Abstract

In this work, we study the photonic band of cumulative Fibonacci lattices, of which the structure is composed of all generated units in a Fibonacci sequence. The results are compared with distributed Bragg reflector (DBR) structures with the same numbers of layers. Photonic bandgaps are found at two characteristic frequencies, symmetrically separated from the central bandgap in the DBR counterpart. Field amplitude and phase distribution in the Fibonacci lattice indicates an interferential origin of the bandgaps. Fourier transform on the refractive index profile is carried out, and the result confirms a determinate long-range periodicity that agrees well with the photonic band structure.

© 2016 Chinese Laser Press

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References

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  1. P. Leonardo, “Fibonacci’s Liber Abaci,” in A Translation into Modern English of the Book of Calculation, translated by S. Laurence, ed. (Springer, 2002).
  2. T. H. Garland, Fascinating Fibonaccis (Dale Seymour, 1990).
  3. C. R. Li, A. L. Ji, and Z. X. Cao, “Stressed Fibonacci spiral patterns of definite chirality,” Appl. Phys. Lett. 90, 1641021 (2007).
  4. I. Adler, “Plant spirals and Fibonacci numbers,” in Proceedings of National Councils of Teachers of Mathematics (1975), pp. 29–41
  5. R. Merlin, K. Bajema, R. Clarke, F. Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
    [Crossref]
  6. D. Lusk, I. Abdulhalim, and F. Placido, “Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal,” Opt. Commun. 198, 273–279 (2001).
    [Crossref]
  7. L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
    [Crossref]
  8. Y. Sheng, K. Koynov, J. Dou, B. Ma, J. J. Li, and D. Z. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
    [Crossref]
  9. L. Moretti, I. Rea, L. D. Stefano, and I. Rendina, “Periodic versus aperiodic: enhancing the sensitivity of porous silicon based optical sensors,” Appl. Phys. Lett. 90, 191112 (2007).
    [Crossref]
  10. K. Tarnowski and W. Salejda, “Photonic band structure of Fibonacci superlattices with metamaterials. Part 2: the algebraic method of calculation for absorptive metamaterial layers,” Photon. Lett. Pol. 1, 127–129 (2009).
  11. V. Passias, N. V. Valappil, Z. Shi, L. Deych, A. A. Lisyansky, and V. M. Menon, “Luminescence properties of a Fibonacci photonic quasicrystal,” Opt. Express 17, 6636–6642 (2009).
    [Crossref]
  12. S. F. Liew, H. Noh, J. Trevino, L. Dal Negro, and H. Cao, “Localized photonic band edge modes and orbital angular momenta of light in a golden-angle spiral,” Opt. Express 19, 23631–23642 (2011).
    [Crossref]
  13. 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]
  14. A. N. Poddubny and E. L. Ivchenko, “Photonic quasicrystalline and aperiodic structures,” Physica E 42, 1871–1895 (2010).
    [Crossref]
  15. T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994).
    [Crossref]
  16. E. Macia, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397–441 (2006).
    [Crossref]
  17. H. Xiong, Y. Y. Fang, Z. H. Wu, J. N. Dai, W. Tian, and C. Q. Chen, “All-optically controlled one-dimensional photonic crystal of AlGaN film via photorefractive effect,” Opt. Commun. 306, 78–82 (2013).
    [Crossref]
  18. J. Zhao, J. T. Li, H. G. Shao, J. W. Wu, J. Y. Zhou, and K. S. Wong, “Reshaping ultrashort light pulses in resonant photonic crystals,” J. Opt. Soc. Am. B 23, 1981–1987 (2006).
    [Crossref]
  19. I.-W. Feng, S. X. Jin, J. Li, J. Y. Lin, and H. X. Jiang, SiO2/TiO2 distributed Bragg reflector near 1.5  μm fabricated by e-beam evaporation, J. Vac. Sci. Technol. A 31, 061514 (2013).
    [Crossref]
  20. J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, “Wave transport in random systems: multiple resonance character of necklace modes and their statistical behavior,” Phys. Rev. E 74, 0356021 (2006).
    [Crossref]
  21. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
    [Crossref]

2013 (2)

H. Xiong, Y. Y. Fang, Z. H. Wu, J. N. Dai, W. Tian, and C. Q. Chen, “All-optically controlled one-dimensional photonic crystal of AlGaN film via photorefractive effect,” Opt. Commun. 306, 78–82 (2013).
[Crossref]

I.-W. Feng, S. X. Jin, J. Li, J. Y. Lin, and H. X. Jiang, SiO2/TiO2 distributed Bragg reflector near 1.5  μm fabricated by e-beam evaporation, J. Vac. Sci. Technol. A 31, 061514 (2013).
[Crossref]

2011 (1)

2010 (1)

A. N. Poddubny and E. L. Ivchenko, “Photonic quasicrystalline and aperiodic structures,” Physica E 42, 1871–1895 (2010).
[Crossref]

2009 (2)

K. Tarnowski and W. Salejda, “Photonic band structure of Fibonacci superlattices with metamaterials. Part 2: the algebraic method of calculation for absorptive metamaterial layers,” Photon. Lett. Pol. 1, 127–129 (2009).

V. Passias, N. V. Valappil, Z. Shi, L. Deych, A. A. Lisyansky, and V. M. Menon, “Luminescence properties of a Fibonacci photonic quasicrystal,” Opt. Express 17, 6636–6642 (2009).
[Crossref]

2008 (1)

Y. Sheng, K. Koynov, J. Dou, B. Ma, J. J. Li, and D. Z. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
[Crossref]

2007 (2)

L. Moretti, I. Rea, L. D. Stefano, and I. Rendina, “Periodic versus aperiodic: enhancing the sensitivity of porous silicon based optical sensors,” Appl. Phys. Lett. 90, 191112 (2007).
[Crossref]

C. R. Li, A. L. Ji, and Z. X. Cao, “Stressed Fibonacci spiral patterns of definite chirality,” Appl. Phys. Lett. 90, 1641021 (2007).

2006 (3)

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, “Wave transport in random systems: multiple resonance character of necklace modes and their statistical behavior,” Phys. Rev. E 74, 0356021 (2006).
[Crossref]

J. Zhao, J. T. Li, H. G. Shao, J. W. Wu, J. Y. Zhou, and K. S. Wong, “Reshaping ultrashort light pulses in resonant photonic crystals,” J. Opt. Soc. Am. B 23, 1981–1987 (2006).
[Crossref]

E. Macia, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397–441 (2006).
[Crossref]

2003 (1)

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[Crossref]

2001 (1)

D. Lusk, I. Abdulhalim, and F. Placido, “Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal,” Opt. Commun. 198, 273–279 (2001).
[Crossref]

1994 (2)

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

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 (1)

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

1985 (1)

R. Merlin, K. Bajema, R. Clarke, F. Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[Crossref]

Abdulhalim, I.

D. Lusk, I. Abdulhalim, and F. Placido, “Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal,” Opt. Commun. 198, 273–279 (2001).
[Crossref]

Adler, I.

I. Adler, “Plant spirals and Fibonacci numbers,” in Proceedings of National Councils of Teachers of Mathematics (1975), pp. 29–41

Andreani, L. C.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, “Wave transport in random systems: multiple resonance character of necklace modes and their statistical behavior,” Phys. Rev. E 74, 0356021 (2006).
[Crossref]

Bajema, K.

R. Merlin, K. Bajema, R. Clarke, F. Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[Crossref]

Bertolotti, J.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, “Wave transport in random systems: multiple resonance character of necklace modes and their statistical behavior,” Phys. Rev. E 74, 0356021 (2006).
[Crossref]

Bhattacharya, P. K.

R. Merlin, K. Bajema, R. Clarke, F. Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[Crossref]

Cao, H.

Cao, Z. X.

C. R. Li, A. L. Ji, and Z. X. Cao, “Stressed Fibonacci spiral patterns of definite chirality,” Appl. Phys. Lett. 90, 1641021 (2007).

Chen, C. Q.

H. Xiong, Y. Y. Fang, Z. H. Wu, J. N. Dai, W. Tian, and C. Q. Chen, “All-optically controlled one-dimensional photonic crystal of AlGaN film via photorefractive effect,” Opt. Commun. 306, 78–82 (2013).
[Crossref]

Clarke, R.

R. Merlin, K. Bajema, R. Clarke, F. Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[Crossref]

Colocci, M.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[Crossref]

Dai, J. N.

H. Xiong, Y. Y. Fang, Z. H. Wu, J. N. Dai, W. Tian, and C. Q. Chen, “All-optically controlled one-dimensional photonic crystal of AlGaN film via photorefractive effect,” Opt. Commun. 306, 78–82 (2013).
[Crossref]

Dal Negro, L.

S. F. Liew, H. Noh, J. Trevino, L. Dal Negro, and H. Cao, “Localized photonic band edge modes and orbital angular momenta of light in a golden-angle spiral,” Opt. Express 19, 23631–23642 (2011).
[Crossref]

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[Crossref]

Deych, L.

Dou, J.

Y. Sheng, K. Koynov, J. Dou, B. Ma, J. J. Li, and D. Z. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
[Crossref]

Fang, Y. Y.

H. Xiong, Y. Y. Fang, Z. H. Wu, J. N. Dai, W. Tian, and C. Q. Chen, “All-optically controlled one-dimensional photonic crystal of AlGaN film via photorefractive effect,” Opt. Commun. 306, 78–82 (2013).
[Crossref]

Feng, I.-W.

I.-W. Feng, S. X. Jin, J. Li, J. Y. Lin, and H. X. Jiang, SiO2/TiO2 distributed Bragg reflector near 1.5  μm fabricated by e-beam evaporation, J. Vac. Sci. Technol. A 31, 061514 (2013).
[Crossref]

Gaburro, Z.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[Crossref]

Galli, M.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, “Wave transport in random systems: multiple resonance character of necklace modes and their statistical behavior,” Phys. Rev. E 74, 0356021 (2006).
[Crossref]

Garland, T. H.

T. H. Garland, Fascinating Fibonaccis (Dale Seymour, 1990).

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]

Ghulinyan, M.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, “Wave transport in random systems: multiple resonance character of necklace modes and their statistical behavior,” Phys. Rev. E 74, 0356021 (2006).
[Crossref]

Gottardo, S.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, “Wave transport in random systems: multiple resonance character of necklace modes and their statistical behavior,” Phys. Rev. E 74, 0356021 (2006).
[Crossref]

Hattori, T.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

Iguchi, K.

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

Ivchenko, E. L.

A. N. Poddubny and E. L. Ivchenko, “Photonic quasicrystalline and aperiodic structures,” Physica E 42, 1871–1895 (2010).
[Crossref]

Ji, A. L.

C. R. Li, A. L. Ji, and Z. X. Cao, “Stressed Fibonacci spiral patterns of definite chirality,” Appl. Phys. Lett. 90, 1641021 (2007).

Jiang, H. X.

I.-W. Feng, S. X. Jin, J. Li, J. Y. Lin, and H. X. Jiang, SiO2/TiO2 distributed Bragg reflector near 1.5  μm fabricated by e-beam evaporation, J. Vac. Sci. Technol. A 31, 061514 (2013).
[Crossref]

Jin, S. X.

I.-W. Feng, S. X. Jin, J. Li, J. Y. Lin, and H. X. Jiang, SiO2/TiO2 distributed Bragg reflector near 1.5  μm fabricated by e-beam evaporation, J. Vac. Sci. Technol. A 31, 061514 (2013).
[Crossref]

Johnson, P.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[Crossref]

Juang, F. Y.

R. Merlin, K. Bajema, R. Clarke, F. Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[Crossref]

Kawato, S.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994).
[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: quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
[Crossref]

Koynov, K.

Y. Sheng, K. Koynov, J. Dou, B. Ma, J. J. Li, and D. Z. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
[Crossref]

Lagendijk, A.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[Crossref]

Leonardo, P.

P. Leonardo, “Fibonacci’s Liber Abaci,” in A Translation into Modern English of the Book of Calculation, translated by S. Laurence, ed. (Springer, 2002).

Li, C. R.

C. R. Li, A. L. Ji, and Z. X. Cao, “Stressed Fibonacci spiral patterns of definite chirality,” Appl. Phys. Lett. 90, 1641021 (2007).

Li, J.

I.-W. Feng, S. X. Jin, J. Li, J. Y. Lin, and H. X. Jiang, SiO2/TiO2 distributed Bragg reflector near 1.5  μm fabricated by e-beam evaporation, J. Vac. Sci. Technol. A 31, 061514 (2013).
[Crossref]

Li, J. J.

Y. Sheng, K. Koynov, J. Dou, B. Ma, J. J. Li, and D. Z. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
[Crossref]

Li, J. T.

Liew, S. F.

Lin, J. Y.

I.-W. Feng, S. X. Jin, J. Li, J. Y. Lin, and H. X. Jiang, SiO2/TiO2 distributed Bragg reflector near 1.5  μm fabricated by e-beam evaporation, J. Vac. Sci. Technol. A 31, 061514 (2013).
[Crossref]

Lisyansky, A. A.

Lusk, D.

D. Lusk, I. Abdulhalim, and F. Placido, “Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal,” Opt. Commun. 198, 273–279 (2001).
[Crossref]

Ma, B.

Y. Sheng, K. Koynov, J. Dou, B. Ma, J. J. Li, and D. Z. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
[Crossref]

Macia, E.

E. Macia, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397–441 (2006).
[Crossref]

Menon, V. M.

Merlin, R.

R. Merlin, K. Bajema, R. Clarke, F. Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs heterostructures,” Phys. Rev. Lett. 55, 1768–1770 (1985).
[Crossref]

Moretti, L.

L. Moretti, I. Rea, L. D. Stefano, and I. Rendina, “Periodic versus aperiodic: enhancing the sensitivity of porous silicon based optical sensors,” Appl. Phys. Lett. 90, 191112 (2007).
[Crossref]

Nakatsuka, H.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

Noh, H.

Oton, C. J.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[Crossref]

Passias, V.

Pavesi, L.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, “Wave transport in random systems: multiple resonance character of necklace modes and their statistical behavior,” Phys. Rev. E 74, 0356021 (2006).
[Crossref]

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[Crossref]

Placido, F.

D. Lusk, I. Abdulhalim, and F. Placido, “Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal,” Opt. Commun. 198, 273–279 (2001).
[Crossref]

Poddubny, A. N.

A. N. Poddubny and E. L. Ivchenko, “Photonic quasicrystalline and aperiodic structures,” Physica E 42, 1871–1895 (2010).
[Crossref]

Rea, I.

L. Moretti, I. Rea, L. D. Stefano, and I. Rendina, “Periodic versus aperiodic: enhancing the sensitivity of porous silicon based optical sensors,” Appl. Phys. Lett. 90, 191112 (2007).
[Crossref]

Rendina, I.

L. Moretti, I. Rea, L. D. Stefano, and I. Rendina, “Periodic versus aperiodic: enhancing the sensitivity of porous silicon based optical sensors,” Appl. Phys. Lett. 90, 191112 (2007).
[Crossref]

Righini, R.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[Crossref]

Salejda, W.

K. Tarnowski and W. Salejda, “Photonic band structure of Fibonacci superlattices with metamaterials. Part 2: the algebraic method of calculation for absorptive metamaterial layers,” Photon. Lett. Pol. 1, 127–129 (2009).

Sapienza, R.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, “Wave transport in random systems: multiple resonance character of necklace modes and their statistical behavior,” Phys. Rev. E 74, 0356021 (2006).
[Crossref]

Shao, H. G.

Sheng, Y.

Y. Sheng, K. Koynov, J. Dou, B. Ma, J. J. Li, and D. Z. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
[Crossref]

Shi, Z.

Stefano, L. D.

L. Moretti, I. Rea, L. D. Stefano, and I. Rendina, “Periodic versus aperiodic: enhancing the sensitivity of porous silicon based optical sensors,” Appl. Phys. Lett. 90, 191112 (2007).
[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: quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
[Crossref]

Tarnowski, K.

K. Tarnowski and W. Salejda, “Photonic band structure of Fibonacci superlattices with metamaterials. Part 2: the algebraic method of calculation for absorptive metamaterial layers,” Photon. Lett. Pol. 1, 127–129 (2009).

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]

Tian, W.

H. Xiong, Y. Y. Fang, Z. H. Wu, J. N. Dai, W. Tian, and C. Q. Chen, “All-optically controlled one-dimensional photonic crystal of AlGaN film via photorefractive effect,” Opt. Commun. 306, 78–82 (2013).
[Crossref]

Trevino, J.

Tsurumachi, N.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

Valappil, N. V.

Wiersma, D. S.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, “Wave transport in random systems: multiple resonance character of necklace modes and their statistical behavior,” Phys. Rev. E 74, 0356021 (2006).
[Crossref]

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003).
[Crossref]

Wong, K. S.

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Figures (4)

Fig. 1.
Fig. 1. Illustration of (a) the Fibonacci lattice and (b) the Bragg lattice, both composed of two dielectric media of a quarter-wavelength in length.
Fig. 2.
Fig. 2. Photonic band structures of the Bragg-spaced lattices of M=(a)20, (c) 33 and (e) 54, and the Fibonacci lattices of N=(b)6, (d) 7, and (f) 8, measured by transmission coefficient as shown by the blue line. In (a) and (b), the reflectance coefficient is shown by the red line.
Fig. 3.
Fig. 3. Distribution of normalized light field amplitude and phase as a function of frequency and position in (a, c) the Fibonacci lattice of N=7 and (b, d) the DBR structure of M=33.
Fig. 4.
Fig. 4. FT spectrum of the Fibonacci lattice of N=7 (blue line) and the Bragg-spaced lattice of M=33 (red line).

Equations (1)

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kT=2πdA+dB=4nAnBnA+nBk0,

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