Abstract

The introduction of defects in photonic lattices generally allows to control the localization and the propagation of light. While point defects are conventionally used in order to obtain localized photonic states, linear defects are introduced for waveguiding EM waves. In this work we demonstrate the possibility of obtaining localized states also in a waveguiding configuration, by using quasicrystalline lattices. This result opens a new range of possibilities in designing optical circuits, in which the localization-propagation switch is easly obtainable by mechanical or opto-electric methods.

© 2012 OSA

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58, 2059–2062 (1987)
    [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58, 2486–2489 (1987)
    [CrossRef] [PubMed]
  3. E. Kuramochi, H. Taniyama, T. Tanabe, A. Shinya, and M. Notomi, “Ultrahigh-Q two-dimentional photonic crystal slab nanocavities in very thin barriers,” Applied Physics Letters93, 111112 (2008)
    [CrossRef]
  4. E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106, 203902 (2011)
    [CrossRef] [PubMed]
  5. F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett.100, 013904 (2008)
    [CrossRef] [PubMed]
  6. J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science282, 5393 (1998)
    [CrossRef]
  7. D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translational symmetry,” Phys. Rev. Lett.53, 1951–1953 (1984)
    [CrossRef]
  8. D. Levine and P. J. Steinhardt, “Quasicrystals: a new class of ordered structures,” Phys. Rev. Lett.53, 2477–2480 (1984)
    [CrossRef]
  9. Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80, 956–959 (1998)
    [CrossRef]
  10. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express8, 3, 173–190 (2001)
    [CrossRef]
  11. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications181, 687–702 (2010)
    [CrossRef]
  12. M. Oxborrow and C. L. Henley, “Random square-triangle tilings: A model for twelvefold-symmetric quasicrystals,” Phys. Rev. B48, 6966–6998 (1993)
    [CrossRef]
  13. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Molding the Flow of Light (Princeton University Press, 2008)
  14. S. R. Davis, S.D. Rommel, G. Farca, and M. H. Anderson, “A new electro-optic waveguide architecture and the unprecedented devices it enables,” Proc. SPIE6975, 697503 (2008)
    [CrossRef]
  15. W. Ruan, G. Li, J. Zeng, L. S. Kanzina, H. Zheng, K. Zhao, L. Zheng, and A. Ding, “Origin of the giant electro-optic Kerr effect in La-doped 75PMN-25PT transparent ceramics,” J. Appl. Phys.110, 074109 (2011)
    [CrossRef]

2011 (2)

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106, 203902 (2011)
[CrossRef] [PubMed]

W. Ruan, G. Li, J. Zeng, L. S. Kanzina, H. Zheng, K. Zhao, L. Zheng, and A. Ding, “Origin of the giant electro-optic Kerr effect in La-doped 75PMN-25PT transparent ceramics,” J. Appl. Phys.110, 074109 (2011)
[CrossRef]

2010 (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications181, 687–702 (2010)
[CrossRef]

2008 (3)

S. R. Davis, S.D. Rommel, G. Farca, and M. H. Anderson, “A new electro-optic waveguide architecture and the unprecedented devices it enables,” Proc. SPIE6975, 697503 (2008)
[CrossRef]

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett.100, 013904 (2008)
[CrossRef] [PubMed]

E. Kuramochi, H. Taniyama, T. Tanabe, A. Shinya, and M. Notomi, “Ultrahigh-Q two-dimentional photonic crystal slab nanocavities in very thin barriers,” Applied Physics Letters93, 111112 (2008)
[CrossRef]

2001 (1)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express8, 3, 173–190 (2001)
[CrossRef]

1998 (2)

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80, 956–959 (1998)
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science282, 5393 (1998)
[CrossRef]

1993 (1)

M. Oxborrow and C. L. Henley, “Random square-triangle tilings: A model for twelvefold-symmetric quasicrystals,” Phys. Rev. B48, 6966–6998 (1993)
[CrossRef]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58, 2059–2062 (1987)
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58, 2486–2489 (1987)
[CrossRef] [PubMed]

1984 (2)

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translational symmetry,” Phys. Rev. Lett.53, 1951–1953 (1984)
[CrossRef]

D. Levine and P. J. Steinhardt, “Quasicrystals: a new class of ordered structures,” Phys. Rev. Lett.53, 2477–2480 (1984)
[CrossRef]

Anderson, M. H.

S. R. Davis, S.D. Rommel, G. Farca, and M. H. Anderson, “A new electro-optic waveguide architecture and the unprecedented devices it enables,” Proc. SPIE6975, 697503 (2008)
[CrossRef]

Arcizet, O.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106, 203902 (2011)
[CrossRef] [PubMed]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications181, 687–702 (2010)
[CrossRef]

Beveratos, A.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106, 203902 (2011)
[CrossRef] [PubMed]

Birks, T. A.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science282, 5393 (1998)
[CrossRef]

Blech, I.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translational symmetry,” Phys. Rev. Lett.53, 1951–1953 (1984)
[CrossRef]

Braive, R.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106, 203902 (2011)
[CrossRef] [PubMed]

Broeng, J.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science282, 5393 (1998)
[CrossRef]

Cahn, J. W.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translational symmetry,” Phys. Rev. Lett.53, 1951–1953 (1984)
[CrossRef]

Chan, C. T.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80, 956–959 (1998)
[CrossRef]

Chan, Y. S.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80, 956–959 (1998)
[CrossRef]

Davis, S. R.

S. R. Davis, S.D. Rommel, G. Farca, and M. H. Anderson, “A new electro-optic waveguide architecture and the unprecedented devices it enables,” Proc. SPIE6975, 697503 (2008)
[CrossRef]

Ding, A.

W. Ruan, G. Li, J. Zeng, L. S. Kanzina, H. Zheng, K. Zhao, L. Zheng, and A. Ding, “Origin of the giant electro-optic Kerr effect in La-doped 75PMN-25PT transparent ceramics,” J. Appl. Phys.110, 074109 (2011)
[CrossRef]

Farca, G.

S. R. Davis, S.D. Rommel, G. Farca, and M. H. Anderson, “A new electro-optic waveguide architecture and the unprecedented devices it enables,” Proc. SPIE6975, 697503 (2008)
[CrossRef]

Gavartin, E.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106, 203902 (2011)
[CrossRef] [PubMed]

Gratias, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translational symmetry,” Phys. Rev. Lett.53, 1951–1953 (1984)
[CrossRef]

Haldane, F. D. M.

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett.100, 013904 (2008)
[CrossRef] [PubMed]

Henley, C. L.

M. Oxborrow and C. L. Henley, “Random square-triangle tilings: A model for twelvefold-symmetric quasicrystals,” Phys. Rev. B48, 6966–6998 (1993)
[CrossRef]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications181, 687–702 (2010)
[CrossRef]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications181, 687–702 (2010)
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express8, 3, 173–190 (2001)
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Molding the Flow of Light (Princeton University Press, 2008)

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58, 2486–2489 (1987)
[CrossRef] [PubMed]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications181, 687–702 (2010)
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express8, 3, 173–190 (2001)
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Molding the Flow of Light (Princeton University Press, 2008)

Kanzina, L. S.

W. Ruan, G. Li, J. Zeng, L. S. Kanzina, H. Zheng, K. Zhao, L. Zheng, and A. Ding, “Origin of the giant electro-optic Kerr effect in La-doped 75PMN-25PT transparent ceramics,” J. Appl. Phys.110, 074109 (2011)
[CrossRef]

Kippenberg, T. J.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106, 203902 (2011)
[CrossRef] [PubMed]

Knight, J. C.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science282, 5393 (1998)
[CrossRef]

Kuramochi, E.

E. Kuramochi, H. Taniyama, T. Tanabe, A. Shinya, and M. Notomi, “Ultrahigh-Q two-dimentional photonic crystal slab nanocavities in very thin barriers,” Applied Physics Letters93, 111112 (2008)
[CrossRef]

Levine, D.

D. Levine and P. J. Steinhardt, “Quasicrystals: a new class of ordered structures,” Phys. Rev. Lett.53, 2477–2480 (1984)
[CrossRef]

Li, G.

W. Ruan, G. Li, J. Zeng, L. S. Kanzina, H. Zheng, K. Zhao, L. Zheng, and A. Ding, “Origin of the giant electro-optic Kerr effect in La-doped 75PMN-25PT transparent ceramics,” J. Appl. Phys.110, 074109 (2011)
[CrossRef]

Liu, Z. Y.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80, 956–959 (1998)
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Molding the Flow of Light (Princeton University Press, 2008)

Notomi, M.

E. Kuramochi, H. Taniyama, T. Tanabe, A. Shinya, and M. Notomi, “Ultrahigh-Q two-dimentional photonic crystal slab nanocavities in very thin barriers,” Applied Physics Letters93, 111112 (2008)
[CrossRef]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications181, 687–702 (2010)
[CrossRef]

Oxborrow, M.

M. Oxborrow and C. L. Henley, “Random square-triangle tilings: A model for twelvefold-symmetric quasicrystals,” Phys. Rev. B48, 6966–6998 (1993)
[CrossRef]

Raghu, S.

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett.100, 013904 (2008)
[CrossRef] [PubMed]

Robert-Philip, I.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106, 203902 (2011)
[CrossRef] [PubMed]

Rommel, S.D.

S. R. Davis, S.D. Rommel, G. Farca, and M. H. Anderson, “A new electro-optic waveguide architecture and the unprecedented devices it enables,” Proc. SPIE6975, 697503 (2008)
[CrossRef]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications181, 687–702 (2010)
[CrossRef]

Ruan, W.

W. Ruan, G. Li, J. Zeng, L. S. Kanzina, H. Zheng, K. Zhao, L. Zheng, and A. Ding, “Origin of the giant electro-optic Kerr effect in La-doped 75PMN-25PT transparent ceramics,” J. Appl. Phys.110, 074109 (2011)
[CrossRef]

Russell, P. S. J.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science282, 5393 (1998)
[CrossRef]

Sagnes, I.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106, 203902 (2011)
[CrossRef] [PubMed]

Shechtman, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translational symmetry,” Phys. Rev. Lett.53, 1951–1953 (1984)
[CrossRef]

Shinya, A.

E. Kuramochi, H. Taniyama, T. Tanabe, A. Shinya, and M. Notomi, “Ultrahigh-Q two-dimentional photonic crystal slab nanocavities in very thin barriers,” Applied Physics Letters93, 111112 (2008)
[CrossRef]

Steinhardt, P. J.

D. Levine and P. J. Steinhardt, “Quasicrystals: a new class of ordered structures,” Phys. Rev. Lett.53, 2477–2480 (1984)
[CrossRef]

Tanabe, T.

E. Kuramochi, H. Taniyama, T. Tanabe, A. Shinya, and M. Notomi, “Ultrahigh-Q two-dimentional photonic crystal slab nanocavities in very thin barriers,” Applied Physics Letters93, 111112 (2008)
[CrossRef]

Taniyama, H.

E. Kuramochi, H. Taniyama, T. Tanabe, A. Shinya, and M. Notomi, “Ultrahigh-Q two-dimentional photonic crystal slab nanocavities in very thin barriers,” Applied Physics Letters93, 111112 (2008)
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Molding the Flow of Light (Princeton University Press, 2008)

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58, 2059–2062 (1987)
[CrossRef] [PubMed]

Zeng, J.

W. Ruan, G. Li, J. Zeng, L. S. Kanzina, H. Zheng, K. Zhao, L. Zheng, and A. Ding, “Origin of the giant electro-optic Kerr effect in La-doped 75PMN-25PT transparent ceramics,” J. Appl. Phys.110, 074109 (2011)
[CrossRef]

Zhao, K.

W. Ruan, G. Li, J. Zeng, L. S. Kanzina, H. Zheng, K. Zhao, L. Zheng, and A. Ding, “Origin of the giant electro-optic Kerr effect in La-doped 75PMN-25PT transparent ceramics,” J. Appl. Phys.110, 074109 (2011)
[CrossRef]

Zheng, H.

W. Ruan, G. Li, J. Zeng, L. S. Kanzina, H. Zheng, K. Zhao, L. Zheng, and A. Ding, “Origin of the giant electro-optic Kerr effect in La-doped 75PMN-25PT transparent ceramics,” J. Appl. Phys.110, 074109 (2011)
[CrossRef]

Zheng, L.

W. Ruan, G. Li, J. Zeng, L. S. Kanzina, H. Zheng, K. Zhao, L. Zheng, and A. Ding, “Origin of the giant electro-optic Kerr effect in La-doped 75PMN-25PT transparent ceramics,” J. Appl. Phys.110, 074109 (2011)
[CrossRef]

Applied Physics Letters (1)

E. Kuramochi, H. Taniyama, T. Tanabe, A. Shinya, and M. Notomi, “Ultrahigh-Q two-dimentional photonic crystal slab nanocavities in very thin barriers,” Applied Physics Letters93, 111112 (2008)
[CrossRef]

Computer Physics Communications (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications181, 687–702 (2010)
[CrossRef]

J. Appl. Phys. (1)

W. Ruan, G. Li, J. Zeng, L. S. Kanzina, H. Zheng, K. Zhao, L. Zheng, and A. Ding, “Origin of the giant electro-optic Kerr effect in La-doped 75PMN-25PT transparent ceramics,” J. Appl. Phys.110, 074109 (2011)
[CrossRef]

Opt. Express (1)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express8, 3, 173–190 (2001)
[CrossRef]

Phys. Rev. B (1)

M. Oxborrow and C. L. Henley, “Random square-triangle tilings: A model for twelvefold-symmetric quasicrystals,” Phys. Rev. B48, 6966–6998 (1993)
[CrossRef]

Phys. Rev. Lett. (7)

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106, 203902 (2011)
[CrossRef] [PubMed]

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett.100, 013904 (2008)
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58, 2059–2062 (1987)
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58, 2486–2489 (1987)
[CrossRef] [PubMed]

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translational symmetry,” Phys. Rev. Lett.53, 1951–1953 (1984)
[CrossRef]

D. Levine and P. J. Steinhardt, “Quasicrystals: a new class of ordered structures,” Phys. Rev. Lett.53, 2477–2480 (1984)
[CrossRef]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80, 956–959 (1998)
[CrossRef]

Proc. SPIE (1)

S. R. Davis, S.D. Rommel, G. Farca, and M. H. Anderson, “A new electro-optic waveguide architecture and the unprecedented devices it enables,” Proc. SPIE6975, 697503 (2008)
[CrossRef]

Science (1)

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science282, 5393 (1998)
[CrossRef]

Other (1)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Molding the Flow of Light (Princeton University Press, 2008)

Supplementary Material (1)

» Media 1: AVI (427 KB)     

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Figures (4)

Fig. 1
Fig. 1

(a) Illustration of the Stampfli inflation rule. (b) Dielectric distribution of the supercell approximant used in the calculations. The rectangular supercell for the calculation of the 2D bulk band structure (full line) contains 116 rods of alumina with ε = 8.6 and radius r = 0.3a, surrounded by vacuum (ε0 = 1). Periodic boundary conditions in x and y directions are imposed, so as to take advantage of translational symmetry. With a 50% extension of the supercell in the x direction (broken line) a vacuum slab is inserted so as to create a periodic array of quasi-crystalline slabs separated by vacuum cavities. In this case small indentations (as the one evidenced by the circle) appear along the slab contours. (c) Photonic band structure of the dodecagonal photonic quasicrystal in slab configuration. An almost perfectly flat branch (red dashed line), corresponding to strongly localized states, occurs in the gap at a frequency (zone-center value) ν = 0.298779c/a. In the inset the irreducible Brillouin zone is shown. (d) On a magnified scale the flat branch shows a little dispersion. At the M point the flat branch is localized in a small gap between two narrow tips of the dispersed branch (inset).

Fig. 2
Fig. 2

(a) TM-polarized electric field distribution of the localized state at the Γ point. The field localization is the same all along the flat branch in the Brillouin zone. (b) A small perturbation in the dielectric constant produces a dispersion near the M point, and a consequent transformation of the electric field into a plane wave through the waveguide. The same result is obtained by slightly decreasing the vacuum region thickness. (c) On the contrary an increase of the vacuum region thickness cause a delocalization of the electric field into the slabs.

Fig. 3
Fig. 3

(a) Z-component of the electric field after 10 a/c, from a gaussian current source pulse J(ω, t) = (−)−1texp(−iωt − (tt0)2/2σ2), centered at ω = 2π · 0.298779 c/a. The source has a frequency width of 1/σ = 0.005 c/a and it is turned off after 600 a/c. (b) After 103a/c the electro-magnetic radiation is almost completely trapped inside the cavity between the slab walls at the circular indentations, provided the vacuum region width is exactly d = ( 3 / 2 + 3 ) a ( Media 1).

Fig. 4
Fig. 4

The integral of the trapped EM energy, after reaching the maximum Im(raise time of ∼ 103a/c), starts a very slow dissipation, linear with time. The dissipation time for the slab thickness of 2d is about 2 · 10−6Imc/a (blue and thin line), but becomes much longer (red and tick line) for a doubled slab thickness of 4d and the same gap width.

Equations (1)

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× ( 1 ε ( r ) × H ( r ) ) = ( w c ) 2 H ( r ) ,

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