Abstract

We propose and investigate ultrafast switching of light beams between different ports of a multibranch waveguide in photonic crystals. The branched waveguide is made of chains of coupled defects with degenerate states providing guided modes. Introduced at the corner of branches is a control cell made of an electro-optical active material. Depending on the symmetry of the refractive index changes, light propagation can be directed to specified direction. Dynamic changes of refractive index then provide ultrafast switching of light beams into a desired branch.

© 2006 Optical Society of America

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  1. T. F. Krauss, "Planar photonic crystal waveguide devices for integrated optics," Phys. Status Solidi A 197, 688-702 (2003).
    [CrossRef]
  2. H. Kosaka, T. Kawashima, A. Tomita, M. Natomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
    [CrossRef]
  3. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999).
    [CrossRef]
  4. 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]
  5. N. Stefanou and A. Modinos, "Impurity bands in photonic insulators," Phys. Rev. B 57, 12127-12133 (1998).
    [CrossRef]
  6. N. Malkova and C. Z. Ning, "Photonic crystal waveguide with acute bending angle," Appl. Phys. Lett. 85, 161113 (2005).
    [CrossRef]
  7. K. Busch and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
    [CrossRef]
  8. K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
    [CrossRef]
  9. S. Xiong and H. Fakshima, "Analysis of light propagation in index-tunable photonic crystals," J. Appl. Phys. 94, 1286-1288 (2003).
    [CrossRef]
  10. D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
    [CrossRef]
  11. Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, W. H. Steier, "Low (sub 1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
    [CrossRef]
  12. A. Lovinger, "Ferroelectric polymers," Science 220, 1115-1121 (1983).
    [CrossRef] [PubMed]
  13. L. R. Dalton, "Rational design of organic electro-optic materials," J. Phys.: Condens. Matter 15, R897-R934 (2003).
    [CrossRef]
  14. A. Yariv and P. Yeh, Optical Waves in Crystals, (Wiley-Interscience, 1984).
  15. K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001).
  16. L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Nauka, 1974).
  17. N. Malkova, S. Kim, and V. Gopalan, "Jahn-Teller effect in two-dimensional photonic crystals," Phys. Rev. B 68, 045105 (2003).
    [CrossRef]
  18. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).
  19. N. Malkova and V. Gopalan, "Strain-tunable optical valves at T-junction waveguides in photonic crystals," Phys. Rev. B 68, 245115 (2003).
    [CrossRef]

2005 (1)

N. Malkova and C. Z. Ning, "Photonic crystal waveguide with acute bending angle," Appl. Phys. Lett. 85, 161113 (2005).
[CrossRef]

2003 (6)

S. Xiong and H. Fakshima, "Analysis of light propagation in index-tunable photonic crystals," J. Appl. Phys. 94, 1286-1288 (2003).
[CrossRef]

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

L. R. Dalton, "Rational design of organic electro-optic materials," J. Phys.: Condens. Matter 15, R897-R934 (2003).
[CrossRef]

N. Malkova, S. Kim, and V. Gopalan, "Jahn-Teller effect in two-dimensional photonic crystals," Phys. Rev. B 68, 045105 (2003).
[CrossRef]

N. Malkova and V. Gopalan, "Strain-tunable optical valves at T-junction waveguides in photonic crystals," Phys. Rev. B 68, 245115 (2003).
[CrossRef]

T. F. Krauss, "Planar photonic crystal waveguide devices for integrated optics," Phys. Status Solidi A 197, 688-702 (2003).
[CrossRef]

2000 (1)

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, W. H. Steier, "Low (sub 1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

1999 (4)

K. Busch and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Natomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999).
[CrossRef]

1998 (1)

N. Stefanou and A. Modinos, "Impurity bands in photonic insulators," Phys. Rev. B 57, 12127-12133 (1998).
[CrossRef]

1996 (1)

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]

1983 (1)

A. Lovinger, "Ferroelectric polymers," Science 220, 1115-1121 (1983).
[CrossRef] [PubMed]

Bechtel, J. H.

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, W. H. Steier, "Low (sub 1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

Busch, K.

K. Busch and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[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]

Dalton, L. R.

L. R. Dalton, "Rational design of organic electro-optic materials," J. Phys.: Condens. Matter 15, R897-R934 (2003).
[CrossRef]

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, W. H. Steier, "Low (sub 1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

Fakshima, H.

S. Xiong and H. Fakshima, "Analysis of light propagation in index-tunable photonic crystals," J. Appl. Phys. 94, 1286-1288 (2003).
[CrossRef]

Fan, S.

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]

Gopalan, V.

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

N. Malkova, S. Kim, and V. Gopalan, "Jahn-Teller effect in two-dimensional photonic crystals," Phys. Rev. B 68, 045105 (2003).
[CrossRef]

N. Malkova and V. Gopalan, "Strain-tunable optical valves at T-junction waveguides in photonic crystals," Phys. Rev. B 68, 245115 (2003).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).

Joannopoulos, J. D.

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]

John, S.

K. Busch and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

Kawagishi, Y.

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Natomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Natomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

Kim, S.

N. Malkova, S. Kim, and V. Gopalan, "Jahn-Teller effect in two-dimensional photonic crystals," Phys. Rev. B 68, 045105 (2003).
[CrossRef]

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Natomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

Krauss, T. F.

T. F. Krauss, "Planar photonic crystal waveguide devices for integrated optics," Phys. Status Solidi A 197, 688-702 (2003).
[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]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Nauka, 1974).

Lee, R. K.

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Nauka, 1974).

Lovinger, A.

A. Lovinger, "Ferroelectric polymers," Science 220, 1115-1121 (1983).
[CrossRef] [PubMed]

Malkova, N.

N. Malkova and C. Z. Ning, "Photonic crystal waveguide with acute bending angle," Appl. Phys. Lett. 85, 161113 (2005).
[CrossRef]

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

N. Malkova, S. Kim, and V. Gopalan, "Jahn-Teller effect in two-dimensional photonic crystals," Phys. Rev. B 68, 045105 (2003).
[CrossRef]

N. Malkova and V. Gopalan, "Strain-tunable optical valves at T-junction waveguides in photonic crystals," Phys. Rev. B 68, 245115 (2003).
[CrossRef]

Mekis, A.

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]

Modinos, A.

N. Stefanou and A. Modinos, "Impurity bands in photonic insulators," Phys. Rev. B 57, 12127-12133 (1998).
[CrossRef]

Nakayama, K.

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

Natomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Natomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

Ning, C. Z.

N. Malkova and C. Z. Ning, "Photonic crystal waveguide with acute bending angle," Appl. Phys. Lett. 85, 161113 (2005).
[CrossRef]

Ozaki, M.

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

Robinson, B. H.

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, W. H. Steier, "Low (sub 1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001).

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Natomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

Scherer, A.

Scrymgeour, D.

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

Shi, Y.

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, W. H. Steier, "Low (sub 1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

Shimoda, Y.

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

Stefanou, N.

N. Stefanou and A. Modinos, "Impurity bands in photonic insulators," Phys. Rev. B 57, 12127-12133 (1998).
[CrossRef]

Steier, W. H.

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, W. H. Steier, "Low (sub 1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Natomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Natomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

Villeneuve, P. R.

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]

Xiong, S.

S. Xiong and H. Fakshima, "Analysis of light propagation in index-tunable photonic crystals," J. Appl. Phys. 94, 1286-1288 (2003).
[CrossRef]

Xu, Y.

Yariv, A.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals, (Wiley-Interscience, 1984).

Yoshino, K.

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

Zhang, C.

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, W. H. Steier, "Low (sub 1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

Zhang, H.

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, W. H. Steier, "Low (sub 1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

Appl. Phys. Lett. (4)

N. Malkova and C. Z. Ning, "Photonic crystal waveguide with acute bending angle," Appl. Phys. Lett. 85, 161113 (2005).
[CrossRef]

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Natomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

J. Appl. Phys. (1)

S. Xiong and H. Fakshima, "Analysis of light propagation in index-tunable photonic crystals," J. Appl. Phys. 94, 1286-1288 (2003).
[CrossRef]

J. Phys.: Condens. Matter (1)

L. R. Dalton, "Rational design of organic electro-optic materials," J. Phys.: Condens. Matter 15, R897-R934 (2003).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (3)

N. Malkova, S. Kim, and V. Gopalan, "Jahn-Teller effect in two-dimensional photonic crystals," Phys. Rev. B 68, 045105 (2003).
[CrossRef]

N. Malkova and V. Gopalan, "Strain-tunable optical valves at T-junction waveguides in photonic crystals," Phys. Rev. B 68, 245115 (2003).
[CrossRef]

N. Stefanou and A. Modinos, "Impurity bands in photonic insulators," Phys. Rev. B 57, 12127-12133 (1998).
[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]

K. Busch and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

Phys. Status Solidi A (1)

T. F. Krauss, "Planar photonic crystal waveguide devices for integrated optics," Phys. Status Solidi A 197, 688-702 (2003).
[CrossRef]

Science (2)

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, W. H. Steier, "Low (sub 1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

A. Lovinger, "Ferroelectric polymers," Science 220, 1115-1121 (1983).
[CrossRef] [PubMed]

Other (4)

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).

A. Yariv and P. Yeh, Optical Waves in Crystals, (Wiley-Interscience, 1984).

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001).

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Nauka, 1974).

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Figures (6)

Fig. 1
Fig. 1

Perturbed potentials that transform through the [(a) and (c)] B 1 and [(b) and (d)] B 2 irreducible representations. (a) and (b) The perturbation caused by the lattice distortions. The filled circle shows the defect rod, and the arrows indicate the lattice displacements. (c) and (d) The perturbation caused by change in the dielectric constant. The plus and minus signs denote an increase or decrease in the dielectric constant of the perturbed rods, ϵ ̃ r ± = ϵ r ± Δ ϵ . The symmetry operations of the C 4 v group are shown in (a).

Fig. 2
Fig. 2

Frequency splitting of the defect level induced by the B 1 mode (solid curve) and by the B 2 mode (dashed curve) versus (a) the dielectric constant change and (b) the lattice distortion. The eigenfunctions for the split states caused by interaction with the [(c) and (d)] B 1 mode and with the [(e) and (f)] B 2 mode are shown.

Fig. 3
Fig. 3

Studied T-shaped coupled-cavity waveguide. Source (S) and two ports (P1, P2) are shown. The insert presents the perturbation of the dielectric constant for the corner cell. The filled black circles show the defect rod.

Fig. 4
Fig. 4

Computed transmission coefficient of the structure for Δ ϵ ϵ r = 0 (dashed curve), 0.1 (dash-dotted curve), 0.2 (solid curve), at (a) port 1 and (b) port 2. The transmission coefficients of the first (solid curve) and second branch (dashed line) without coupling are shown in (c). The frequency of the double-degenerate defect state of the undistorted corner cell is shown by the solid vertical line. Frequencies of the p x + p y and p x p y states at Δ ϵ ϵ r = 0.20 are shown by the dash-dotted and dotted vertical lines, respectively. The distribution of the z component of the electric field in the frequency domain for the resonant frequency corresponding to the maximum of the transmission at ports 1 and 2 at (d) Δ ϵ ϵ r = 0 and (e) 0.20 are shown.

Fig. 5
Fig. 5

Calculated switching characteristics of the T-shaped waveguide shown in Fig. 3. The maximum transmission in the frequency range ω ̃ = [ 0.353 , 0.356 ] at ports 1 and 2 is shown by the dashed and solid curves, respectively.

Fig. 6
Fig. 6

Switch cycle at the frequency ω ̃ = 0.355 . (a) The externally applied electric field to the corner cell drives the index change of the rods nearest to the corner defect to the required value. This results in dynamic switching of the light from (b) port 1 to (c) port 2.

Tables (1)

Tables Icon

Table 1 Character Table for the B 1 and B 2 Representations

Equations (7)

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

Δ n i j = 1 2 n i j 3 ( r i j k E k + s i j k l E k E l ) ,
H = H o + V ( Q r ) .
H o = 1 ϵ ( r ) × .
V i j = ϕ i * V ( Q r ) ϕ j d r .
V ( Q r ) m V ( Q r ) Q r m o Q r m .
V ( Δ ϵ ) = Δ ϵ ( r ) ϵ 2 × ,
V ( Δ R ) = Δ R ( r ) ϵ 2 ϵ r × ,

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