Abstract

Quasiperiodic Fibonacci-like and fractal Cantor-like single- and multiple-row nanopillar waveguides are investigated theoretically by employing the finite-difference time-domain method. It is shown that resonant modes of the Fibonacci and Cantor waveguides can have a Q factor comparable with that of a point-defect resonator embedded in a periodic nanopillar waveguide, while the radiation is preferably emitted into the waveguide direction, thus improving coupling to an unstructured dielectric waveguide located along the structure axis. This is especially so when the dielectric waveguide introduces a small perturbation in the aperiodic structure, breaking the structure symmetry while staying well apart from the main localization area of the resonant mode. The high-Q factor and increased coupling with the external dielectric waveguide suggest using the proposed deterministically aperiodic nanopillar waveguides in photonic integrated circuits.

© 2006 Optical Society of America

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  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).
  2. K. Sakoda, Optical Properties of Photonic Crystals (Princeton Springer, Berlin, 2001).
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    [CrossRef] [PubMed]
  4. H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Kassagne, A. Béraud, 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]
  5. C. Kim, W. J. Kim, A. Stapleton, J.-R. Cao, J. D. O'Brien, and P. D. Dapkus, "Quality factors in single-defect photonic-crystal lasers with asymmetric cladding layers," J. Opt. Soc. Am. B 19, 1777-1781 (2002).
    [CrossRef]
  6. S.-H. Kwon and Y.-H. Lee, "High index-contrast 2D photonic band-edge laser," IEICE Trans. Electron. E87-C, 308-315 (2004).
  7. H. Cao, "Review on latest developments in random lasers with coherent feedback," J. Phys. A 38, 10497-10535 (2005).
    [CrossRef]
  8. A. L. Burin, H. Cao, G. C. Schatz, and M. A. Ratner, "High-quality modes in low-dimensional array of nanoparticles: application to random lasers," J. Opt. Soc. Am. B 21, 121-131 (2004).
    [CrossRef]
  9. S. Fan, J. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, "Guided and defect modes in periodic dielectric waveguides," J. Opt. Soc. Am. B 12, 1267-1272 (1995).
    [CrossRef]
  10. D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor-Torres, "Nanopillars photonic crystal waveguides," Opt. Express 12, 617-622 (2004).
    [CrossRef] [PubMed]
  11. D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor-Torres, "Numerical characterization of nanopillar photonic crystal waveguides and directional couplers," Opt. Quantum Electron. 37, 331-341 (2005).
    [CrossRef]
  12. M. Tokushima, H. Yamada, and Y. Arakawa, "1.5−μm-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
    [CrossRef]
  13. S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
    [CrossRef]
  14. E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
    [CrossRef]
  15. J. C. Johnson, H. Yan, R. D. Schaller, L. H. Haber, R. J. Saykally, and P. Yang, "Single nanowire lasers," J. Phys. Chem. B 105, 11387-11390 (2001).
    [CrossRef]
  16. S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, "Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78, 3388-3390 (2001).
    [CrossRef]
  17. M. Kohmoto, B. Sutherland, and C. Tang, "Critical wave function and a Cantor-set spectrum of a one-dimensional quasicrystal model," Phys. Rev. B 35, 1020-1033 (1987).
    [CrossRef]
  18. A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirskii, and S. V. Gaponenko, "Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter," Phys. Rev. E 65, 036621 (2002).
    [CrossRef]
  19. C. Janot, Quasicrystals: A Primer (Clarendon, 1994).
  20. S. V. Zhukovsky, A. V. Lavrinenko, and S. V. Gaponenko, "Spectral scalability as a result of geometrical self-similarity in fractal multilayers," Europhys. Lett. 66, 455-461 (2004).
    [CrossRef]
  21. A. V. Lavrinenko, P. I. Borel, L. H. Fradsen, M. Thorhauge, A. Harpøth, M. Kristensen, T. Niemi, and H. Chong, "Comprehensive FDTD modelling of photonic crystal waveguide components," Opt. Express 12, 234-248 (2004).
    [CrossRef] [PubMed]
  22. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
    [CrossRef]
  23. V. V. Zosimov and L. M. Lyamshev, "Fractals in wave processes," Phys. Usp. 38, 347-384 (2005).
    [CrossRef]

2005

D. Englund, I. Fushman, and J. Vuckovic, "General recipe for designing photonic crystal cavities," Opt. Express 13, 5961-5975 (2005).
[CrossRef] [PubMed]

H. Cao, "Review on latest developments in random lasers with coherent feedback," J. Phys. A 38, 10497-10535 (2005).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor-Torres, "Numerical characterization of nanopillar photonic crystal waveguides and directional couplers," Opt. Quantum Electron. 37, 331-341 (2005).
[CrossRef]

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

V. V. Zosimov and L. M. Lyamshev, "Fractals in wave processes," Phys. Usp. 38, 347-384 (2005).
[CrossRef]

2004

D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor-Torres, "Nanopillars photonic crystal waveguides," Opt. Express 12, 617-622 (2004).
[CrossRef] [PubMed]

S. V. Zhukovsky, A. V. Lavrinenko, and S. V. Gaponenko, "Spectral scalability as a result of geometrical self-similarity in fractal multilayers," Europhys. Lett. 66, 455-461 (2004).
[CrossRef]

A. V. Lavrinenko, P. I. Borel, L. H. Fradsen, M. Thorhauge, A. Harpøth, M. Kristensen, T. Niemi, and H. Chong, "Comprehensive FDTD modelling of photonic crystal waveguide components," Opt. Express 12, 234-248 (2004).
[CrossRef] [PubMed]

M. Tokushima, H. Yamada, and Y. Arakawa, "1.5−μm-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
[CrossRef]

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

A. L. Burin, H. Cao, G. C. Schatz, and M. A. Ratner, "High-quality modes in low-dimensional array of nanoparticles: application to random lasers," J. Opt. Soc. Am. B 21, 121-131 (2004).
[CrossRef]

S.-H. Kwon and Y.-H. Lee, "High index-contrast 2D photonic band-edge laser," IEICE Trans. Electron. E87-C, 308-315 (2004).

2002

C. Kim, W. J. Kim, A. Stapleton, J.-R. Cao, J. D. O'Brien, and P. D. Dapkus, "Quality factors in single-defect photonic-crystal lasers with asymmetric cladding layers," J. Opt. Soc. Am. B 19, 1777-1781 (2002).
[CrossRef]

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirskii, and S. V. Gaponenko, "Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter," Phys. Rev. E 65, 036621 (2002).
[CrossRef]

2001

J. C. Johnson, H. Yan, R. D. Schaller, L. H. Haber, R. J. Saykally, and P. Yang, "Single nanowire lasers," J. Phys. Chem. B 105, 11387-11390 (2001).
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, "Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78, 3388-3390 (2001).
[CrossRef]

2000

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Kassagne, A. Béraud, 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]

1995

1994

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

1987

M. Kohmoto, B. Sutherland, and C. Tang, "Critical wave function and a Cantor-set spectrum of a one-dimensional quasicrystal model," Phys. Rev. B 35, 1020-1033 (1987).
[CrossRef]

Arakawa, Y.

M. Tokushima, H. Yamada, and Y. Arakawa, "1.5−μm-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
[CrossRef]

Assefa, S.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Benisty, H.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Kassagne, A. Béraud, 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]

Béraud, A.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Kassagne, A. Béraud, 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]

Berenger, J. P.

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Bienstman, P.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Borel, P. I.

Burin, A. L.

Cao, H.

Cao, J.-R.

Chen, J. C.

Chigrin, D. N.

D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor-Torres, "Numerical characterization of nanopillar photonic crystal waveguides and directional couplers," Opt. Quantum Electron. 37, 331-341 (2005).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor-Torres, "Nanopillars photonic crystal waveguides," Opt. Express 12, 617-622 (2004).
[CrossRef] [PubMed]

Chong, H.

Dapkus, P. D.

Devenyi, A.

Englund, D.

Fan, S.

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, "Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78, 3388-3390 (2001).
[CrossRef]

S. Fan, J. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, "Guided and defect modes in periodic dielectric waveguides," J. Opt. Soc. Am. B 12, 1267-1272 (1995).
[CrossRef]

Fradsen, L. H.

Fushman, I.

Gaponenko, S. V.

S. V. Zhukovsky, A. V. Lavrinenko, and S. V. Gaponenko, "Spectral scalability as a result of geometrical self-similarity in fractal multilayers," Europhys. Lett. 66, 455-461 (2004).
[CrossRef]

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirskii, and S. V. Gaponenko, "Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter," Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Haber, L. H.

J. C. Johnson, H. Yan, R. D. Schaller, L. H. Haber, R. J. Saykally, and P. Yang, "Single nanowire lasers," J. Phys. Chem. B 105, 11387-11390 (2001).
[CrossRef]

Harpøth, A.

Ippen, E. P.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Janot, C.

C. Janot, Quasicrystals: A Primer (Clarendon, 1994).

Joannopoulos, J. D.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, "Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78, 3388-3390 (2001).
[CrossRef]

S. Fan, J. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, "Guided and defect modes in periodic dielectric waveguides," J. Opt. Soc. Am. B 12, 1267-1272 (1995).
[CrossRef]

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

Johnson, J. C.

J. C. Johnson, H. Yan, R. D. Schaller, L. H. Haber, R. J. Saykally, and P. Yang, "Single nanowire lasers," J. Phys. Chem. B 105, 11387-11390 (2001).
[CrossRef]

Johnson, S. G.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, "Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78, 3388-3390 (2001).
[CrossRef]

Jouanin, C.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Kassagne, A. Béraud, 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]

Kassagne, D.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Kassagne, A. Béraud, 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]

Kim, C.

Kim, W. J.

Kohmoto, M.

M. Kohmoto, B. Sutherland, and C. Tang, "Critical wave function and a Cantor-set spectrum of a one-dimensional quasicrystal model," Phys. Rev. B 35, 1020-1033 (1987).
[CrossRef]

Kolodziejski, L. A.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Krauss, T. F.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Kassagne, A. Béraud, 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]

Kristensen, M.

Kwon, S.-H.

S.-H. Kwon and Y.-H. Lee, "High index-contrast 2D photonic band-edge laser," IEICE Trans. Electron. E87-C, 308-315 (2004).

Labilloy, D.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Kassagne, A. Béraud, 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]

Lavrinenko, A. V.

D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor-Torres, "Numerical characterization of nanopillar photonic crystal waveguides and directional couplers," Opt. Quantum Electron. 37, 331-341 (2005).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor-Torres, "Nanopillars photonic crystal waveguides," Opt. Express 12, 617-622 (2004).
[CrossRef] [PubMed]

S. V. Zhukovsky, A. V. Lavrinenko, and S. V. Gaponenko, "Spectral scalability as a result of geometrical self-similarity in fractal multilayers," Europhys. Lett. 66, 455-461 (2004).
[CrossRef]

A. V. Lavrinenko, P. I. Borel, L. H. Fradsen, M. Thorhauge, A. Harpøth, M. Kristensen, T. Niemi, and H. Chong, "Comprehensive FDTD modelling of photonic crystal waveguide components," Opt. Express 12, 234-248 (2004).
[CrossRef] [PubMed]

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirskii, and S. V. Gaponenko, "Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter," Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Lee, J.-B.

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Lee, Y.-H.

S.-H. Kwon and Y.-H. Lee, "High index-contrast 2D photonic band-edge laser," IEICE Trans. Electron. E87-C, 308-315 (2004).

Lyamshev, L. M.

V. V. Zosimov and L. M. Lyamshev, "Fractals in wave processes," Phys. Usp. 38, 347-384 (2005).
[CrossRef]

Meade, R. D.

Mekis, A.

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, "Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78, 3388-3390 (2001).
[CrossRef]

Niemi, T.

O'Brien, J. D.

Park, W.

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Petrich, G. S.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Rakich, P. T.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Ratner, M. A.

Sakoda, K.

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

Sandomirskii, K. S.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirskii, and S. V. Gaponenko, "Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter," Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Saykally, R. J.

J. C. Johnson, H. Yan, R. D. Schaller, L. H. Haber, R. J. Saykally, and P. Yang, "Single nanowire lasers," J. Phys. Chem. B 105, 11387-11390 (2001).
[CrossRef]

Schaller, R. D.

J. C. Johnson, H. Yan, R. D. Schaller, L. H. Haber, R. J. Saykally, and P. Yang, "Single nanowire lasers," J. Phys. Chem. B 105, 11387-11390 (2001).
[CrossRef]

Schatz, G. C.

Schonbrun, E.

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Smith, C. J. M.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Kassagne, A. Béraud, 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]

Smith, H. I.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Sotomayor-Torres, C. M.

D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor-Torres, "Numerical characterization of nanopillar photonic crystal waveguides and directional couplers," Opt. Quantum Electron. 37, 331-341 (2005).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor-Torres, "Nanopillars photonic crystal waveguides," Opt. Express 12, 617-622 (2004).
[CrossRef] [PubMed]

Stapleton, A.

Sutherland, B.

M. Kohmoto, B. Sutherland, and C. Tang, "Critical wave function and a Cantor-set spectrum of a one-dimensional quasicrystal model," Phys. Rev. B 35, 1020-1033 (1987).
[CrossRef]

Tang, C.

M. Kohmoto, B. Sutherland, and C. Tang, "Critical wave function and a Cantor-set spectrum of a one-dimensional quasicrystal model," Phys. Rev. B 35, 1020-1033 (1987).
[CrossRef]

Thorhauge, M.

Tinker, M.

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Tokushima, M.

M. Tokushima, H. Yamada, and Y. Arakawa, "1.5−μm-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
[CrossRef]

Vuckovic, J.

Weisbuch, C.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Kassagne, A. Béraud, 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]

Winn, J.

Winn, J. N.

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

Yamada, H.

M. Tokushima, H. Yamada, and Y. Arakawa, "1.5−μm-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
[CrossRef]

Yan, H.

J. C. Johnson, H. Yan, R. D. Schaller, L. H. Haber, R. J. Saykally, and P. Yang, "Single nanowire lasers," J. Phys. Chem. B 105, 11387-11390 (2001).
[CrossRef]

Yang, P.

J. C. Johnson, H. Yan, R. D. Schaller, L. H. Haber, R. J. Saykally, and P. Yang, "Single nanowire lasers," J. Phys. Chem. B 105, 11387-11390 (2001).
[CrossRef]

Zhukovsky, S. V.

S. V. Zhukovsky, A. V. Lavrinenko, and S. V. Gaponenko, "Spectral scalability as a result of geometrical self-similarity in fractal multilayers," Europhys. Lett. 66, 455-461 (2004).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Top views of (a) a point-defect periodic reference waveguide, (b) a third-generation Cantor nonopilliar waveguide, (c) a seven-stage Fibonacci waveguide, and (d) a three-row Cantor waveguide wit row spacing Δ = 0.75 a . Solid circles correspond to cylinders with ϵ = 13.0 , extending infinitely in the third dimension and located in air. For the finite-difference time-domain (FDTD) calculations a spatial grid with 16 mesh point per unit length a was used. The whole area of computation is a 7 a × 22 a rectangle surrounded by perfectly matched layer boundaries; see Subsection 2A for details.

Fig. 2
Fig. 2

Normalized energy density spectra of Cantor [Fig. 1b] and Fibonacci [Fig. 1c] waveguides versus a point-defect reference waveguide [Fig. 1a]. The inset shows the resonance peaks under study, located in the vicinity of the point-defect resonance.

Fig. 3
Fig. 3

Numerical setup for energy-flux calculations. The rectangular closed contour is divided into a dissipation part outside the terminal (red) and the terminal part inside (cyan). The waveguide shown here is a Cantor structure with the leftmost nanopillar removed. The terminal width is 0.5 a .

Fig. 4
Fig. 4

Spectral energy-flux densities, normalized to the total spectral flux S 0 ( ω ) , through the terminal, S t ( ω ) θ t (red solid curve), and elsewhere, S d ( ω ) θ d (black dashed curve), for (a) the reference point-defect structure, a Cantor waveguide (b) without and (c) with structure symmetry breaking, and a Fibonacci waveguide (e) without and (f) with structure symmetry breaking. (d) The plot corresponds to a point defect located three nonopillars away from the terminal.

Fig. 5
Fig. 5

Energy density profiles along the longitudinal waveguide axis for the (a) reference point-defect and (b) Cantor systems. The corresponding structures are shown as insets. The terminal is located to the left of each structure.

Fig. 6
Fig. 6

Electric field distributions, normalized to their respective maximum values, for the resonant modes under study in the presence of an external terminal (a) in the reference point-defect structure as seen in Fig. 1a; (b) in the Fibonacci and (c) Cantor structures as depicted in Figs. 1b, 1c; and (d) in the same Cantor structure when the terminal in positioned so as to cover the first nanopillar and thus break the structure internal symmetry. The system was excited by a single monochromatic dipole source in the center of the structure at the respective resonance frequency.

Fig. 7
Fig. 7

Normalized energy flux through the terminal (red solid curve) and elsewhere (black dashed curve) for a three-row Cantor waveguide with (a) Δ = 0.75 a and (b) Δ = a . Arrows indicate the resonant peaks under study, shown in Table 1.

Fig. 8
Fig. 8

Normalized electric field distribution of resonant modes for the three-row Cantor nanopillar waveguide with the distance (a), (b) Δ = 0.75 a and (c), (d) Δ = a for the two different resonant peaks (designated by arrows in Fig. 7).

Tables (1)

Tables Icon

Table 1 Normalized Peak Frequencies and Corresponding Q Factors of Some Resonant Modes For Single- and Multiple-Row Nanopillar Structures Similar to Those Shown in Fig. 1

Equations (12)

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L L S , S L
L L S L S L L S L L S L S L L S L S L L S L L S L S L L S L L S .
L L S L , S S S S
L L S L L S L S S S L S L L S L S S S L S L S S S S S S S S S L S L S S S L S L .
d ( n ) = d S n + ( d L d S ) n 1 τ ,
d ( n ) = d S n + ( d L d S ) j = 1 n k = 1 [ N ] ( 1 2 { 1 2 j 1 3 k } ) .
j ( r , t ) = i ω 0 d δ ( r ) exp { i [ ω 0 t + ϕ ( r ) ] } exp [ ( t t 0 ) 2 σ ] .
Q = ω Δ t α , α d d j log E ( j ) ,
S ( ω , r ) ¯ = 0 2 π ω ω d t 2 π E ( ω , r ) × H ( ω , r ) cos 2 ( ω t ) = 1 2 Re [ E ( ω , r ) × H * ( ω , r ) ] .
S 0 ( ω ) S 0 ( ω , r ) ¯ n d l σ 2 ω ω 0 2 exp [ σ 2 ( ω ω 0 ) 2 ] ,
η ( ω ) S t ( ω ) S d ( ω )
ζ ( ω ) S t ( ω ) θ d S d ( ω ) θ t .

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