Abstract

We proposed a novel method to determine the perfect transmission (PT) of photonics through the Thue–Morse dielectric multilayers for arbitrary basis thickness and generation orders based on the band edge map diagram. As the order of the system increases, the density of resonance peaks increases exponentially. However, the PTs of the resonance peaks are kept even if the peaks become denser for higher-order systems. We present two iterative rules to determine the frequency of the resonance peaks for an arbitrary order of the multilayers. In addition, simple equations are proposed to approximate the repeated band edges and the PT for the arbitrary incident angle of the system with arbitrary order and basis thickness.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
    [CrossRef] [PubMed]
  4. D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
    [CrossRef]
  5. D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
    [CrossRef]
  6. I. Nusinsky and A. A. Hardy, “Band-gap analysis of one-dimensional photonic crystals and conditions for gap closing,” Phys. Rev. B 73, 125104 (2006).
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  13. 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).
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  14. E. L. Albuquerque and M. G. Cottam, “Theory of elementary excitations in quasiperiodic structures,” Phys. Rep. 376, 225–337(2003).
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  15. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization in optics: quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438(1987).
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  18. X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: Extensions and applications,” Phys. Rev. B 62, 14020–14031 (2000).
    [CrossRef]
  19. N. H. Liu, “Propagation of light waves in Thue-Morse dielectric multilayers,” Phys. Rev. B 55, 3543–3547 (1997).
    [CrossRef]
  20. M. S. Vasconcelos and E. L. Albuquerque, “Transmission fingerprints in quasiperiodic dielectric multilayers,” Phys. Rev. B 59, 11128–11131 (1999).
    [CrossRef]
  21. R. Pelster, V. Gasparian, and G. Nimtz, “Propagation of plane waves and of waveguide modes in quasiperiodic dielectric heterostructures,” Phys. Rev. E 55, 7645–7655 (1997).
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    [CrossRef]
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  26. W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystal with metamaterials using a band-edge formalism,” Phys. Rev. A 78, 013836 (2008).
    [CrossRef]
  27. H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, “Photonic band gap structures in the Thue-Morse lattice,” Phys. Rev. B 75, 205109 (2007).
    [CrossRef]
  28. X. Jiang, Y. Zhang, and S. Feng, “Photonic band gaps and localization in the Thue-Morse structures,” Appl. Phys. Lett. 86, 201110 (2005).
    [CrossRef]
  29. L. Moretti, I. Rea, L. Rotiroti, I. Rendina, G. Abbate, A. Marino, and L. De Stefano, “Photonic bandgap analysis of Thue-Morse multilayers made of porous silicon,” Opt. Express 14, 6264–6272(2006).
    [CrossRef] [PubMed]
  30. L. Moretti and V. Mocella, “Two-dimensional photonic aperiodic crystals based on Thue-Morse sequence,” Opt. Express 15, 15314–15323 (2007).
    [CrossRef] [PubMed]
  31. F. Qiu, R. W. Peng, X. Q. Huang, X. F. Hu, M. Wang, A. Hu, S. S. Jiang, and D. Feng, “Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers,” Europhys. Lett. 68, 658–663 (2004).
    [CrossRef]
  32. R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, and S. S. Jiang, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80, 3063–3065 (2002).
    [CrossRef]
  33. X. Q. Huang, S. S. Jiang, R. W. Peng, and A. Hu, “Perfect transmission and self-similar optical transmission spectra in symmetric Fibonacci-class multilayers,” Phys. Rev. B 63, 245104(2001).
    [CrossRef]
  34. R. Nava, J. Taguena-Martinez, J. A. Del Rio, and G. G. Naumis, “Perfect light transmission in Fibonacci arrays of dielectric multilayers,” J. Phys. Condens. Matter 21, 155901 (2009).
    [CrossRef] [PubMed]
  35. E. Macia, “Optical engineering with Fibonacci dielectric multilayers,” Appl. Phys. Lett. 73, 3330–3332 (1998).
    [CrossRef]
  36. F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, “Resonant transmission and frequency trifurcation of light waves in Thue-Morse dielectric multilayers,” Europhys. Lett. 63, 853–859 (2003).
    [CrossRef]
  37. M. S. Vasconcelos, E. L. Albuquerquey, and A. M. Mariz, “Optical localization in quasi-periodic multilayers,” J. Phys. Condens. Matter 10, 5839–5849 (1998).
    [CrossRef]
  38. F. Axel, J. P. Allouche, M. Kleman, M. Mendes-France, and J. Peyriere, “Vibrational modes in a one dimensional quasi-qlloy: the Morse case,” J. Phys. (Paris), Colloq. 47, C3–181 (1986).
    [CrossRef]
  39. F. Axel and J. Peyriere, “Spectrum and extended states in a harmonic chain with controlled disorder: effects of the Thue-Morse symmetry,” J. Stat. Phys. 57, 1013–1047 (1989).
    [CrossRef]
  40. C. S. Ryu, G. Y. Oh, and M. H. Lee, “Extended and critical wave functions in a Thue-Morse chain,” Phys. Rev. B 46, 5162–5168(1992).
    [CrossRef]
  41. A. Ghosh and S. N. Karmakar, “Trace map of a general aperiodic Thue-Morse chain: electronic properties,” Phys. Rev. B 58, 2586–2590 (1998).
    [CrossRef]
  42. S. F. Cheng and G. J. Jin, “Trace map and eigenstates of a Thue-Morse chain in a general model,” Phys. Rev. B 65, 134206(2002).
    [CrossRef]

2011 (1)

2010 (2)

2009 (2)

V. R. Tuz, “Optical properties of a quasi-periodic generalized Fibonacci structure of chiral and material layers,” J. Opt. Soc. Am. B 26, 627–632 (2009).
[CrossRef]

R. Nava, J. Taguena-Martinez, J. A. Del Rio, and G. G. Naumis, “Perfect light transmission in Fibonacci arrays of dielectric multilayers,” J. Phys. Condens. Matter 21, 155901 (2009).
[CrossRef] [PubMed]

2008 (1)

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystal with metamaterials using a band-edge formalism,” Phys. Rev. A 78, 013836 (2008).
[CrossRef]

2007 (4)

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, “Photonic band gap structures in the Thue-Morse lattice,” Phys. Rev. B 75, 205109 (2007).
[CrossRef]

W. J. Hsueh and J. C. Lin, “Numerical stable method for the analysis of Bloch waves in a general one-dimensional photonic crystal cavity,” J. Opt. Soc. Am. B 24, 2249–2258 (2007).
[CrossRef]

L. Moretti and V. Mocella, “Two-dimensional photonic aperiodic crystals based on Thue-Morse sequence,” Opt. Express 15, 15314–15323 (2007).
[CrossRef] [PubMed]

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

2006 (2)

I. Nusinsky and A. A. Hardy, “Band-gap analysis of one-dimensional photonic crystals and conditions for gap closing,” Phys. Rev. B 73, 125104 (2006).
[CrossRef]

L. Moretti, I. Rea, L. Rotiroti, I. Rendina, G. Abbate, A. Marino, and L. De Stefano, “Photonic bandgap analysis of Thue-Morse multilayers made of porous silicon,” Opt. Express 14, 6264–6272(2006).
[CrossRef] [PubMed]

2005 (4)

X. Jiang, Y. Zhang, and S. Feng, “Photonic band gaps and localization in the Thue-Morse structures,” Appl. Phys. Lett. 86, 201110 (2005).
[CrossRef]

L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. 86, 261905 (2005).
[CrossRef]

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. S. Wiersma, “Light-pause propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

Y. Lu, R. W. Peng, Z. Wang, Z. H. Tang, X. Q. Huang, M. Wang, Y. Qiu, A. Hu, S. S. Jiang, and D. Feng, “Resonant transmission of light waves in dielectric heterostructures,” J. Appl. Phys. 97, 123106 (2005).
[CrossRef]

2004 (3)

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, “Dimerlike positional correlation and resonant transmission of electromagnetic waves in aperiodic multilayers,” Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, X. F. Hu, M. Wang, A. Hu, S. S. Jiang, and D. Feng, “Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers,” Europhys. Lett. 68, 658–663 (2004).
[CrossRef]

2003 (2)

E. L. Albuquerque and M. G. Cottam, “Theory of elementary excitations in quasiperiodic structures,” Phys. Rep. 376, 225–337(2003).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, “Resonant transmission and frequency trifurcation of light waves in Thue-Morse dielectric multilayers,” Europhys. Lett. 63, 853–859 (2003).
[CrossRef]

2002 (2)

S. F. Cheng and G. J. Jin, “Trace map and eigenstates of a Thue-Morse chain in a general model,” Phys. Rev. B 65, 134206(2002).
[CrossRef]

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, and S. S. Jiang, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80, 3063–3065 (2002).
[CrossRef]

2001 (1)

X. Q. Huang, S. S. Jiang, R. W. Peng, and A. Hu, “Perfect transmission and self-similar optical transmission spectra in symmetric Fibonacci-class multilayers,” Phys. Rev. B 63, 245104(2001).
[CrossRef]

2000 (1)

X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: Extensions and applications,” Phys. Rev. B 62, 14020–14031 (2000).
[CrossRef]

1999 (3)

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
[CrossRef]

X. Yang, Y. Liu, and X. Fu, “Transmission properties of light through the Fibonacci-class multilayers,” Phys. Rev. B 59, 4545–4548 (1999).
[CrossRef]

M. S. Vasconcelos and E. L. Albuquerque, “Transmission fingerprints in quasiperiodic dielectric multilayers,” Phys. Rev. B 59, 11128–11131 (1999).
[CrossRef]

1998 (5)

E. Macia, “Optical engineering with Fibonacci dielectric multilayers,” Appl. Phys. Lett. 73, 3330–3332 (1998).
[CrossRef]

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

A. Ghosh and S. N. Karmakar, “Trace map of a general aperiodic Thue-Morse chain: electronic properties,” Phys. Rev. B 58, 2586–2590 (1998).
[CrossRef]

M. S. Vasconcelos, E. L. Albuquerquey, and A. M. Mariz, “Optical localization in quasi-periodic multilayers,” J. Phys. Condens. Matter 10, 5839–5849 (1998).
[CrossRef]

1997 (2)

N. H. Liu, “Propagation of light waves in Thue-Morse dielectric multilayers,” Phys. Rev. B 55, 3543–3547 (1997).
[CrossRef]

R. Pelster, V. Gasparian, and G. Nimtz, “Propagation of plane waves and of waveguide modes in quasiperiodic dielectric heterostructures,” Phys. Rev. E 55, 7645–7655 (1997).
[CrossRef]

1992 (1)

C. S. Ryu, G. Y. Oh, and M. H. Lee, “Extended and critical wave functions in a Thue-Morse chain,” Phys. Rev. B 46, 5162–5168(1992).
[CrossRef]

1990 (1)

M. Dulea, M. Severin, and R. Riklund, “Transmission of light through deterministic aperiodic non-Fibonacci multilayers,” Phys. Rev. B 42, 3680–3689 (1990).
[CrossRef]

1989 (1)

F. Axel and J. Peyriere, “Spectrum and extended states in a harmonic chain with controlled disorder: effects of the Thue-Morse symmetry,” J. Stat. Phys. 57, 1013–1047 (1989).
[CrossRef]

1987 (2)

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

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

1986 (1)

F. Axel, J. P. Allouche, M. Kleman, M. Mendes-France, and J. Peyriere, “Vibrational modes in a one dimensional quasi-qlloy: the Morse case,” J. Phys. (Paris), Colloq. 47, C3–181 (1986).
[CrossRef]

1984 (1)

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]

Abbate, G.

Akjou, A.

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

Albuquerque, E. L.

E. L. Albuquerque and M. G. Cottam, “Theory of elementary excitations in quasiperiodic structures,” Phys. Rep. 376, 225–337(2003).
[CrossRef]

M. S. Vasconcelos and E. L. Albuquerque, “Transmission fingerprints in quasiperiodic dielectric multilayers,” Phys. Rev. B 59, 11128–11131 (1999).
[CrossRef]

Albuquerquey, E. L.

M. S. Vasconcelos, E. L. Albuquerquey, and A. M. Mariz, “Optical localization in quasi-periodic multilayers,” J. Phys. Condens. Matter 10, 5839–5849 (1998).
[CrossRef]

Allouche, J. P.

F. Axel, J. P. Allouche, M. Kleman, M. Mendes-France, and J. Peyriere, “Vibrational modes in a one dimensional quasi-qlloy: the Morse case,” J. Phys. (Paris), Colloq. 47, C3–181 (1986).
[CrossRef]

Axel, F.

F. Axel and J. Peyriere, “Spectrum and extended states in a harmonic chain with controlled disorder: effects of the Thue-Morse symmetry,” J. Stat. Phys. 57, 1013–1047 (1989).
[CrossRef]

F. Axel, J. P. Allouche, M. Kleman, M. Mendes-France, and J. Peyriere, “Vibrational modes in a one dimensional quasi-qlloy: the Morse case,” J. Phys. (Paris), Colloq. 47, C3–181 (1986).
[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]

Bria, D.

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

Busch, K.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[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]

Chen, C.

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

Chen, C. H.

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystal with metamaterials using a band-edge formalism,” Phys. Rev. A 78, 013836 (2008).
[CrossRef]

Chen, C. T.

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystal with metamaterials using a band-edge formalism,” Phys. Rev. A 78, 013836 (2008).
[CrossRef]

Chen, J.

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, “Photonic band gap structures in the Thue-Morse lattice,” Phys. Rev. B 75, 205109 (2007).
[CrossRef]

Cheng, S. F.

S. F. Cheng and G. J. Jin, “Trace map and eigenstates of a Thue-Morse chain in a general model,” Phys. Rev. B 65, 134206(2002).
[CrossRef]

Chigrin, D. N.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
[CrossRef]

Colocci, M.

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. S. Wiersma, “Light-pause propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

Cottam, M. G.

E. L. Albuquerque and M. G. Cottam, “Theory of elementary excitations in quasiperiodic structures,” Phys. Rep. 376, 225–337(2003).
[CrossRef]

Dal Negro, L.

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. S. Wiersma, “Light-pause propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. 86, 261905 (2005).
[CrossRef]

De Stefano, L.

Del Rio, J. A.

R. Nava, J. Taguena-Martinez, J. A. Del Rio, and G. G. Naumis, “Perfect light transmission in Fibonacci arrays of dielectric multilayers,” J. Phys. Condens. Matter 21, 155901 (2009).
[CrossRef] [PubMed]

Djafari-Rouhani, B.

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

Dobrzynski, L.

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

Dulea, M.

M. Dulea, M. Severin, and R. Riklund, “Transmission of light through deterministic aperiodic non-Fibonacci multilayers,” Phys. Rev. B 42, 3680–3689 (1990).
[CrossRef]

El Boudouti, E. H.

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

Fan, S.

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

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

Feng, D.

Y. Lu, R. W. Peng, Z. Wang, Z. H. Tang, X. Q. Huang, M. Wang, Y. Qiu, A. Hu, S. S. Jiang, and D. Feng, “Resonant transmission of light waves in dielectric heterostructures,” J. Appl. Phys. 97, 123106 (2005).
[CrossRef]

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, “Dimerlike positional correlation and resonant transmission of electromagnetic waves in aperiodic multilayers,” Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, X. F. Hu, M. Wang, A. Hu, S. S. Jiang, and D. Feng, “Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers,” Europhys. Lett. 68, 658–663 (2004).
[CrossRef]

Feng, S.

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, “Photonic band gap structures in the Thue-Morse lattice,” Phys. Rev. B 75, 205109 (2007).
[CrossRef]

X. Jiang, Y. Zhang, and S. Feng, “Photonic band gaps and localization in the Thue-Morse structures,” Appl. Phys. Lett. 86, 201110 (2005).
[CrossRef]

Fink, Y.

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

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

Fu, X.

X. Yang, Y. Liu, and X. Fu, “Transmission properties of light through the Fibonacci-class multilayers,” Phys. Rev. B 59, 4545–4548 (1999).
[CrossRef]

Gaponenko, S. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
[CrossRef]

Gasparian, V.

R. Pelster, V. Gasparian, and G. Nimtz, “Propagation of plane waves and of waveguide modes in quasiperiodic dielectric heterostructures,” Phys. Rev. E 55, 7645–7655 (1997).
[CrossRef]

Ghosh, A.

A. Ghosh and S. N. Karmakar, “Trace map of a general aperiodic Thue-Morse chain: electronic properties,” Phys. Rev. B 58, 2586–2590 (1998).
[CrossRef]

Ghulinyan, M.

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. S. Wiersma, “Light-pause propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

Gong, Q.

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, “Photonic band gap structures in the Thue-Morse lattice,” Phys. Rev. B 75, 205109 (2007).
[CrossRef]

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]

Grimm, U.

X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: Extensions and applications,” Phys. Rev. B 62, 14020–14031 (2000).
[CrossRef]

Hardy, A. A.

I. Nusinsky and A. A. Hardy, “Band-gap analysis of one-dimensional photonic crystals and conditions for gap closing,” Phys. Rev. B 73, 125104 (2006).
[CrossRef]

Hsueh, W. J.

Hu, A.

Y. Lu, R. W. Peng, Z. Wang, Z. H. Tang, X. Q. Huang, M. Wang, Y. Qiu, A. Hu, S. S. Jiang, and D. Feng, “Resonant transmission of light waves in dielectric heterostructures,” J. Appl. Phys. 97, 123106 (2005).
[CrossRef]

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, “Dimerlike positional correlation and resonant transmission of electromagnetic waves in aperiodic multilayers,” Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, X. F. Hu, M. Wang, A. Hu, S. S. Jiang, and D. Feng, “Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers,” Europhys. Lett. 68, 658–663 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, “Resonant transmission and frequency trifurcation of light waves in Thue-Morse dielectric multilayers,” Europhys. Lett. 63, 853–859 (2003).
[CrossRef]

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, and S. S. Jiang, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80, 3063–3065 (2002).
[CrossRef]

X. Q. Huang, S. S. Jiang, R. W. Peng, and A. Hu, “Perfect transmission and self-similar optical transmission spectra in symmetric Fibonacci-class multilayers,” Phys. Rev. B 63, 245104(2001).
[CrossRef]

Hu, X. F.

F. Qiu, R. W. Peng, X. Q. Huang, X. F. Hu, M. Wang, A. Hu, S. S. Jiang, and D. Feng, “Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers,” Europhys. Lett. 68, 658–663 (2004).
[CrossRef]

Huang, X. Q.

Y. Lu, R. W. Peng, Z. Wang, Z. H. Tang, X. Q. Huang, M. Wang, Y. Qiu, A. Hu, S. S. Jiang, and D. Feng, “Resonant transmission of light waves in dielectric heterostructures,” J. Appl. Phys. 97, 123106 (2005).
[CrossRef]

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, “Dimerlike positional correlation and resonant transmission of electromagnetic waves in aperiodic multilayers,” Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, X. F. Hu, M. Wang, A. Hu, S. S. Jiang, and D. Feng, “Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers,” Europhys. Lett. 68, 658–663 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, “Resonant transmission and frequency trifurcation of light waves in Thue-Morse dielectric multilayers,” Europhys. Lett. 63, 853–859 (2003).
[CrossRef]

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, and S. S. Jiang, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80, 3063–3065 (2002).
[CrossRef]

X. Q. Huang, S. S. Jiang, R. W. Peng, and A. Hu, “Perfect transmission and self-similar optical transmission spectra in symmetric Fibonacci-class multilayers,” Phys. Rev. B 63, 245104(2001).
[CrossRef]

Iguchi, K.

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

Jiang, S. S.

Y. Lu, R. W. Peng, Z. Wang, Z. H. Tang, X. Q. Huang, M. Wang, Y. Qiu, A. Hu, S. S. Jiang, and D. Feng, “Resonant transmission of light waves in dielectric heterostructures,” J. Appl. Phys. 97, 123106 (2005).
[CrossRef]

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, “Dimerlike positional correlation and resonant transmission of electromagnetic waves in aperiodic multilayers,” Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, X. F. Hu, M. Wang, A. Hu, S. S. Jiang, and D. Feng, “Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers,” Europhys. Lett. 68, 658–663 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, “Resonant transmission and frequency trifurcation of light waves in Thue-Morse dielectric multilayers,” Europhys. Lett. 63, 853–859 (2003).
[CrossRef]

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, and S. S. Jiang, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80, 3063–3065 (2002).
[CrossRef]

X. Q. Huang, S. S. Jiang, R. W. Peng, and A. Hu, “Perfect transmission and self-similar optical transmission spectra in symmetric Fibonacci-class multilayers,” Phys. Rev. B 63, 245104(2001).
[CrossRef]

Jiang, X.

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, “Photonic band gap structures in the Thue-Morse lattice,” Phys. Rev. B 75, 205109 (2007).
[CrossRef]

X. Jiang, Y. Zhang, and S. Feng, “Photonic band gaps and localization in the Thue-Morse structures,” Appl. Phys. Lett. 86, 201110 (2005).
[CrossRef]

Jin, G. J.

S. F. Cheng and G. J. Jin, “Trace map and eigenstates of a Thue-Morse chain in a general model,” Phys. Rev. B 65, 134206(2002).
[CrossRef]

Joannopoulos, J. D.

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

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

Karmakar, S. N.

A. Ghosh and S. N. Karmakar, “Trace map of a general aperiodic Thue-Morse chain: electronic properties,” Phys. Rev. B 58, 2586–2590 (1998).
[CrossRef]

Kimerling, L. C.

L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. 86, 261905 (2005).
[CrossRef]

Kleman, M.

F. Axel, J. P. Allouche, M. Kleman, M. Mendes-France, and J. Peyriere, “Vibrational modes in a one dimensional quasi-qlloy: the Morse case,” J. Phys. (Paris), Colloq. 47, C3–181 (1986).
[CrossRef]

Kohmoto, M.

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

Lavrinenko, A. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
[CrossRef]

Lee, M. H.

C. S. Ryu, G. Y. Oh, and M. H. Lee, “Extended and critical wave functions in a Thue-Morse chain,” Phys. Rev. B 46, 5162–5168(1992).
[CrossRef]

Lei, H.

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, “Photonic band gap structures in the Thue-Morse lattice,” Phys. Rev. B 75, 205109 (2007).
[CrossRef]

Lin, J. C.

Linden, S.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Liu, N. H.

N. H. Liu, “Propagation of light waves in Thue-Morse dielectric multilayers,” Phys. Rev. B 55, 3543–3547 (1997).
[CrossRef]

Liu, Y.

X. Yang, Y. Liu, and X. Fu, “Transmission properties of light through the Fibonacci-class multilayers,” Phys. Rev. B 59, 4545–4548 (1999).
[CrossRef]

Liu, Y. M.

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, “Dimerlike positional correlation and resonant transmission of electromagnetic waves in aperiodic multilayers,” Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, “Resonant transmission and frequency trifurcation of light waves in Thue-Morse dielectric multilayers,” Europhys. Lett. 63, 853–859 (2003).
[CrossRef]

Lu, Y.

Y. Lu, R. W. Peng, Z. Wang, Z. H. Tang, X. Q. Huang, M. Wang, Y. Qiu, A. Hu, S. S. Jiang, and D. Feng, “Resonant transmission of light waves in dielectric heterostructures,” J. Appl. Phys. 97, 123106 (2005).
[CrossRef]

Macia, E.

E. Macia, “Optical engineering with Fibonacci dielectric multilayers,” Appl. Phys. Lett. 73, 3330–3332 (1998).
[CrossRef]

Marino, A.

Mariz, A. M.

M. S. Vasconcelos, E. L. Albuquerquey, and A. M. Mariz, “Optical localization in quasi-periodic multilayers,” J. Phys. Condens. Matter 10, 5839–5849 (1998).
[CrossRef]

Mendes-France, M.

F. Axel, J. P. Allouche, M. Kleman, M. Mendes-France, and J. Peyriere, “Vibrational modes in a one dimensional quasi-qlloy: the Morse case,” J. Phys. (Paris), Colloq. 47, C3–181 (1986).
[CrossRef]

Michel, J.

L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. 86, 261905 (2005).
[CrossRef]

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

Mingaleev, S. F.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Mocella, V.

Moretti, L.

Naumis, G. G.

R. Nava, J. Taguena-Martinez, J. A. Del Rio, and G. G. Naumis, “Perfect light transmission in Fibonacci arrays of dielectric multilayers,” J. Phys. Condens. Matter 21, 155901 (2009).
[CrossRef] [PubMed]

Nava, R.

R. Nava, J. Taguena-Martinez, J. A. Del Rio, and G. G. Naumis, “Perfect light transmission in Fibonacci arrays of dielectric multilayers,” J. Phys. Condens. Matter 21, 155901 (2009).
[CrossRef] [PubMed]

Nguyen, V.

L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. 86, 261905 (2005).
[CrossRef]

Nimtz, G.

R. Pelster, V. Gasparian, and G. Nimtz, “Propagation of plane waves and of waveguide modes in quasiperiodic dielectric heterostructures,” Phys. Rev. E 55, 7645–7655 (1997).
[CrossRef]

Nouet, G.

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, “Photonic band gap structures in the Thue-Morse lattice,” Phys. Rev. B 75, 205109 (2007).
[CrossRef]

Nougaoui, A.

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

Nusinsky, I.

I. Nusinsky and A. A. Hardy, “Band-gap analysis of one-dimensional photonic crystals and conditions for gap closing,” Phys. Rev. B 73, 125104 (2006).
[CrossRef]

Oh, G. Y.

C. S. Ryu, G. Y. Oh, and M. H. Lee, “Extended and critical wave functions in a Thue-Morse chain,” Phys. Rev. B 46, 5162–5168(1992).
[CrossRef]

Oton, C. J.

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. S. Wiersma, “Light-pause propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

Ouyang, L. Z.

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, “Dimerlike positional correlation and resonant transmission of electromagnetic waves in aperiodic multilayers,” Phys. Rev. B 69, 165109 (2004).
[CrossRef]

Pavesi, L.

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. S. Wiersma, “Light-pause propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

Pelster, R.

R. Pelster, V. Gasparian, and G. Nimtz, “Propagation of plane waves and of waveguide modes in quasiperiodic dielectric heterostructures,” Phys. Rev. E 55, 7645–7655 (1997).
[CrossRef]

Peng, R. W.

Y. Lu, R. W. Peng, Z. Wang, Z. H. Tang, X. Q. Huang, M. Wang, Y. Qiu, A. Hu, S. S. Jiang, and D. Feng, “Resonant transmission of light waves in dielectric heterostructures,” J. Appl. Phys. 97, 123106 (2005).
[CrossRef]

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, “Dimerlike positional correlation and resonant transmission of electromagnetic waves in aperiodic multilayers,” Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, X. F. Hu, M. Wang, A. Hu, S. S. Jiang, and D. Feng, “Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers,” Europhys. Lett. 68, 658–663 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, “Resonant transmission and frequency trifurcation of light waves in Thue-Morse dielectric multilayers,” Europhys. Lett. 63, 853–859 (2003).
[CrossRef]

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, and S. S. Jiang, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80, 3063–3065 (2002).
[CrossRef]

X. Q. Huang, S. S. Jiang, R. W. Peng, and A. Hu, “Perfect transmission and self-similar optical transmission spectra in symmetric Fibonacci-class multilayers,” Phys. Rev. B 63, 245104(2001).
[CrossRef]

Peyriere, J.

F. Axel and J. Peyriere, “Spectrum and extended states in a harmonic chain with controlled disorder: effects of the Thue-Morse symmetry,” J. Stat. Phys. 57, 1013–1047 (1989).
[CrossRef]

F. Axel, J. P. Allouche, M. Kleman, M. Mendes-France, and J. Peyriere, “Vibrational modes in a one dimensional quasi-qlloy: the Morse case,” J. Phys. (Paris), Colloq. 47, C3–181 (1986).
[CrossRef]

Qiu, F.

F. Qiu, R. W. Peng, X. Q. Huang, X. F. Hu, M. Wang, A. Hu, S. S. Jiang, and D. Feng, “Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers,” Europhys. Lett. 68, 658–663 (2004).
[CrossRef]

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, “Dimerlike positional correlation and resonant transmission of electromagnetic waves in aperiodic multilayers,” Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, “Resonant transmission and frequency trifurcation of light waves in Thue-Morse dielectric multilayers,” Europhys. Lett. 63, 853–859 (2003).
[CrossRef]

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, and S. S. Jiang, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80, 3063–3065 (2002).
[CrossRef]

Qiu, Y.

Y. Lu, R. W. Peng, Z. Wang, Z. H. Tang, X. Q. Huang, M. Wang, Y. Qiu, A. Hu, S. S. Jiang, and D. Feng, “Resonant transmission of light waves in dielectric heterostructures,” J. Appl. Phys. 97, 123106 (2005).
[CrossRef]

Rea, I.

Rendina, I.

Riklund, R.

M. Dulea, M. Severin, and R. Riklund, “Transmission of light through deterministic aperiodic non-Fibonacci multilayers,” Phys. Rev. B 42, 3680–3689 (1990).
[CrossRef]

Rotiroti, L.

Ryu, C. S.

C. S. Ryu, G. Y. Oh, and M. H. Lee, “Extended and critical wave functions in a Thue-Morse chain,” Phys. Rev. B 46, 5162–5168(1992).
[CrossRef]

Sapienza, R.

M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. S. Wiersma, “Light-pause propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[CrossRef]

Schreiber, M.

X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: Extensions and applications,” Phys. Rev. B 62, 14020–14031 (2000).
[CrossRef]

Severin, M.

M. Dulea, M. Severin, and R. Riklund, “Transmission of light through deterministic aperiodic non-Fibonacci multilayers,” Phys. Rev. B 42, 3680–3689 (1990).
[CrossRef]

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]

Sutherland, B.

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

Taguena-Martinez, J.

R. Nava, J. Taguena-Martinez, J. A. Del Rio, and G. G. Naumis, “Perfect light transmission in Fibonacci arrays of dielectric multilayers,” J. Phys. Condens. Matter 21, 155901 (2009).
[CrossRef] [PubMed]

Tang, Z. H.

Y. Lu, R. W. Peng, Z. Wang, Z. H. Tang, X. Q. Huang, M. Wang, Y. Qiu, A. Hu, S. S. Jiang, and D. Feng, “Resonant transmission of light waves in dielectric heterostructures,” J. Appl. Phys. 97, 123106 (2005).
[CrossRef]

Thomas, E. L.

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

Tkeshelashvili, L.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Tuz, V. R.

Vasconcelos, M. S.

M. S. Vasconcelos and E. L. Albuquerque, “Transmission fingerprints in quasiperiodic dielectric multilayers,” Phys. Rev. B 59, 11128–11131 (1999).
[CrossRef]

M. S. Vasconcelos, E. L. Albuquerquey, and A. M. Mariz, “Optical localization in quasi-periodic multilayers,” J. Phys. Condens. Matter 10, 5839–5849 (1998).
[CrossRef]

Vigneron, J. P.

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

von Freymann, G.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Wang, M.

Y. Lu, R. W. Peng, Z. Wang, Z. H. Tang, X. Q. Huang, M. Wang, Y. Qiu, A. Hu, S. S. Jiang, and D. Feng, “Resonant transmission of light waves in dielectric heterostructures,” J. Appl. Phys. 97, 123106 (2005).
[CrossRef]

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, “Dimerlike positional correlation and resonant transmission of electromagnetic waves in aperiodic multilayers,” Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, X. F. Hu, M. Wang, A. Hu, S. S. Jiang, and D. Feng, “Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers,” Europhys. Lett. 68, 658–663 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, “Resonant transmission and frequency trifurcation of light waves in Thue-Morse dielectric multilayers,” Europhys. Lett. 63, 853–859 (2003).
[CrossRef]

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, and S. S. Jiang, “Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers,” Appl. Phys. Lett. 80, 3063–3065 (2002).
[CrossRef]

Wang, X.

X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: Extensions and applications,” Phys. Rev. B 62, 14020–14031 (2000).
[CrossRef]

Wang, Z.

Y. Lu, R. W. Peng, Z. Wang, Z. H. Tang, X. Q. Huang, M. Wang, Y. Qiu, A. Hu, S. S. Jiang, and D. Feng, “Resonant transmission of light waves in dielectric heterostructures,” J. Appl. Phys. 97, 123106 (2005).
[CrossRef]

Wegener, M.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
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Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
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Figures (8)

Fig. 1
Fig. 1

Transmission spectra of the fourth-order TMDMs with (a)  n C = n 0 , (b)  n C = n A , and (c)  n C = n B for normal incidence and (d) eigenfunction cos ( K L ) of the ones. Parameters of the system are n A = 3.0 , n B = 2.0 , and d A = d B = 0.5 μm . The circles in (a)–(c) and rectangles in (d) mark the PTs and RUBs, respectively. The dashed (blue) lines correspond to the frequency of the RUBs.

Fig. 2
Fig. 2

(a) Eigenfunction cos ( K L ) and transmission spectra of the fourth-order TMDMs for incident angles (b)  30 ° , (c)  45 ° , and (d)  60 ° . Parameters of the system are n A = 3.0 , n B = 2.0 , n C = 1.0 , and d A = d B = 0.5 μm .

Fig. 3
Fig. 3

BM of the fourth-order TMDMs versus the normalized frequency for normal incidence. Parameters of the system are n A = 3.0 , n B = 2.0 , n C = 1.0 , and D = 1.0 μm . The gray areas correspond to the band gaps. The thin solid curves (black) correspond to gap edges. The thick (red and orange) curves correspond to half-wave lines. The circles and rectangles mark the RBLs and RBPs, respectively, for F = 0.4 , 0.5, and 0.73.

Fig. 4
Fig. 4

Transmission spectra of the fourth-order TMDMs with (a)  F = 0.4 and (b)  F = 0.73 for normal incidence versus the normalized frequency. Parameters of the system are the same as those in Fig. 3. In (a), (b), the circles and rectangles correspond to the RBLs and RBPs, respectively, in the gap map at F = 0.4 and F = 0.73 , as shown in Fig. 3.

Fig. 5
Fig. 5

BM of the TMDM with generation order v = 3 . Parameters of the system are the same as those used in Fig. 3. The rectangles mark the control points of region R 1 , 1 .

Fig. 6
Fig. 6

BM of the TMDM with generation order v = 5 . Parameters of the system are the same as those used in Fig. 3. The rectangles mark the RBPs.

Fig. 7
Fig. 7

Eigenfunction cos ( K L ) of the TMDMs with F = 0.4 for generation orders (a)  v = 2 , (b)  v = 3 , (c)  v = 4 , and (d)  v = 5 . Parameters of the system are the same as those used in Fig. 3.

Fig. 8
Fig. 8

Error of the approximated expression, Eq. (25), for the RBLs passing (a)  R 0 , 0 and (b)  R 1 , 1 of the fifth TMDMs versus the thickness filling factor. Parameters of the system are the same as those used in Fig. 3. Lines 1 / 4 π , 1 / 2 π , , 15 / 4 π correspond to error of Eq. (25) with p = 0 , 1, j = 1 , 2, 3, 5, 6, and 7 relative to RBL 1 , RBL 2 , , RBL 12 .

Tables (1)

Tables Icon

Table 1 Number of RBLs in Each Region and That of RBPs on One Edge of Each Region for the TMDM with Various Orders

Equations (31)

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E ^ ( j , x , y , z ) = y ^ E y ( j , x ) exp ( i ω t i β z ) ,
E y ( j , x ) = A j exp ( i k j ( x x j 1 ) ) + B j exp ( i k j ( x x j 1 ) ) ,
H z ( j , x ) = i k j k 0 η 0 ( A j exp ( i k j ( x x j 1 ) ) + B j exp ( i k j ( x x j 1 ) ) ) ,
E ¯ j = f j E ¯ j 1 + h j H ¯ j ,
H ¯ j 1 = g j E ¯ j 1 + f j H ¯ j ,
E ¯ N = f E ¯ 0 + h H ¯ N ,
H ¯ 0 = g E ¯ 0 + f H ¯ N ,
S p , q = s = 0 q p i 2 s = p + s q i 2 s 1 = p + s 1 i 2 s 1 i 2 s 1 = p + s 1 i 2 s 1 i 2 s 2 = p + s 2 i 2 s 1 1 i 2 = p + 1 i 3 i 1 = p i 2 1 u = 1 s ( L i 2 u 1 , i 2 u ) ,
E ¯ 0 = a C A C + c C H ¯ 0 ,
B C = b C A C + d C H ¯ 0 ,
A S = a S E ¯ N ,
H ¯ N = b S E ¯ N ,
t = a C a S f Δ 1 ,
r = b C + [ a C d C g f 2 b S + a C d C g ( 1 h b S ) ] Δ 1 ,
H ¯ N = H ¯ 0 exp ( i K L ) ,
E ¯ N = E ¯ 0 exp ( i K L ) ,
1 g h + f 2 2 f cos ( K L ) = 0 .
J s = 1 + f 2 g h + 2 s f .
J c ( v + 2 ) = 4 ( J c ( v + 1 ) ) 2 ( J c ( v ) 1 ) + 1 .
J + 1 = 0 ,
d J + 1 / d Ω = 0 .
F = p k B q k A + p k B ,
Ω = k 0 ( p k B + q k A ) 2 k A k B ,
Rule   A 1 : J c ( v + 2 )   should be equal to 1 if   J c ( v + 1 )   is equal to 1.
Rule   A 2 :   For the case of   J c ( v + 1 ) 1 , J c ( v + 2 )   is equal to 1 if   J c ( v )   is equal to 0.
d J c ( v + 2 ) d Ω = 4 J c ( v ) [ 2 d J c ( v ) d Ω ( J c ( v + 1 ) 1 ) + J c ( v ) d J c ( v + 1 ) d Ω ] .
Rule   A 3 : d J c ( v + 2 ) / d Ω = 0 , if J c ( v ) = 0 ,
Rule   A 4 :   For the case of   J c ( v + 1 ) = 1 , we have   d J c ( v + 2 ) / d Ω = 0 , if   d J c ( v + 1 ) / d Ω = 0.
Rule   B 1 : Repeated band edges exist for order   n due to   J c ( n ) = 1  and   d J c ( n ) / d Ω = 0 , if   J c ( n 1 ) = 1  and   d J c ( n 1 ) / d Ω = 0.
Rule   B 2 :  Repeated band edges exist for order  n due to   J c ( n ) = 1  and    d J c ( n ) / d Ω = 0 , if   J c ( n 2 ) = 0.
k A d A + k B d B = 2 ( p + j / 2 v 1 ) π ,

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