Abstract

A properly designed composite waveguide consisting of a one-dimensional photonic crystal waveguide and a conventional dielectric waveguide is proposed for the realization of a localized “light wheel”. Light confinedly rotating between the two waveguides is numerically demonstrated and explained physically in detail. A delocalized “light wheel” is found at the band gap edge caused by contra-directional coupling between the two waveguides. Because of this delocalized “light wheel” , the composite waveguide can be used to trap light as a cavity, and a quality factor of 9×103 is achieved as an example. The present structure is completely dielectric and thus easy to realize with a low loss.

© 2009 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, NJ, 1995).
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    [Crossref] [PubMed]
  3. T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett.  79, 4289 (2001)
    [Crossref]
  4. 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 = 1.55μm wavelengths,” Opt. Lett.  26, 286 (2001).
    [Crossref]
  5. S. Rennon, F. Klopf, J. P. Reithmaier, and A. Forchel, “12μm long edge-emitting quantum-dot laser ” Electron. Lett.  37, 690 (2001).
    [Crossref]
  6. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, ”Coupled-resonator optical waveguide: A proposal and analysis,” Opt. Lett.  24, 711 (1999)
    [Crossref]
  7. S. H. Kwon, H. Y. Ryu, G. H. Kim, and Y. H. Lee, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett.  83, 3870 (2003).
    [Crossref]
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  10. P. H. Tichit, A. Moreau, and G. Granet, “Localization of light in a lamellar structure with left-handed medium : the Light Wheel,” Opt. Express 15, 14961 (2007).
    [Crossref] [PubMed]
  11. V. G. Veselago, “Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities,” Usp. Fiz. Nauk.  92, 517 (1967).
  12. W. Yan and L. F. Shen, “Open waveguide cavity using a negative index medium,” Opt. Lett 33, 2806 (2008).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  21. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.  87, 253902 (2001).
    [Crossref] [PubMed]

2008 (3)

2007 (2)

2005 (2)

Z. Xu, J. Wang, Q. He, L. Cao, P. Su, and G. Jin, “Optical filter based on contra-directional waveguide coupling in a 2D photonic crystal with square lattice of dielectric rods,” Opt. Express 13, 5608 (2005).
[Crossref] [PubMed]

B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdré, “Fourier analysis of Bloch wave propagation in photonic crystals,” J. Opt. Soc. Am. B  22, 1179 (2005).
[Crossref]

2003 (2)

S. H. Kwon, H. Y. Ryu, G. H. Kim, and Y. H. Lee, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett.  83, 3870 (2003).
[Crossref]

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

2001 (4)

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett.  79, 4289 (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 = 1.55μm wavelengths,” Opt. Lett.  26, 286 (2001).
[Crossref]

S. Rennon, F. Klopf, J. P. Reithmaier, and A. Forchel, “12μm long edge-emitting quantum-dot laser ” Electron. Lett.  37, 690 (2001).
[Crossref]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.  87, 253902 (2001).
[Crossref] [PubMed]

1999 (1)

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, ”Coupled-resonator optical waveguide: A proposal and analysis,” Opt. Lett.  24, 711 (1999)
[Crossref]

1997 (1)

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys.  107, 6756 (1997).
[Crossref]

1991 (1)

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, NY, 1991).

1987 (1)

D. Marcuse, ”Bandwidth of Forward and Backward Coupling Directional Couplers,” IEEE J. Lightwave Technol.  5, 1773–1777 (1987).
[Crossref]

1980 (1)

P. Yeh and H. F. Taylor, ”Contradirectional frequency-selective couplers for guided-wave optics,” Appl. Opt.  19, 2848 (1980).
[Crossref] [PubMed]

1967 (1)

V. G. Veselago, “Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities,” Usp. Fiz. Nauk.  92, 517 (1967).

Akahane, Y.

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

Asano, T.

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

Banyal, R. K.

Cao, L.

Chen, H.

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett.  79, 4289 (2001)
[Crossref]

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 = 1.55μm wavelengths,” Opt. Lett.  26, 286 (2001).
[Crossref]

Deppe, D.

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett.  79, 4289 (2001)
[Crossref]

Drouard, E.

Dunbar, L. A.

B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdré, “Fourier analysis of Bloch wave propagation in photonic crystals,” J. Opt. Soc. Am. B  22, 1179 (2005).
[Crossref]

Ferrier, L.

Ferrini, R.

B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdré, “Fourier analysis of Bloch wave propagation in photonic crystals,” J. Opt. Soc. Am. B  22, 1179 (2005).
[Crossref]

Forchel, A.

S. Rennon, F. Klopf, J. P. Reithmaier, and A. Forchel, “12μm long edge-emitting quantum-dot laser ” Electron. Lett.  37, 690 (2001).
[Crossref]

Granet, G.

He, J.

He, Q.

He, S.

Hong, Z.

Houdré, R.

B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdré, “Fourier analysis of Bloch wave propagation in photonic crystals,” J. Opt. Soc. Am. B  22, 1179 (2005).
[Crossref]

Huang, Y. J.

Jin, G.

Jin, Y.

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 = 1.55μm wavelengths,” Opt. Lett.  26, 286 (2001).
[Crossref]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding The Flow of Light (Princeton, NJ, 1995).

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 = 1.55μm wavelengths,” Opt. Lett.  26, 286 (2001).
[Crossref]

Kim, G. H.

S. H. Kwon, H. Y. Ryu, G. H. Kim, and Y. H. Lee, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett.  83, 3870 (2003).
[Crossref]

Klopf, F.

S. Rennon, F. Klopf, J. P. Reithmaier, and A. Forchel, “12μm long edge-emitting quantum-dot laser ” Electron. Lett.  37, 690 (2001).
[Crossref]

Kwon, S. H.

S. H. Kwon, H. Y. Ryu, G. H. Kim, and Y. H. Lee, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett.  83, 3870 (2003).
[Crossref]

Lee, R. K.

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, ”Coupled-resonator optical waveguide: A proposal and analysis,” Opt. Lett.  24, 711 (1999)
[Crossref]

Lee, Y. H.

S. H. Kwon, H. Y. Ryu, G. H. Kim, and Y. H. Lee, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett.  83, 3870 (2003).
[Crossref]

Letartre, X.

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 = 1.55μm wavelengths,” Opt. Lett.  26, 286 (2001).
[Crossref]

Lombardet, B.

B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdré, “Fourier analysis of Bloch wave propagation in photonic crystals,” J. Opt. Soc. Am. B  22, 1179 (2005).
[Crossref]

Lu, W. T.

Mandelshtam, V. A.

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys.  107, 6756 (1997).
[Crossref]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, NY, 1991).

D. Marcuse, ”Bandwidth of Forward and Backward Coupling Directional Couplers,” IEEE J. Lightwave Technol.  5, 1773–1777 (1987).
[Crossref]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding The Flow of Light (Princeton, NJ, 1995).

Moreau, A.

Noda, S.

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

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.  87, 253902 (2001).
[Crossref] [PubMed]

Perry, C. H.

Reithmaier, J. P.

S. Rennon, F. Klopf, J. P. Reithmaier, and A. Forchel, “12μm long edge-emitting quantum-dot laser ” Electron. Lett.  37, 690 (2001).
[Crossref]

Rennon, S.

S. Rennon, F. Klopf, J. P. Reithmaier, and A. Forchel, “12μm long edge-emitting quantum-dot laser ” Electron. Lett.  37, 690 (2001).
[Crossref]

Rojo-Romeo, P.

Ryu, H. Y.

S. H. Kwon, H. Y. Ryu, G. H. Kim, and Y. H. Lee, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett.  83, 3870 (2003).
[Crossref]

Scherer, A.

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett.  79, 4289 (2001)
[Crossref]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, ”Coupled-resonator optical waveguide: A proposal and analysis,” Opt. Lett.  24, 711 (1999)
[Crossref]

Shen, L. F.

W. Yan and L. F. Shen, “Open waveguide cavity using a negative index medium,” Opt. Lett 33, 2806 (2008).
[Crossref] [PubMed]

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.  87, 253902 (2001).
[Crossref] [PubMed]

Song, B. S.

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

Sridhar, S.

Su, P.

Taflove, A.

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

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.  87, 253902 (2001).
[Crossref] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.  87, 253902 (2001).
[Crossref] [PubMed]

Taylor, H. F.

P. Yeh and H. F. Taylor, ”Contradirectional frequency-selective couplers for guided-wave optics,” Appl. Opt.  19, 2848 (1980).
[Crossref] [PubMed]

Taylor, H. S.

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys.  107, 6756 (1997).
[Crossref]

Tichit, P. H.

Veselago, V. G.

V. G. Veselago, “Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities,” Usp. Fiz. Nauk.  92, 517 (1967).

Viktorovitch, P.

Vodo, P.

Vuckovic, J.

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett.  79, 4289 (2001)
[Crossref]

Wang, J.

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 = 1.55μm wavelengths,” Opt. Lett.  26, 286 (2001).
[Crossref]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding The Flow of Light (Princeton, NJ, 1995).

Xu, Y.

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, ”Coupled-resonator optical waveguide: A proposal and analysis,” Opt. Lett.  24, 711 (1999)
[Crossref]

Xu, Z.

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.  87, 253902 (2001).
[Crossref] [PubMed]

Yan, W.

W. Yan and L. F. Shen, “Open waveguide cavity using a negative index medium,” Opt. Lett 33, 2806 (2008).
[Crossref] [PubMed]

Yariv, A.

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, ”Coupled-resonator optical waveguide: A proposal and analysis,” Opt. Lett.  24, 711 (1999)
[Crossref]

Yeh, P.

P. Yeh and H. F. Taylor, ”Contradirectional frequency-selective couplers for guided-wave optics,” Appl. Opt.  19, 2848 (1980).
[Crossref] [PubMed]

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.  87, 253902 (2001).
[Crossref] [PubMed]

Yoshie, T.

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett.  79, 4289 (2001)
[Crossref]

Appl. Opt (1)

P. Yeh and H. F. Taylor, ”Contradirectional frequency-selective couplers for guided-wave optics,” Appl. Opt.  19, 2848 (1980).
[Crossref] [PubMed]

Appl. Phys. Lett (2)

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett.  79, 4289 (2001)
[Crossref]

S. H. Kwon, H. Y. Ryu, G. H. Kim, and Y. H. Lee, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett.  83, 3870 (2003).
[Crossref]

Electron. Lett (1)

S. Rennon, F. Klopf, J. P. Reithmaier, and A. Forchel, “12μm long edge-emitting quantum-dot laser ” Electron. Lett.  37, 690 (2001).
[Crossref]

IEEE J. Lightwave Technol (1)

D. Marcuse, ”Bandwidth of Forward and Backward Coupling Directional Couplers,” IEEE J. Lightwave Technol.  5, 1773–1777 (1987).
[Crossref]

J. Chem. Phys (1)

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys.  107, 6756 (1997).
[Crossref]

J. Opt. Soc. Am (1)

B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdré, “Fourier analysis of Bloch wave propagation in photonic crystals,” J. Opt. Soc. Am. B  22, 1179 (2005).
[Crossref]

Nature (1)

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

Opt. Express (5)

Opt. Lett (3)

W. Yan and L. F. Shen, “Open waveguide cavity using a negative index medium,” Opt. Lett 33, 2806 (2008).
[Crossref] [PubMed]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, ”Coupled-resonator optical waveguide: A proposal and analysis,” Opt. Lett.  24, 711 (1999)
[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 = 1.55μm wavelengths,” Opt. Lett.  26, 286 (2001).
[Crossref]

Phys. Rev. Lett (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett.  87, 253902 (2001).
[Crossref] [PubMed]

Usp. Fiz. Nauk (1)

V. G. Veselago, “Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities,” Usp. Fiz. Nauk.  92, 517 (1967).

Other (3)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding The Flow of Light (Princeton, NJ, 1995).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, NY, 1991).

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

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Figures (6)

Fig. 1.
Fig. 1.

(a) Schematic diagram of the proposed composite dielectric waveguide structure. (b) Unit cell used in the calculation of the dispersion curves for the composite waveguide shown in (a). In all the numerical examples we choose the following geometric parameters: d 1 = 0.5a, d 2 = 0.5a, w 1 = 1.4a, and w 2 = 1.2a.

Fig. 2.
Fig. 2.

Extended band diagram of the 1D PhC waveguide (solid line) and the dispersion curve of a conventional dielectric waveguide (dashed line). A (in the second Brillouin zone) is the cross point between the two dispersion curves, while A’ is its corresponding point in the first Brillouin zone.

Fig. 3.
Fig. 3.

The band structures for the composite waveguide with different separation distance d. The star (*) points B and C indicate the band edge modes for the cases of separation distances d = 0 and d = 0.6a, respectively.

Fig. 4.
Fig. 4.

(a) The modulus of Hy field in a domain of 15a height and 70a length. White arrows show the propagation direction of light. A Gauss beam is coupled into (a) the composite waveguide; and (b) a single conventional waveguide.

Fig. 5.
Fig. 5.

FDTD-simulated H-field pattern for (a) band edge mode B and (b) band edge mode C. Arrows shows the time averaged Poynting vector.

Fig. 6.
Fig. 6.

The Q-factor of the resonant mode near the band gap edge as the composite waveguide length varies. The inset shows H-field pattern of the resonant mode in the composite waveguide consisting of 27 unit cells. The numbers denote the resonant frequencies in the unit of 2πc/a

Equations (2)

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

Δω = Δλ λ 0 2 = 4 κ π ( c v g + c v g ) ,
L = tanh 1 ( 1 T ) / κ ,

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