Abstract

The origin of the passband in one-dimensional photonic crystals and Fibonacci quasi-crystals is investigated by the transmission spectra and effective medium theory. The interference and coupling effects influence the formation and properties of the passbands, which can be divided into the basic band and subband formed by coupling interference modes and inhomogeneous dielectric constants, respectively. The optimal length can be obtained through a transcendental equation to show the maximum bandgap for a photonic crystal at the balance condition between interference and coupling effects. By changing the sequence of the two dielectric materials to fabricate a photonic crystal heterostructure, composed of the photonic crystal and quasi-crystal, an enlarging photonic bandgap can be obtained, since the width of the dielectric and air bands can be narrowed by decreasing the photon coupling effect, and the subband and defective band can be eliminated. The effective medium theory provides a good understanding about the formation mechanism of passbands in photonic and quasi-crystals.

© 2014 Optical Society of America

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef]
  3. J. D. Joannopoulos, R. D. Meads, and J. N. Winn, Photonic Crystal: Molding the Flow of Light (Princeton University, 1995).
  4. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasi-periodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
    [CrossRef]
  5. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
    [CrossRef]
  6. Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasi-crystals,” Nat. Photonics 7, 177–187 (2013).
    [CrossRef]
  7. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
    [CrossRef]
  8. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
    [CrossRef]
  9. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
    [CrossRef]
  10. Y. Fink, J. N. Winn, S. H. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. D. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
    [CrossRef]
  11. J. N. Winn, Y. Fink, S. H. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
    [CrossRef]
  12. A. Poddubny, L. Pilozzi, M. Voronov, and E. Ivchenko, “Resonant Fibonacci quantum well structures in one dimension,” Phys. Rev. B 77, 113306 (2008).
    [CrossRef]
  13. M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasi-crystals,” Nature 404, 740–743 (2000).
    [CrossRef]
  14. J. Lin, I. Bita, and E. L. Thomas, “Impact of geometry on the TM photonic band gaps of photonic crystals and quasi-crystals,” Phys. Rev. Lett. 107, 193901 (2011).
    [CrossRef]
  15. J. Lin, I. Bita, and E. L. Thomas, “Photonic density of states of two-dimensional quasi-crystalline photonic structures,” Phys. Rev. A 84, 023831 (2011).
    [CrossRef]
  16. J. Lin, I. Bita, and E. L. Thomas, “Level set photonic quasi-crystals with phase parameters,” Adv. Funct. Mater. 22, 1150–1157 (2012).
    [CrossRef]
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    [CrossRef]
  18. 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]
  19. M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
    [CrossRef]
  20. S. H. Xu, X. M. Ding, and Z. Q. Zhu, “TE and TM defective bands splitting in one-dimensional coupled cavity waveguides,” Opt. Commun. 269, 304–309 (2007).
    [CrossRef]
  21. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).
  22. P. Yeh, A. Yariv, and C. S. Hong, “Electromagnetic propagation in period stratified media: I. general theory,” J. Opt. Soc. Am. B 67, 423–438 (1977).
    [CrossRef]
  23. A. Yariv and P. Yeh, “Electromagnetic propagation in period stratified media: II. birefringence, phase matching, and x-ray lasers,” J. Opt. Soc. Am. B 67, 438–448 (1977).
    [CrossRef]
  24. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
  25. E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interfaces,” Rev. Mod. Phys. 78, 455–481 (2006).
    [CrossRef]

2013 (1)

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasi-crystals,” Nat. Photonics 7, 177–187 (2013).
[CrossRef]

2012 (1)

J. Lin, I. Bita, and E. L. Thomas, “Level set photonic quasi-crystals with phase parameters,” Adv. Funct. Mater. 22, 1150–1157 (2012).
[CrossRef]

2011 (2)

J. Lin, I. Bita, and E. L. Thomas, “Impact of geometry on the TM photonic band gaps of photonic crystals and quasi-crystals,” Phys. Rev. Lett. 107, 193901 (2011).
[CrossRef]

J. Lin, I. Bita, and E. L. Thomas, “Photonic density of states of two-dimensional quasi-crystalline photonic structures,” Phys. Rev. A 84, 023831 (2011).
[CrossRef]

2010 (1)

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

2008 (1)

A. Poddubny, L. Pilozzi, M. Voronov, and E. Ivchenko, “Resonant Fibonacci quantum well structures in one dimension,” Phys. Rev. B 77, 113306 (2008).
[CrossRef]

2007 (1)

S. H. Xu, X. M. Ding, and Z. Q. Zhu, “TE and TM defective bands splitting in one-dimensional coupled cavity waveguides,” Opt. Commun. 269, 304–309 (2007).
[CrossRef]

2006 (2)

2000 (2)

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef]

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasi-crystals,” Nature 404, 740–743 (2000).
[CrossRef]

1999 (2)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (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 (3)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Y. Fink, J. N. Winn, S. H. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. D. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

J. N. Winn, Y. Fink, S. H. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
[CrossRef]

1994 (1)

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[CrossRef]

1987 (3)

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

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

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasi-periodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
[CrossRef]

1977 (2)

P. Yeh, A. Yariv, and C. S. Hong, “Electromagnetic propagation in period stratified media: I. general theory,” J. Opt. Soc. Am. B 67, 423–438 (1977).
[CrossRef]

A. Yariv and P. Yeh, “Electromagnetic propagation in period stratified media: II. birefringence, phase matching, and x-ray lasers,” J. Opt. Soc. Am. B 67, 438–448 (1977).
[CrossRef]

Agrawal, A.

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasi-crystals,” Nat. Photonics 7, 177–187 (2013).
[CrossRef]

Baumberg, J. J.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasi-crystals,” Nature 404, 740–743 (2000).
[CrossRef]

Bayindir, M.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef]

Bita, I.

J. Lin, I. Bita, and E. L. Thomas, “Level set photonic quasi-crystals with phase parameters,” Adv. Funct. Mater. 22, 1150–1157 (2012).
[CrossRef]

J. Lin, I. Bita, and E. L. Thomas, “Impact of geometry on the TM photonic band gaps of photonic crystals and quasi-crystals,” Phys. Rev. Lett. 107, 193901 (2011).
[CrossRef]

J. Lin, I. Bita, and E. L. Thomas, “Photonic density of states of two-dimensional quasi-crystalline photonic structures,” Phys. Rev. A 84, 023831 (2011).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Charlton, M. D. B.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasi-crystals,” Nature 404, 740–743 (2000).
[CrossRef]

Chen, C.

Y. Fink, J. N. Winn, S. H. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. D. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Ding, X. M.

S. H. Xu, X. M. Ding, and Z. Q. Zhu, “TE and TM defective bands splitting in one-dimensional coupled cavity waveguides,” Opt. Commun. 269, 304–309 (2007).
[CrossRef]

Ebbesen, T. W.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Fan, S. H.

Y. Fink, J. N. Winn, S. H. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. D. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

J. N. Winn, Y. Fink, S. H. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
[CrossRef]

Fink, Y.

J. N. Winn, Y. Fink, S. H. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
[CrossRef]

Y. Fink, J. N. Winn, S. H. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. D. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

Gellermann, W.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Hong, C. S.

P. Yeh, A. Yariv, and C. S. Hong, “Electromagnetic propagation in period stratified media: I. general theory,” J. Opt. Soc. Am. B 67, 423–438 (1977).
[CrossRef]

Iguchi, K.

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasi-periodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
[CrossRef]

Istrate, E.

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interfaces,” Rev. Mod. Phys. 78, 455–481 (2006).
[CrossRef]

Ivchenko, E.

A. Poddubny, L. Pilozzi, M. Voronov, and E. Ivchenko, “Resonant Fibonacci quantum well structures in one dimension,” Phys. Rev. B 77, 113306 (2008).
[CrossRef]

Joannopoulos, J. D.

J. N. Winn, Y. Fink, S. H. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
[CrossRef]

Y. Fink, J. N. Winn, S. H. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. D. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

J. D. Joannopoulos, R. D. Meads, and J. N. Winn, Photonic Crystal: Molding the Flow of Light (Princeton University, 1995).

John, S.

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

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Kohmoto, M.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[CrossRef]

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasi-periodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
[CrossRef]

Kuipers, L.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

Lederer, F.

Lee, R. K.

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

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Lin, J.

J. Lin, I. Bita, and E. L. Thomas, “Level set photonic quasi-crystals with phase parameters,” Adv. Funct. Mater. 22, 1150–1157 (2012).
[CrossRef]

J. Lin, I. Bita, and E. L. Thomas, “Impact of geometry on the TM photonic band gaps of photonic crystals and quasi-crystals,” Phys. Rev. Lett. 107, 193901 (2011).
[CrossRef]

J. Lin, I. Bita, and E. L. Thomas, “Photonic density of states of two-dimensional quasi-crystalline photonic structures,” Phys. Rev. A 84, 023831 (2011).
[CrossRef]

Martin-Moreno, L.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

Meads, R. D.

J. D. Joannopoulos, R. D. Meads, and J. N. Winn, Photonic Crystal: Molding the Flow of Light (Princeton University, 1995).

Michel, J.

Y. Fink, J. N. Winn, S. H. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. D. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

Nahata, A.

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasi-crystals,” Nat. Photonics 7, 177–187 (2013).
[CrossRef]

Netti, M. C.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasi-crystals,” Nature 404, 740–743 (2000).
[CrossRef]

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Ozbay, E.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef]

Painter, O.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Parker, G. J.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasi-crystals,” Nature 404, 740–743 (2000).
[CrossRef]

Peschel, U.

Pilozzi, L.

A. Poddubny, L. Pilozzi, M. Voronov, and E. Ivchenko, “Resonant Fibonacci quantum well structures in one dimension,” Phys. Rev. B 77, 113306 (2008).
[CrossRef]

Poddubny, A.

A. Poddubny, L. Pilozzi, M. Voronov, and E. Ivchenko, “Resonant Fibonacci quantum well structures in one dimension,” Phys. Rev. B 77, 113306 (2008).
[CrossRef]

Rockstuhl, C.

Sargent, E. H.

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interfaces,” Rev. Mod. Phys. 78, 455–481 (2006).
[CrossRef]

Scherer, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (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]

Sutherland, B.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[CrossRef]

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasi-periodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
[CrossRef]

Taylor, P. C.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[CrossRef]

Temelkuran, B.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Thomas, E. D.

Y. Fink, J. N. Winn, S. H. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. D. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

Thomas, E. L.

J. Lin, I. Bita, and E. L. Thomas, “Level set photonic quasi-crystals with phase parameters,” Adv. Funct. Mater. 22, 1150–1157 (2012).
[CrossRef]

J. Lin, I. Bita, and E. L. Thomas, “Photonic density of states of two-dimensional quasi-crystalline photonic structures,” Phys. Rev. A 84, 023831 (2011).
[CrossRef]

J. Lin, I. Bita, and E. L. Thomas, “Impact of geometry on the TM photonic band gaps of photonic crystals and quasi-crystals,” Phys. Rev. Lett. 107, 193901 (2011).
[CrossRef]

Vardeny, Z. V.

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasi-crystals,” Nat. Photonics 7, 177–187 (2013).
[CrossRef]

Voronov, M.

A. Poddubny, L. Pilozzi, M. Voronov, and E. Ivchenko, “Resonant Fibonacci quantum well structures in one dimension,” Phys. Rev. B 77, 113306 (2008).
[CrossRef]

Winn, J. N.

J. N. Winn, Y. Fink, S. H. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
[CrossRef]

Y. Fink, J. N. Winn, S. H. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. D. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

J. D. Joannopoulos, R. D. Meads, and J. N. Winn, Photonic Crystal: Molding the Flow of Light (Princeton University, 1995).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Xu, S. H.

S. H. Xu, X. M. Ding, and Z. Q. Zhu, “TE and TM defective bands splitting in one-dimensional coupled cavity waveguides,” Opt. Commun. 269, 304–309 (2007).
[CrossRef]

Xu, Y.

Yablonovitch, E.

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

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (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]

P. Yeh, A. Yariv, and C. S. Hong, “Electromagnetic propagation in period stratified media: I. general theory,” J. Opt. Soc. Am. B 67, 423–438 (1977).
[CrossRef]

A. Yariv and P. Yeh, “Electromagnetic propagation in period stratified media: II. birefringence, phase matching, and x-ray lasers,” J. Opt. Soc. Am. B 67, 438–448 (1977).
[CrossRef]

Yeh, P.

A. Yariv and P. Yeh, “Electromagnetic propagation in period stratified media: II. birefringence, phase matching, and x-ray lasers,” J. Opt. Soc. Am. B 67, 438–448 (1977).
[CrossRef]

P. Yeh, A. Yariv, and C. S. Hong, “Electromagnetic propagation in period stratified media: I. general theory,” J. Opt. Soc. Am. B 67, 423–438 (1977).
[CrossRef]

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Zhu, Z. Q.

S. H. Xu, X. M. Ding, and Z. Q. Zhu, “TE and TM defective bands splitting in one-dimensional coupled cavity waveguides,” Opt. Commun. 269, 304–309 (2007).
[CrossRef]

Zoorob, M. E.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of one-dimensional photonic crystal (PC), Fibonacci quasi-crystal (FQC), and coupled cavity waveguide (CCW) structures composed of two dielectric layers (A and B). (b) Transmission spectra of FQC F2 with length LA increasing from 0.1 to 0.9 (marked as numbers 1–9) for the case of εA=6. (c) First interference frequencies (solid line) of FQC F2 with different length LA for the three cases of εA=13 (A, left), 6 (B, middle), and 3 (C, right). The widths of the first bandgap of the photonic crystals (bold line), and the lower (dotted line) and upper (dashed line) edge frequency of the bandgap are also shown here, for comparison.

Fig. 2.
Fig. 2.

Transmission spectra of FQC F2 (A), F3 (B), F5 (C), F7 (D), and F9 (E), with high dielectric index layer εA=6 and length LA=0.15 (a), 0.235 (b), 0.29 (c), 0.39 (d), and 0.6 (e). The transmission spectra of CCW (F) and photonic crystal (G) are also shown.

Fig. 3.
Fig. 3.

For εA=6 with different lengths LA, (a) the first bandgap width of photonic crystal obtained from the transmission spectra (dots) and calculated results from effective medium theory (line). (b) Comparison results between transmission spectra (dots) and effective medium theory (lines). The low (square) and high (circle) frequency positions of sub-resonance modes and bandgap obtained from transmission spectra of FQC F3 (solid) and photonic crystals (hollow), respectively. The corresponding results obtained from effective medium theory include the bandgap edges (solid lines), sub-resonance modes (dashed lines). The first interference frequencies (bold dot line), the defective modes (bold solid line), and the middle frequency position of the bandgap (thin line) are shown here, for comparison. The widths of the defective band are marked between the two dotted lines around the defective modes.

Fig. 4.
Fig. 4.

For εA=6 with different lengths LA, (a) function Nu/(NvNu) (solid line) and the tangent function with the different index m=0 (dashed line), 1 (dotted line), and 2 (dashed–dotted line) are shown. (b) Comparing the bandgap width of a photonic crystal for cases of maximum bandgap (dotted line) and phase matching condition (solid line), obtained from the transmission spectra (dots) and calculated results from effective medium theory (line).

Fig. 5.
Fig. 5.

For εA=6: (a) first bandgap width of heterostructures composed of CCW and period PC (upper), and the ratio parameter compared with the Δf (down) are shown. (b) At phase matching condition, the first bandgap width of heterostructures with different series number of defective layers, with zero corresponding to the data of period PC. The ratio parameter compared with the Δf are also shown.

Equations (12)

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T=4/(|Mj|2+2),
neff=cK(ω)/ω,
cosKL=coskALAcoskBLBΔsinkALAsinkBLB,
Nu=(nALA+nBLB)/L,
Nv=(nALAnBLB)/L.
sin2KL/2=0.5[(Δ+1)χ1(Δ1)χ2],
sin2(Nuω/2Lc)=1(Δ1)cos2(Nvω/2Lc)/(Δ+1).
ωH,L=ωm±Δω.
ωm=c/NuL(2m1)π
Δω=2c/NuLsin1[(Δ1)/(Δ+1)cos(Nv(m0.5)π/Nu)].
Δωgap=2Δω.
tan(Nv(m0.5)π/Nu)=Nu/(NvNu).

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