Abstract

Transmission properties of the periodic dielectric waveguide (PDWG) formed by aligning a sequence of dielectric cylinders in air are investigated theoretically. Unlike photonic crystal waveguides (PCWs), light confinement in a PDWG is due to total internal reflection. Besides, the dispersion relation of the guided modes is strongly influenced by the dielectric periodicity along the waveguide. The band structure for the guided modes is calculated using a finite-difference time-domain (FDTD) method. The first band is used for guiding light, which makes PDWG single mode. Transmission is calculated using the multiple scattering method for various S shaped PDWGs, each containing two opposite bends. When PDWG operates in appropriate frequency ranges, high transmission (above 90%) is observed, even if the radius of curvature of the bends is reduced to three wavelengths. This feature indicates that the guiding ability of PDWG can be made better than the conventional waveguide when used in an optical circuit. In addition, PDWG has the advantage that it can be bent to any arbitrary shape while still preserves the high transmission, avoiding the geometric restriction that PCW is subject to.

© 2006 Optical Society of America

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References

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  1. J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals-Molding the Flow of Light (Princeton University Press, 1995).
  2. Kazuaki Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).
  3. C. Kittel, Introduction to Solid State Physics, 7th ed., (John Wiley & Sons, Inc., 1996).
  4. Attila Mekis, J. C. Chen, I. Kurland, Shanhui Fan, Pierre R. Villeneuve, and J.D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
    [CrossRef] [PubMed]
  5. A. Talneau, L. Le Gouezigou, N. Bouadma,M. Kafesaki, and C.M. Soukoulis, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).
    [CrossRef]
  6. A. Chutinan, M. Okano, and S. Noda, "Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 80, 1698-1700 (2002).
    [CrossRef]
  7. Amnon Yariv, Yong Xu, Reginald K. Lee, and Axel Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999).
    [CrossRef]
  8. Shayan Mookherjea, "Dispersion characteristics of coupled-resonator optical waveguides," Opt. Lett. 30, 2406-2408 (2005).
    [CrossRef] [PubMed]
  9. S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, "Analysis of defect coupling in oneand two-dimensional photonic crystals," Phys. Rev. B 65, 165208 (2002).
    [CrossRef]
  10. Shanhui Fan, N. Winn, Adrian Devenyi, J. C. Chen, Robert D. Meade, and J.D. Joannopoulos, "Guided and defect modes in periodic dielectric waveguides," J. Opt. Soc. Am. B 12, 1267-1272 (1995).
    [CrossRef]
  11. DmitryN. Chigrin, Andrei V. Lavrinenko, Clivia M. Sotomayer Torres, "Nanopillars photonic crystal waveguides," Opt. Express 12, 617-622 (2004).
    [CrossRef] [PubMed]
  12. M. Qiu and S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," J. Appl. Phys. 87, 8268-8275 (2000).
    [CrossRef]
  13. 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, 855-858 (2000).
    [CrossRef]
  14. BikashC. Gupta, Chao Hsien Kuo, and Zhen Ye, "Propagation inhibition and localization of electromagnetic waves in two-dimensional random dielectric systems," Phys. Rev. E 69, 066615 (2004).
    [CrossRef]
  15. Katsunari Okamoto, Fundamentals of Optical Waveguides (Academic Press, first Edition, 2000).

2005

2004

DmitryN. Chigrin, Andrei V. Lavrinenko, Clivia M. Sotomayer Torres, "Nanopillars photonic crystal waveguides," Opt. Express 12, 617-622 (2004).
[CrossRef] [PubMed]

BikashC. Gupta, Chao Hsien Kuo, and Zhen Ye, "Propagation inhibition and localization of electromagnetic waves in two-dimensional random dielectric systems," Phys. Rev. E 69, 066615 (2004).
[CrossRef]

2002

A. Talneau, L. Le Gouezigou, N. Bouadma,M. Kafesaki, and C.M. Soukoulis, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

A. Chutinan, M. Okano, and S. Noda, "Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 80, 1698-1700 (2002).
[CrossRef]

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, "Analysis of defect coupling in oneand two-dimensional photonic crystals," Phys. Rev. B 65, 165208 (2002).
[CrossRef]

2000

M. Qiu and S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," J. Appl. Phys. 87, 8268-8275 (2000).
[CrossRef]

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, 855-858 (2000).
[CrossRef]

1999

1996

Attila Mekis, J. C. Chen, I. Kurland, Shanhui Fan, Pierre R. Villeneuve, and J.D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

1995

Asakawa, K.

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, "Analysis of defect coupling in oneand two-dimensional photonic crystals," Phys. Rev. B 65, 165208 (2002).
[CrossRef]

Attila Mekis,

Attila Mekis, J. C. Chen, I. Kurland, Shanhui Fan, Pierre R. Villeneuve, and J.D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Bayindir, M.

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, 855-858 (2000).
[CrossRef]

Bikash,

BikashC. Gupta, Chao Hsien Kuo, and Zhen Ye, "Propagation inhibition and localization of electromagnetic waves in two-dimensional random dielectric systems," Phys. Rev. E 69, 066615 (2004).
[CrossRef]

Bouadma, N.

A. Talneau, L. Le Gouezigou, N. Bouadma,M. Kafesaki, and C.M. Soukoulis, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

Chutinan, A.

A. Chutinan, M. Okano, and S. Noda, "Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 80, 1698-1700 (2002).
[CrossRef]

Dmitry,

He, S.

M. Qiu and S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," J. Appl. Phys. 87, 8268-8275 (2000).
[CrossRef]

Ikeda, N.

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, "Analysis of defect coupling in oneand two-dimensional photonic crystals," Phys. Rev. B 65, 165208 (2002).
[CrossRef]

Ishikawa, H.

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, "Analysis of defect coupling in oneand two-dimensional photonic crystals," Phys. Rev. B 65, 165208 (2002).
[CrossRef]

Kafesaki, M.

A. Talneau, L. Le Gouezigou, N. Bouadma,M. Kafesaki, and C.M. Soukoulis, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

Lan, S.

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, "Analysis of defect coupling in oneand two-dimensional photonic crystals," Phys. Rev. B 65, 165208 (2002).
[CrossRef]

Le Gouezigou, L.

A. Talneau, L. Le Gouezigou, N. Bouadma,M. Kafesaki, and C.M. Soukoulis, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

Nishikawa, S.

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, "Analysis of defect coupling in oneand two-dimensional photonic crystals," Phys. Rev. B 65, 165208 (2002).
[CrossRef]

Noda, S.

A. Chutinan, M. Okano, and S. Noda, "Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 80, 1698-1700 (2002).
[CrossRef]

Okano, M.

A. Chutinan, M. Okano, and S. Noda, "Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 80, 1698-1700 (2002).
[CrossRef]

Ozbay, E.

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, 855-858 (2000).
[CrossRef]

Qiu, M.

M. Qiu and S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," J. Appl. Phys. 87, 8268-8275 (2000).
[CrossRef]

Shanhui Fan,

Soukoulis, C.M.

A. Talneau, L. Le Gouezigou, N. Bouadma,M. Kafesaki, and C.M. Soukoulis, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

Sugimoto, Y.

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, "Analysis of defect coupling in oneand two-dimensional photonic crystals," Phys. Rev. B 65, 165208 (2002).
[CrossRef]

Talneau, A.

A. Talneau, L. Le Gouezigou, N. Bouadma,M. Kafesaki, and C.M. Soukoulis, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

Temelkuran, B.

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, 855-858 (2000).
[CrossRef]

Appl. Phys. Lett.

A. Talneau, L. Le Gouezigou, N. Bouadma,M. Kafesaki, and C.M. Soukoulis, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).
[CrossRef]

A. Chutinan, M. Okano, and S. Noda, "Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 80, 1698-1700 (2002).
[CrossRef]

J. Appl. Phys.

M. Qiu and S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," J. Appl. Phys. 87, 8268-8275 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rev. B

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, 855-858 (2000).
[CrossRef]

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, "Analysis of defect coupling in oneand two-dimensional photonic crystals," Phys. Rev. B 65, 165208 (2002).
[CrossRef]

Phys. Rev. E

BikashC. Gupta, Chao Hsien Kuo, and Zhen Ye, "Propagation inhibition and localization of electromagnetic waves in two-dimensional random dielectric systems," Phys. Rev. E 69, 066615 (2004).
[CrossRef]

Phys. Rev. Lett.

Attila Mekis, J. C. Chen, I. Kurland, Shanhui Fan, Pierre R. Villeneuve, and J.D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Other

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

Kazuaki Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).

C. Kittel, Introduction to Solid State Physics, 7th ed., (John Wiley & Sons, Inc., 1996).

Katsunari Okamoto, Fundamentals of Optical Waveguides (Academic Press, first Edition, 2000).

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Figures (7)

Fig. 1.
Fig. 1.

(a) Band structure (the first and second bands) of the TM (E-polarization) modes of the PDWG. The part of dispersion curve inside the shaded region corresponds to the extended modes, which cannot be used to guide light. Inset also shows the a×9a sized supercell, which is used in calculating the band structure. The radius of the dielectric cylinder is r = 0.2a, and its dielectric constant is ε = 11.56. (b) The group velocity derived from the dispersion curve of the first band.

Fig. 2.
Fig. 2.

(a) The snapshot of E-field pattern (the real part of the complex amplitude) for the mode with frequency ω = 0.25(2πc/a) and Bloch wavevector k = 0.4(2π/a)x̂. (b) The field pattern in (a), when multiplied by the factor (-1) n and evaluated at the center of the nth cylinder, fits to a sinusoidal wave. The wavelength is about 10a.

Fig. 3.
Fig. 3.

The transmission properties of PDWGs. (a1) A typical straight PDWG. Two planes of width 6a inserted at x = 19.5a and x = (N - 1.5)a for an N-cylinder PDWG are used for evaluating the input power Pi and output power Po . The transmission is defined as T =Po /Pi . (a2) Transmission as function of frequency for three straight PDWGs of different lengths. (b1) A typical 90° bent PDWG. (b2) Transmission as function of frequency for four cases of different radii. One lattice period in the bend region for the R = 57.3a,19.1a,11.5a,5.7a waveguides correspond to δ = 1°,3°,5°,10°, respectively. The total number of cylinders of the four waveguides are 114, 54, 42, and 33, respectively.

Fig. 4.
Fig. 4.

The S shaped PDWG. The bend angle is θ, and the total length is 79a (80 cylinders). The S shaped section of the waveguide contains 38 cylinders. The radius of curvature is R = 11.5a, corresponding to δ = 5°.

Fig. 5.
Fig. 5.

Transmission properties of the S shaped PDWGs. (a) Transmission as function of frequency for four different bend angles. (b) Transmission as function of bend angle for four different frequencies.

Fig. 6.
Fig. 6.

Three types of bent waveguides. (a1) A straight waveguide without any bend. (a2) An S-shaped waveguide formed by combining two 45°-bent waveguides. (a3) A U-shaped waveguide formed by combining two 90°-bent waveguides. Transmission in these waveguides is higher than 90% when the working frequency is chosen as ω = 0.25(2πc/a)

Fig. 7.
Fig. 7.

Comparison of the transmission and reflection characteristics between PDWG and CWG. (a) The effective index. (b) The reflection (insertion loss) for the straight waveguides. (c) Transmission as functions of frequency for 90° bent waveguides of two different radii

Equations (10)

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

E ( r , t ) = E ( r ) e i ω t = U ( r ) e i ( kx ω t ) ,
U ( x + a , y ) = U ( x , y ) ,
U ( x , ) = U ( x , ) = 0 .
u = 1 4 ( ε E 2 + μ H 2 ) dydz
J = 1 2 Re ( E y H z * E z H y * ) dydz .
v e = 0 a J d x 0 a u d x ,
k ' = k π a ,
E ( na , y ) = U ( na , y ) e ikna = ( 1 ) n U ( na , y ) e ik na = ( 1 ) n U ( na , y ) e i k ' na .
n eff = c v g
R = 1 P out P inc ,

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