Abstract

We present a three-dimensional (3-D) finite-difference time-domain (FDTD) analysis of the transmission and the waveguiding properties of dielectric structures of finite height. A two-dimensional (2-D) photonic-crystal geometry is used for lateral confinement, and traditional waveguiding by dielectric mismatch is used for vertical confinement. We investigate different types of waveguide in photonic crystals with a finite height. We examine the dependence of the guiding properties on the lengths of the holes that constitute the photonic crystal and the widths of the layers of the waveguide. The role of the filling ratio of the holes and the dielectric constants of the upper and the lower layers for the guiding properties is presented. Also, a comparison between the 3-D and the 2-D FDTD results is given.

© 2002 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2001 (4)

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, “Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides,” Phys. Rev. B 63, R-081107 (2001).
[CrossRef]

E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ=1.55 μm wavelength,” Opt. Lett. 26, 286–288 (2001).
[CrossRef]

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

T. Ochiai and K. Sakoda, “Nearly free-photon approximation for two-dimensional photonic crystal slabs,” Phys. Rev. B 64, 045108 (2001).
[CrossRef]

2000 (8)

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

A. Chutinan and S. Noda, “Design for waveguides in three-dimensional photonic crystals,” Jpn. J. Appl. Phys., Part 1 39, 2353–2356 (2000).
[CrossRef]

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

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

S. Y. Lin, E. Chow, and S. G. Johnson, “Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength,” Opt. Lett. 25, 1297–1299 (2000).
[CrossRef]

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

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

1999 (8)

S. Lin and J. G. Fleming, “A three-dimensional optical photonic crystal,” J. Lightwave Technol. 17, 1944–1947 (1999).
[CrossRef]

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, D. Turner, B. Vasiliu, S. C. Kothari, and S. Lin, “Waveguide bends in three-dimensional layer-by-layer photonic bandgap materials,” Microwave Opt. Technol. Lett. 23, 56–59 (1999).
[CrossRef]

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

I. El-Kady, M. M. Sigalas, R. Biswas, and K. M. Ho, “Dielectric waveguides in two-dimensional photonic bandgap materials,” J. Lightwave Technol. 17, 2042–2049 (1999).
[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]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De la Rue, R. Houdre, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999), and references therein.
[CrossRef]

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]

O. Painter, J. Vuckovic, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
[CrossRef]

1998 (3)

A. Mekis, S. H. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends,” Phys. Rev. B 58, 4809–4817 (1998).
[CrossRef]

B. D’Urso, O. Painter, J. O’Brien, T. Tombrello, A. Yariv, and A. Scherer, “Modal reflectivity in finite-depth two-dimensional photonic-crystal microcavities,” J. Opt. Soc. Am. B 15, 1155–1159 (1998).
[CrossRef]

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, 274–276 (1998).
[CrossRef] [PubMed]

1997 (1)

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdre, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

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

T. F. Krauss, R. M. de la Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 649 (1996).
[CrossRef]

1994 (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]

1984 (1)

Liao boundary conditions are based on extrapolation of the fields in space and time by use of a Newton backward-difference polynomial. They are introduced in Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sin., Ser. A 27, 1063–1076 (1984). Liao boundary conditions are also described in detail in Ref. 31.

Alleman, A.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Baba, T.

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]

Bardinal, V.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdre, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Bayindir, M.

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, “Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides,” Phys. Rev. B 63, R-081107 (2001).
[CrossRef]

Benisty, H.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De la Rue, R. Houdre, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999), and references therein.
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdre, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Beraud, A.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

Biswas, R.

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, “Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides,” Phys. Rev. B 63, R-081107 (2001).
[CrossRef]

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, D. Turner, B. Vasiliu, S. C. Kothari, and S. Lin, “Waveguide bends in three-dimensional layer-by-layer photonic bandgap materials,” Microwave Opt. Technol. Lett. 23, 56–59 (1999).
[CrossRef]

I. El-Kady, M. M. Sigalas, R. Biswas, and K. M. Ho, “Dielectric waveguides in two-dimensional photonic bandgap materials,” J. Lightwave Technol. 17, 2042–2049 (1999).
[CrossRef]

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]

Brand, S.

T. F. Krauss, R. M. de la Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 649 (1996).
[CrossRef]

Cassagne, D.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De la Rue, R. Houdre, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999), and references therein.
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdre, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Chan, C. T.

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]

Chen, J. C.

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]

Chow, E.

E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ=1.55 μm wavelength,” Opt. Lett. 26, 286–288 (2001).
[CrossRef]

S. Y. Lin, E. Chow, and S. G. Johnson, “Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength,” Opt. Lett. 25, 1297–1299 (2000).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[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, 274–276 (1998).
[CrossRef] [PubMed]

Chutinan, A.

A. Chutinan and S. Noda, “Design for waveguides in three-dimensional photonic crystals,” Jpn. J. Appl. Phys., Part 1 39, 2353–2356 (2000).
[CrossRef]

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

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

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

D’Urso, B.

De la Rue, R. M.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De la Rue, R. Houdre, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999), and references therein.
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdre, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

T. F. Krauss, R. M. de la Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 649 (1996).
[CrossRef]

Doll, T.

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

El-Kady, I.

Fan, S.

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]

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]

Fan, S. H.

A. Mekis, S. H. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends,” Phys. Rev. B 58, 4809–4817 (1998).
[CrossRef]

Fleming, J. G.

Fukaya, N.

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]

Hietala, V.

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, 274–276 (1998).
[CrossRef] [PubMed]

Ho, K. M.

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, “Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides,” Phys. Rev. B 63, R-081107 (2001).
[CrossRef]

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, D. Turner, B. Vasiliu, S. C. Kothari, and S. Lin, “Waveguide bends in three-dimensional layer-by-layer photonic bandgap materials,” Microwave Opt. Technol. Lett. 23, 56–59 (1999).
[CrossRef]

I. El-Kady, M. M. Sigalas, R. Biswas, and K. M. Ho, “Dielectric waveguides in two-dimensional photonic bandgap materials,” J. Lightwave Technol. 17, 2042–2049 (1999).
[CrossRef]

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]

Hou, H.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Houdre, R.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De la Rue, R. Houdre, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999), and references therein.
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdre, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Joannopoulos, J. D.

E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ=1.55 μm wavelength,” Opt. Lett. 26, 286–288 (2001).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

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]

A. Mekis, S. H. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends,” Phys. Rev. B 58, 4809–4817 (1998).
[CrossRef]

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, 274–276 (1998).
[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]

Johnson, S. G.

E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ=1.55 μm wavelength,” Opt. Lett. 26, 286–288 (2001).
[CrossRef]

S. Y. Lin, E. Chow, and S. G. Johnson, “Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength,” Opt. Lett. 25, 1297–1299 (2000).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

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]

Jouanin, C.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De la Rue, R. Houdre, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999), and references therein.
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdre, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Kolodziejski, L. A.

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]

Kosaka, H.

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

Kothari, S. C.

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, D. Turner, B. Vasiliu, S. C. Kothari, and S. Lin, “Waveguide bends in three-dimensional layer-by-layer photonic bandgap materials,” Microwave Opt. Technol. Lett. 23, 56–59 (1999).
[CrossRef]

Krauss, T. F.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De la Rue, R. Houdre, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999), and references therein.
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdre, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

T. F. Krauss, R. M. de la Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 649 (1996).
[CrossRef]

Kurland, I.

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]

Labilloy, D.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De la Rue, R. Houdre, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999), and references therein.
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdre, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Liao, Z. P.

Liao boundary conditions are based on extrapolation of the fields in space and time by use of a Newton backward-difference polynomial. They are introduced in Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sin., Ser. A 27, 1063–1076 (1984). Liao boundary conditions are also described in detail in Ref. 31.

Lin, S.

S. Lin and J. G. Fleming, “A three-dimensional optical photonic crystal,” J. Lightwave Technol. 17, 1944–1947 (1999).
[CrossRef]

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, D. Turner, B. Vasiliu, S. C. Kothari, and S. Lin, “Waveguide bends in three-dimensional layer-by-layer photonic bandgap materials,” Microwave Opt. Technol. Lett. 23, 56–59 (1999).
[CrossRef]

Lin, S. Y.

E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ=1.55 μm wavelength,” Opt. Lett. 26, 286–288 (2001).
[CrossRef]

S. Y. Lin, E. Chow, and S. G. Johnson, “Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength,” Opt. Lett. 25, 1297–1299 (2000).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[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, 274–276 (1998).
[CrossRef] [PubMed]

Loncar, M.

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

Mekis, A.

A. Mekis, S. H. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends,” Phys. Rev. B 58, 4809–4817 (1998).
[CrossRef]

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]

Nedeljkovic, D.

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

Noda, S.

A. Chutinan and S. Noda, “Design for waveguides in three-dimensional photonic crystals,” Jpn. J. Appl. Phys., Part 1 39, 2353–2356 (2000).
[CrossRef]

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

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

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

O’Brien, J.

Ochiai, T.

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

T. Ochiai and K. Sakoda, “Nearly free-photon approximation for two-dimensional photonic crystal slabs,” Phys. Rev. B 64, 045108 (2001).
[CrossRef]

Oesterle, U.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De la Rue, R. Houdre, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999), and references therein.
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdre, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Ozbay, E.

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, “Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides,” Phys. Rev. B 63, R-081107 (2001).
[CrossRef]

Painter, O.

Pearsall, T. P.

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

Rattier, M.

Sakoda, K.

T. Ochiai and K. Sakoda, “Nearly free-photon approximation for two-dimensional photonic crystal slabs,” Phys. Rev. B 64, 045108 (2001).
[CrossRef]

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

Scherer, A.

Sigalas, M.

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]

Sigalas, M. M.

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, “Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides,” Phys. Rev. B 63, R-081107 (2001).
[CrossRef]

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, D. Turner, B. Vasiliu, S. C. Kothari, and S. Lin, “Waveguide bends in three-dimensional layer-by-layer photonic bandgap materials,” Microwave Opt. Technol. Lett. 23, 56–59 (1999).
[CrossRef]

I. El-Kady, M. M. Sigalas, R. Biswas, and K. M. Ho, “Dielectric waveguides in two-dimensional photonic bandgap materials,” J. Lightwave Technol. 17, 2042–2049 (1999).
[CrossRef]

Smith, C. J. M.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De la Rue, R. Houdre, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999), and references therein.
[CrossRef]

Soukoulis, C. M.

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, “Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides,” Phys. Rev. B 63, R-081107 (2001).
[CrossRef]

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, D. Turner, B. Vasiliu, S. C. Kothari, and S. Lin, “Waveguide bends in three-dimensional layer-by-layer photonic bandgap materials,” Microwave Opt. Technol. Lett. 23, 56–59 (1999).
[CrossRef]

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]

Temelkuran, B.

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, “Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides,” Phys. Rev. B 63, R-081107 (2001).
[CrossRef]

Tokushima, M.

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

Tombrello, T.

Tomita, A.

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

Tomoda, K.

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

Turner, D.

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, D. Turner, B. Vasiliu, S. C. Kothari, and S. Lin, “Waveguide bends in three-dimensional layer-by-layer photonic bandgap materials,” Microwave Opt. Technol. Lett. 23, 56–59 (1999).
[CrossRef]

Vasiliu, B.

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, D. Turner, B. Vasiliu, S. C. Kothari, and S. Lin, “Waveguide bends in three-dimensional layer-by-layer photonic bandgap materials,” Microwave Opt. Technol. Lett. 23, 56–59 (1999).
[CrossRef]

Vawter, G. A.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Villeneuve, P. B.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Villeneuve, P. R.

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]

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, 274–276 (1998).
[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]

Vuckovic, J.

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

O. Painter, J. Vuckovic, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
[CrossRef]

Weisbuch, C.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De la Rue, R. Houdre, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999), and references therein.
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdre, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Wendt, J. R.

E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ=1.55 μm wavelength,” Opt. Lett. 26, 286–288 (2001).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Wong, H. L.

Liao boundary conditions are based on extrapolation of the fields in space and time by use of a Newton backward-difference polynomial. They are introduced in Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sin., Ser. A 27, 1063–1076 (1984). Liao boundary conditions are also described in detail in Ref. 31.

Yamada, H.

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

Yamamoto, N.

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

Yang, B. P.

Liao boundary conditions are based on extrapolation of the fields in space and time by use of a Newton backward-difference polynomial. They are introduced in Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sin., Ser. A 27, 1063–1076 (1984). Liao boundary conditions are also described in detail in Ref. 31.

Yariv, A.

Yonekura, J.

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]

Yuan, Y. F.

Liao boundary conditions are based on extrapolation of the fields in space and time by use of a Newton backward-difference polynomial. They are introduced in Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sin., Ser. A 27, 1063–1076 (1984). Liao boundary conditions are also described in detail in Ref. 31.

Zubrzycki, W.

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Appl. Phys. Lett. (4)

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

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

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

Electron. Lett. (1)

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]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (2)

Jpn. J. Appl. Phys., Part 1 (1)

A. Chutinan and S. Noda, “Design for waveguides in three-dimensional photonic crystals,” Jpn. J. Appl. Phys., Part 1 39, 2353–2356 (2000).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, D. Turner, B. Vasiliu, S. C. Kothari, and S. Lin, “Waveguide bends in three-dimensional layer-by-layer photonic bandgap materials,” Microwave Opt. Technol. Lett. 23, 56–59 (1999).
[CrossRef]

Nature (2)

T. F. Krauss, R. M. de la Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 649 (1996).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. B (6)

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]

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

T. Ochiai and K. Sakoda, “Nearly free-photon approximation for two-dimensional photonic crystal slabs,” Phys. Rev. B 64, 045108 (2001).
[CrossRef]

A. Mekis, S. H. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends,” Phys. Rev. B 58, 4809–4817 (1998).
[CrossRef]

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, “Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides,” Phys. Rev. B 63, R-081107 (2001).
[CrossRef]

Phys. Rev. Lett. (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, 3787–3790 (1996).
[CrossRef] [PubMed]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdre, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Sci. Sin., Ser. A (1)

Liao boundary conditions are based on extrapolation of the fields in space and time by use of a Newton backward-difference polynomial. They are introduced in Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sin., Ser. A 27, 1063–1076 (1984). Liao boundary conditions are also described in detail in Ref. 31.

Science (2)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[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, 274–276 (1998).
[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]

Other (7)

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, and D. D. Cronch, “Waveguides in photonic band gap materials,” paper presented at the Fourteenth Annual Review on Progress and Applications in Computational Electrodynamics, Monterey, Calif., 1998.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals—Molding the Flow of Light (Princeton U. Press, Princeton, N. J., 1995).

C. M. Soukoulis, ed., Photonic Band Gap Materials, Vol. 315 of NATO Advanced Scientific Institutes Series E, Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1996).

Special section on Electromagnetic Crystal Structures, Design, Synthesis, and Applications, A. Scherer, T. Doll, E. Yablonovitch, E. O. Everitt, and J. A. Higgins, eds., J. Lightwave Technol. 17(11), (1999).

C. M. Soukoulis, Photonic Crystals and Light Localization in the 21st Century (Kluwer Academic, Dordrecht, The Netherlands, 2001).

A. Taflove, Computational Electrodynamics, The Finite Difference Time Domain Method (Artech House, Boston, Mass., 1995).

L. C. Andreani and M. Agio, “Photonic bands and gap maps in a photonic crystal slab,” IEEE J. Quantum Electron. (to be published).

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Figures (15)

Fig. 1
Fig. 1

Three-layer waveguide slab with (a) a PC and (b) a W1 guide (a PC waveguide formed by removing one row of holes from the PC).

Fig. 2
Fig. 2

Field |E| over a yz cross section of the layered structure described for case A (without a PC) at two different times [t1=t0 (top) and t2=2t0 (bottom); t028×10-15 s]. Horizontal lines show the layer interfaces. The units on the axis are grid cells (dy,dz): dy=a/13, dz=a/26; a=400 nm.

Fig. 3
Fig. 3

(Normalized) component of the Poynting vector in the direction of propagation (y) for the layered structure described for case A (without a PC). Syi is the component close to the source, and Sy is the component away from the source. λ is the free-space wavelength, and a=400 nm.

Fig. 4
Fig. 4

Field |E| over a yz cross section of the structure described for case A (three-layer structure with a PC) at t=56×10-15 s. Solid horizontal lines show the layer interfaces; dashed line shows the bottom of the air holes. The units on the axis are grid cells; for the y axis 1 grid cell=dy=a/13; for the z axis dz=a/26. a is the lattice constant (400 nm). Our computational cell consists of eight lattice constants in the propagation direction and eight in the perpendicular direction.

Fig. 5
Fig. 5

ΓK transmission coefficient T plotted versus dimensionless frequency a/λ for the three layer structure that is described for case A with a PC (dashed curve) and with a PC with a W1 guide (solid curve). a is the lattice constant, and λ is the free-space wavelength.

Fig. 6
Fig. 6

Field |E| over a yz cross section of the layered structure described for case B (three-layer structure without a PC) at t=15×10-15 s. Horizontal lines show the layer interfaces. The units on the axis are grid cells (dy,dz): dy=a/14, dz=a/28; a=420 nm.

Fig. 7
Fig. 7

(a) ΓK transmission coefficient (T) versus dimensionless frequency a/λ for the structure described for case B. The source is a Gaussian pulse with a vertical profile that approximates the layers’ guided-mode profile. Dashed curve shows the transmission for a PC; solid curve shows the transmission for a PC with a W1 guide. The cylinder’s depth in the substrate is 400 nm. a is the lattice constant, and λ is the free-space wavelength. (b) Same as in (a) but here we calculate the transmission by normalizing the transmitted power by the power transmitted through the layered heterostructure (the structure without PBG material).

Fig. 8
Fig. 8

(a) Field |E| over a yz cross section of the layered structure described for case C (without a PC) at time t=80×10-15 s. Horizontal lines show the layer interfaces. The units on the axis are grid cells (dy,dz): dy=a/14, dz=a/28; a=420 nm. (b) Poynting vector component in the propagation direction close to the source and away from the source for the system described for (a).

Fig. 9
Fig. 9

Field |E| over a yz cross section of the layered structure described for case C (with a PC) at time t=60×10-15 s. Solid horizontal lines indicate layer interfaces. Dashed horizontal lines indicate lengths of the holes. The hole depth in the InP substrate is (a) ds=400 nm and (b) ds=600 nm. The units on the axis are grid cells (dy,dz): dy=a/14, dz=a/28; a=420 nm.

Fig. 10
Fig. 10

ΓK transmission coefficient T versus dimensionless frequency a/λ for the structure of case C, with an air filling ratio of f=0.4. Dashed curves show the transmission for a PC; solid curves show the transmission for a PC with a W1 guide. The cylinder’s depth in the substrate is 400 nm for (a) and 600 nm for (b). a is the lattice constant, and λ is the free-space wavelength.

Fig. 11
Fig. 11

Field |E| over a yz cross section of the structure described for case C (layered structure with a W1 guide) at time t=80×10-15 s. Solid horizontal lines show the layer interfaces. Dashed horizontal line shows the depth of the holes. The holes’ depth in the InP substrate is ds=600 nm. Units on the axis are grid cells (dy,dz): dy=a/14, dz=a/28; a=420 nm.

Fig. 12
Fig. 12

ΓK transmission coefficient T versus dimensionless frequency a/λ for the structure of case C, with air-filling ratios of (a) f=0.3 and (b) f=0.45. Dashed curves show the transmission for a PC; solid curves show the transmission for a PC with a W1 guide. The holes’ depth in the substrate is 600 nm. a is the lattice constant, and λ is the free-space wavelength.

Fig. 13
Fig. 13

ΓK transmission coefficient T plotted versus dimensionless frequency a/λ for a system of infinite air cylinders (with dielectric constant 1+iim) in a host with =11.56. (a) im=0, (b) im=0.22. Dashed curves show the transmission for a periodic system; solid curves show the transmission for a W1 guide. a is the lattice constant, and λ is the free-space wavelength. The air-filling ratio is f=0.4, and the grid’s pitch is a/34.

Fig. 14
Fig. 14

Same as in Fig. 13 for a host with dielectric constant =10.5. (a) im=0, (b) im=0.2.

Fig. 15
Fig. 15

Upper (filled circles) and lower (open circles) edges of the 2-D gap plotted as a function of ratio r/a for the system shown in Fig. 14. The two gap edges are calculated by the plane-wave method.2 Dashed horizontal lines show the upper and the lower edges of the 3-D gap for an air-filling ratio of f=40%.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

×E=-μμ0 Ht,
×H=0 Et,
Einc(x, y, z, t)=sin{ω[ny0/c-(t-t0)]}×exp{-bt2[ny0/c-(t-t0)]2}×exp[-bx2(x-x0)2]exp[-bz2(z-z0)2].

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