. Xu, A. Yariv, and A. Scherer, ???Design of photonic crystal optical waveguides with singlemode propagation in the photonic bandgap,??? Electron. Lett. 36, 1376-1378 (2000).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. S. Yee, ???Numerical solution of initial boundary value problems involving Maxwell???s equations in isotropic media,??? IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).

J. Comput. Phys. (1)

J. P. Brenger, ???A perfectly matched layer for the absorption of electromagnetic???waves,??? J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

J. Lightwave Technol. (1)

Phys. Rev. B (4)

C. T. Chan, Q. L. Yu, and K. M. Ho, ???Order-N spectral method for electromagnetic-waves,??? Phys. Rev. B 51, 16635-16642 (1995).
[CrossRef]

A. Adibi, Y. Xu, R. K. Lee, A. Yariv, and A. Scherer, ???Guiding mechanism in dielectric-core crystal optical waveguides,??? Phys. Rev. B 64, 033308 (1-4) (2001).
[CrossRef]

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, and A. Scherer, ???Role of distributed Bragg reflection in photonic-crystal optical waveguides,??? Phys. Rev. B 64, 041102 (1-4) (2001).
[CrossRef]

D. Cassagne, C. Jouanin, and D. Bertho, ???Hexagonal photonic-band-gap structures,??? Phys. Rev. B 53, 7134-7142 (1996).
[CrossRef]

Phys. Rev. Lett. (3)

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]

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, 3787-3790 (1996).
[CrossRef] [PubMed]

Physics Rev. B (1)

D. Cassagne, C. Jouanin, and D. Bertho, ???Photonic band gaps in a two-dimensional graphite structure,???Physics Rev. B 52, R2217-R2220 (1995).
[CrossRef]

Science (1)

S. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, ???Experimental demonstration of guiding and bending electromagnetic waves in a photonic crystal,??? Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Other (1)

A. Taflov and S. C. Hagness, Computaional electrodynamics: The finite-difference time-domain method, (Artech House, 2000).

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Figures (3)

Fig. 1.
Fig. 1.

Maps of photonic bandgap for TE (electric field perpendicular to the computation plane) and TM polarizations in a two-dimensional hexagonal-lattice structure of air cylinders in GaAs (ε=12.96) as functions of the ratio r/a.

Fig. 2.
Fig. 2.

(a)–(d) One period of the waveguide structure and magnetic field pattern in a PBG waveguide made by putting a dielectric slab of thickness d between two hexagonal lattice PBG mirrors. The radii of air holes in all cases are r=0.38a, with a being the distance between the centers of nearest neighbor air holes. The thickness of the middle slab in (a) and (b) is d=0.66a, and that in (c) and (d) is d=0.52a. The dispersion diagrams for the two dominant guided TM modes of these PBG waveguides calculated by the FDTD technique are shown in (e). The dielectric material is GaAs with relative permittivity ε=12.96. The distance between the centers of the nearest neighbor holes and the radius of each hole in the photonic crystal are a=29 calculation cells and r=0.38a, respectively. The frequency ranges of bandgap (PBG) and single-mode guiding for d=0.52a are shown in the figure.

Fig. 3.
Fig. 3.

(a) One unit cell of the waveguide structure and the magnetic field patterns for different TM modes of: (a), (b) a specially designed waveguide as discussed in the text, and (c) the equivalent corrugated waveguide made by considering only two rows of the photonic crystal adjacent to the middle slab with air above these two rows. (d) Dispersion diagrams of the dominant guided modes corresponding to hexagonal lattice waveguide and corrugated waveguide shown in (a), (b), and (c). The dielectric material in all waveguides is GaAs (εs =12.96). The cladding region of the corrugated waveguides is air (ε=1). The period of the hexagonal lattice and the radius of each air column in the PBG waveguide are a=29 calculation cells and r=0.38a, respectively.

Tables (1)

Tables Icon

Table 1. Comparison of the maximum photonic bandgap size and the corresponding radius of the air holes in different photonic crystal lattices. The radius of the air holes and the distance between the centers of the nearest neighbor air holes are represented by r, and a, respectively.

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