Abstract

We present occurrence of the effective Bragg conditions with wide gapwidth and high reflectance in a Fibonacci superlattice, which is a typical one-dimensional quasicrystal. In the Fibonacci material, the number of effective Bragg conditions is two rather than one which appears in traditional periodic structures. Based on the effective Bragg conditions, this study proposes existence of omnidirectional, wideband and high reflectance in the quasiperiodic materials analogous to that in traditional materials.

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  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(20), 1951–1953 (1984).
    [Crossref]
  2. D. Levine and P. J. Steinhardt, “Quasicrystals: A new class of ordered structures,” Phys. Rev. Lett. 53(26), 2477–2480 (1984).
    [Crossref]
  3. E. Abe, Y. Yan, and S. J. Pennycook, “Quasicrystals as cluster aggregates,” Nat. Mater. 3(11), 759–767 (2004).
    [Crossref] [PubMed]
  4. J. Mikhael, J. Roth, L. Helden, and C. Bechinger, “Archimedean-like tiling on decagonal quasicrystalline surfaces,” Nature 454(7203), 501–504 (2008).
    [Crossref] [PubMed]
  5. K. Ueda, T. Dotera, and T. Gemma, “Photonic band structure calculations of two-dimensional Archimedean tiling patterns,” Phys. Rev. B 75(19), 195122 (2007).
    [Crossref]
  6. G. J. Parker, M. E. Zoorob, M. D. B. Charlton, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
    [Crossref] [PubMed]
  7. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
    [Crossref] [PubMed]
  8. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
    [Crossref] [PubMed]
  9. S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, “Fractal independently tunable multichannel filters,” Appl. Phys. Lett. 90(21), 211113 (2007).
    [Crossref]
  10. 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(5), 055501 (2003).
    [Crossref] [PubMed]
  11. W. J. Hsueh, S. J. Wun, and C. W. Tsao, “Branching features of photonic bandgaps in Fibonacci dielectric heterostructures,” Opt. Commun. 284(7), 1880–1886 (2011).
    [Crossref]
  12. A. N. Poddubny and E. L. Ivchenko, “Photonic quasicrystalline and aperiodic structures,” Physica E 42(7), 1871–1895 (2010).
    [Crossref]
  13. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
    [Crossref]
  14. S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53(22), 2169–2172 (1984).
    [Crossref]
  15. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
    [Crossref]
  16. Y. V. Shvyd’kol, S. Stoupin, A. Cunsolo, A. H. Said, and X. Huang, “High-reflectivity high-resolution X-ray crystal optics with diamonds,” Nat. Phys. 6, 196–199 (2010).
  17. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
    [Crossref] [PubMed]
  18. B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
    [Crossref]
  19. Y. Taniyasu, M. Kasu, and T. Makimoto, “An aluminium nitride light-emitting diode with a wavelength of 210 nanometres,” Nature 441(7091), 325–328 (2006).
    [Crossref] [PubMed]
  20. E. Yablonovitch, “Engineered omnidirectional external-reflectivity spectra from one-dimensional layered interference filters,” Opt. Lett. 23(21), 1648–1649 (1998).
    [Crossref] [PubMed]
  21. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
    [Crossref] [PubMed]
  22. R. G. DeCorby, H. T. Nguyen, P. K. Dwivedi, and T. J. Clement, “Planar omnidirectional reflectors in chalcogenide glass and polymer,” Opt. Express 13(16), 6228–6233 (2005).
    [Crossref] [PubMed]
  23. W. J. Hsueh and S. J. Wun, “Simple expressions for the maximum omnidirectional bandgap of bilayer photonic crystals,” Opt. Lett. 36(9), 1581–1583 (2011).
    [Crossref] [PubMed]
  24. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [Crossref] [PubMed]
  25. P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Photonic crystals: Imaging by flat lens using negative refraction,” Nature 426(6965), 404 (2003).
    [Crossref] [PubMed]
  26. W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystals with metamaterials using a band-edge formalism,” Phys. Rev. A 78(1), 013836 (2008).
    [Crossref]
  27. J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90(8), 083901 (2003).
    [Crossref] [PubMed]
  28. N. M. Litchinitser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett. 33(20), 2350–2352 (2008).
    [Crossref] [PubMed]

2011 (2)

W. J. Hsueh, S. J. Wun, and C. W. Tsao, “Branching features of photonic bandgaps in Fibonacci dielectric heterostructures,” Opt. Commun. 284(7), 1880–1886 (2011).
[Crossref]

W. J. Hsueh and S. J. Wun, “Simple expressions for the maximum omnidirectional bandgap of bilayer photonic crystals,” Opt. Lett. 36(9), 1581–1583 (2011).
[Crossref] [PubMed]

2010 (2)

A. N. Poddubny and E. L. Ivchenko, “Photonic quasicrystalline and aperiodic structures,” Physica E 42(7), 1871–1895 (2010).
[Crossref]

Y. V. Shvyd’kol, S. Stoupin, A. Cunsolo, A. H. Said, and X. Huang, “High-reflectivity high-resolution X-ray crystal optics with diamonds,” Nat. Phys. 6, 196–199 (2010).

2008 (3)

J. Mikhael, J. Roth, L. Helden, and C. Bechinger, “Archimedean-like tiling on decagonal quasicrystalline surfaces,” Nature 454(7203), 501–504 (2008).
[Crossref] [PubMed]

N. M. Litchinitser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett. 33(20), 2350–2352 (2008).
[Crossref] [PubMed]

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystals with metamaterials using a band-edge formalism,” Phys. Rev. A 78(1), 013836 (2008).
[Crossref]

2007 (3)

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[Crossref]

K. Ueda, T. Dotera, and T. Gemma, “Photonic band structure calculations of two-dimensional Archimedean tiling patterns,” Phys. Rev. B 75(19), 195122 (2007).
[Crossref]

S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, “Fractal independently tunable multichannel filters,” Appl. Phys. Lett. 90(21), 211113 (2007).
[Crossref]

2006 (1)

Y. Taniyasu, M. Kasu, and T. Makimoto, “An aluminium nitride light-emitting diode with a wavelength of 210 nanometres,” Nature 441(7091), 325–328 (2006).
[Crossref] [PubMed]

2005 (1)

2004 (1)

E. Abe, Y. Yan, and S. J. Pennycook, “Quasicrystals as cluster aggregates,” Nat. Mater. 3(11), 759–767 (2004).
[Crossref] [PubMed]

2003 (3)

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(5), 055501 (2003).
[Crossref] [PubMed]

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Photonic crystals: Imaging by flat lens using negative refraction,” Nature 426(6965), 404 (2003).
[Crossref] [PubMed]

J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90(8), 083901 (2003).
[Crossref] [PubMed]

2000 (2)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

G. J. Parker, M. E. Zoorob, M. D. B. Charlton, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
[Crossref] [PubMed]

1998 (2)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[Crossref] [PubMed]

E. Yablonovitch, “Engineered omnidirectional external-reflectivity spectra from one-dimensional layered interference filters,” Opt. Lett. 23(21), 1648–1649 (1998).
[Crossref] [PubMed]

1997 (1)

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

1994 (2)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[Crossref] [PubMed]

1987 (1)

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[Crossref] [PubMed]

1984 (3)

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(20), 1951–1953 (1984).
[Crossref]

D. Levine and P. J. Steinhardt, “Quasicrystals: A new class of ordered structures,” Phys. Rev. Lett. 53(26), 2477–2480 (1984).
[Crossref]

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53(22), 2169–2172 (1984).
[Crossref]

1958 (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Abe, E.

E. Abe, Y. Yan, and S. J. Pennycook, “Quasicrystals as cluster aggregates,” Nat. Mater. 3(11), 759–767 (2004).
[Crossref] [PubMed]

Anderson, P. W.

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Bartolini, P.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

Baumberg, J. J.

G. J. Parker, M. E. Zoorob, M. D. B. Charlton, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
[Crossref] [PubMed]

Bechinger, C.

J. Mikhael, J. Roth, L. Helden, and C. Bechinger, “Archimedean-like tiling on decagonal quasicrystalline surfaces,” Nature 454(7203), 501–504 (2008).
[Crossref] [PubMed]

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(20), 1951–1953 (1984).
[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(20), 1951–1953 (1984).
[Crossref]

Capasso, F.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Chan, C. T.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90(8), 083901 (2003).
[Crossref] [PubMed]

Charlton, M. D. B.

G. J. Parker, M. E. Zoorob, M. D. B. Charlton, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
[Crossref] [PubMed]

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(5394), 1679–1682 (1998).
[Crossref] [PubMed]

Chen, C. H.

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystals with metamaterials using a band-edge formalism,” Phys. Rev. A 78(1), 013836 (2008).
[Crossref]

Chen, C. T.

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystals with metamaterials using a band-edge formalism,” Phys. Rev. A 78(1), 013836 (2008).
[Crossref]

Chen, X.

S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, “Fractal independently tunable multichannel filters,” Appl. Phys. Lett. 90(21), 211113 (2007).
[Crossref]

Cho, A. Y.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Clement, T. J.

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(5), 055501 (2003).
[Crossref] [PubMed]

Cunsolo, A.

Y. V. Shvyd’kol, S. Stoupin, A. Cunsolo, A. H. Said, and X. Huang, “High-reflectivity high-resolution X-ray crystal optics with diamonds,” Nat. Phys. 6, 196–199 (2010).

Dal Negro, L.

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(5), 055501 (2003).
[Crossref] [PubMed]

DeCorby, R. G.

Dotera, T.

K. Ueda, T. Dotera, and T. Gemma, “Photonic band structure calculations of two-dimensional Archimedean tiling patterns,” Phys. Rev. B 75(19), 195122 (2007).
[Crossref]

Dwivedi, P. K.

Faist, J.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

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(5394), 1679–1682 (1998).
[Crossref] [PubMed]

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(5394), 1679–1682 (1998).
[Crossref] [PubMed]

Gabitov, I. R.

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(5), 055501 (2003).
[Crossref] [PubMed]

Gellermann, W.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[Crossref] [PubMed]

Gemma, T.

K. Ueda, T. Dotera, and T. Gemma, “Photonic band structure calculations of two-dimensional Archimedean tiling patterns,” Phys. Rev. B 75(19), 195122 (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(20), 1951–1953 (1984).
[Crossref]

Helden, L.

J. Mikhael, J. Roth, L. Helden, and C. Bechinger, “Archimedean-like tiling on decagonal quasicrystalline surfaces,” Nature 454(7203), 501–504 (2008).
[Crossref] [PubMed]

Hsueh, W. J.

W. J. Hsueh, S. J. Wun, and C. W. Tsao, “Branching features of photonic bandgaps in Fibonacci dielectric heterostructures,” Opt. Commun. 284(7), 1880–1886 (2011).
[Crossref]

W. J. Hsueh and S. J. Wun, “Simple expressions for the maximum omnidirectional bandgap of bilayer photonic crystals,” Opt. Lett. 36(9), 1581–1583 (2011).
[Crossref] [PubMed]

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystals with metamaterials using a band-edge formalism,” Phys. Rev. A 78(1), 013836 (2008).
[Crossref]

Huang, X.

Y. V. Shvyd’kol, S. Stoupin, A. Cunsolo, A. H. Said, and X. Huang, “High-reflectivity high-resolution X-ray crystal optics with diamonds,” Nat. Phys. 6, 196–199 (2010).

Hutchinson, A. L.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Iguchi, K.

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[Crossref] [PubMed]

Ivchenko, E. L.

A. N. Poddubny and E. L. Ivchenko, “Photonic quasicrystalline and aperiodic structures,” Physica E 42(7), 1871–1895 (2010).
[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(5394), 1679–1682 (1998).
[Crossref] [PubMed]

John, S.

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53(22), 2169–2172 (1984).
[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(5), 055501 (2003).
[Crossref] [PubMed]

Kasu, M.

Y. Taniyasu, M. Kasu, and T. Makimoto, “An aluminium nitride light-emitting diode with a wavelength of 210 nanometres,” Nature 441(7091), 325–328 (2006).
[Crossref] [PubMed]

Kohmoto, M.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[Crossref] [PubMed]

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[Crossref] [PubMed]

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(5), 055501 (2003).
[Crossref] [PubMed]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

Levine, D.

D. Levine and P. J. Steinhardt, “Quasicrystals: A new class of ordered structures,” Phys. Rev. Lett. 53(26), 2477–2480 (1984).
[Crossref]

Li, J.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90(8), 083901 (2003).
[Crossref] [PubMed]

Li, M.

S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, “Fractal independently tunable multichannel filters,” Appl. Phys. Lett. 90(21), 211113 (2007).
[Crossref]

Litchinitser, N. M.

Lu, W.

S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, “Fractal independently tunable multichannel filters,” Appl. Phys. Lett. 90(21), 211113 (2007).
[Crossref]

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Photonic crystals: Imaging by flat lens using negative refraction,” Nature 426(6965), 404 (2003).
[Crossref] [PubMed]

Maimistov, A. I.

Makimoto, T.

Y. Taniyasu, M. Kasu, and T. Makimoto, “An aluminium nitride light-emitting diode with a wavelength of 210 nanometres,” Nature 441(7091), 325–328 (2006).
[Crossref] [PubMed]

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[Crossref] [PubMed]

Mikhael, J.

J. Mikhael, J. Roth, L. Helden, and C. Bechinger, “Archimedean-like tiling on decagonal quasicrystalline surfaces,” Nature 454(7203), 501–504 (2008).
[Crossref] [PubMed]

Netti, M. C.

G. J. Parker, M. E. Zoorob, M. D. B. Charlton, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
[Crossref] [PubMed]

Nguyen, H. T.

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(5), 055501 (2003).
[Crossref] [PubMed]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Photonic crystals: Imaging by flat lens using negative refraction,” Nature 426(6965), 404 (2003).
[Crossref] [PubMed]

Parker, G. J.

G. J. Parker, M. E. Zoorob, M. D. B. Charlton, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
[Crossref] [PubMed]

Pavesi, L.

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(5), 055501 (2003).
[Crossref] [PubMed]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Pennycook, S. J.

E. Abe, Y. Yan, and S. J. Pennycook, “Quasicrystals as cluster aggregates,” Nat. Mater. 3(11), 759–767 (2004).
[Crossref] [PubMed]

Poddubny, A. N.

A. N. Poddubny and E. L. Ivchenko, “Photonic quasicrystalline and aperiodic structures,” Physica E 42(7), 1871–1895 (2010).
[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(5), 055501 (2003).
[Crossref] [PubMed]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

Roth, J.

J. Mikhael, J. Roth, L. Helden, and C. Bechinger, “Archimedean-like tiling on decagonal quasicrystalline surfaces,” Nature 454(7203), 501–504 (2008).
[Crossref] [PubMed]

Sagdeev, R. Z.

Said, A. H.

Y. V. Shvyd’kol, S. Stoupin, A. Cunsolo, A. H. Said, and X. Huang, “High-reflectivity high-resolution X-ray crystal optics with diamonds,” Nat. Phys. 6, 196–199 (2010).

Shalaev, V. M.

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(20), 1951–1953 (1984).
[Crossref]

Sheng, P.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90(8), 083901 (2003).
[Crossref] [PubMed]

Shvyd’kol, Y. V.

Y. V. Shvyd’kol, S. Stoupin, A. Cunsolo, A. H. Said, and X. Huang, “High-reflectivity high-resolution X-ray crystal optics with diamonds,” Nat. Phys. 6, 196–199 (2010).

Sirtori, C.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Sivco, D. L.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Photonic crystals: Imaging by flat lens using negative refraction,” Nature 426(6965), 404 (2003).
[Crossref] [PubMed]

Steinhardt, P. J.

D. Levine and P. J. Steinhardt, “Quasicrystals: A new class of ordered structures,” Phys. Rev. Lett. 53(26), 2477–2480 (1984).
[Crossref]

Stoupin, S.

Y. V. Shvyd’kol, S. Stoupin, A. Cunsolo, A. H. Said, and X. Huang, “High-reflectivity high-resolution X-ray crystal optics with diamonds,” Nat. Phys. 6, 196–199 (2010).

Sutherland, B.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[Crossref] [PubMed]

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[Crossref] [PubMed]

Taniyasu, Y.

Y. Taniyasu, M. Kasu, and T. Makimoto, “An aluminium nitride light-emitting diode with a wavelength of 210 nanometres,” Nature 441(7091), 325–328 (2006).
[Crossref] [PubMed]

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(5), 633–636 (1994).
[Crossref] [PubMed]

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(5394), 1679–1682 (1998).
[Crossref] [PubMed]

Tsao, C. W.

W. J. Hsueh, S. J. Wun, and C. W. Tsao, “Branching features of photonic bandgaps in Fibonacci dielectric heterostructures,” Opt. Commun. 284(7), 1880–1886 (2011).
[Crossref]

Ueda, K.

K. Ueda, T. Dotera, and T. Gemma, “Photonic band structure calculations of two-dimensional Archimedean tiling patterns,” Phys. Rev. B 75(19), 195122 (2007).
[Crossref]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Photonic crystals: Imaging by flat lens using negative refraction,” Nature 426(6965), 404 (2003).
[Crossref] [PubMed]

Wang, H.

S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, “Fractal independently tunable multichannel filters,” Appl. Phys. Lett. 90(21), 211113 (2007).
[Crossref]

Wang, S. W.

S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, “Fractal independently tunable multichannel filters,” Appl. Phys. Lett. 90(21), 211113 (2007).
[Crossref]

Wiersma, D. S.

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(5), 055501 (2003).
[Crossref] [PubMed]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

Williams, B. S.

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[Crossref]

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[Crossref] [PubMed]

Wun, S. J.

W. J. Hsueh and S. J. Wun, “Simple expressions for the maximum omnidirectional bandgap of bilayer photonic crystals,” Opt. Lett. 36(9), 1581–1583 (2011).
[Crossref] [PubMed]

W. J. Hsueh, S. J. Wun, and C. W. Tsao, “Branching features of photonic bandgaps in Fibonacci dielectric heterostructures,” Opt. Commun. 284(7), 1880–1886 (2011).
[Crossref]

Yablonovitch, E.

Yan, Y.

E. Abe, Y. Yan, and S. J. Pennycook, “Quasicrystals as cluster aggregates,” Nat. Mater. 3(11), 759–767 (2004).
[Crossref] [PubMed]

Zhou, L.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90(8), 083901 (2003).
[Crossref] [PubMed]

Zoorob, M. E.

G. J. Parker, M. E. Zoorob, M. D. B. Charlton, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, “Fractal independently tunable multichannel filters,” Appl. Phys. Lett. 90(21), 211113 (2007).
[Crossref]

Nat. Mater. (1)

E. Abe, Y. Yan, and S. J. Pennycook, “Quasicrystals as cluster aggregates,” Nat. Mater. 3(11), 759–767 (2004).
[Crossref] [PubMed]

Nat. Photonics (1)

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[Crossref]

Nat. Phys. (1)

Y. V. Shvyd’kol, S. Stoupin, A. Cunsolo, A. H. Said, and X. Huang, “High-reflectivity high-resolution X-ray crystal optics with diamonds,” Nat. Phys. 6, 196–199 (2010).

Nature (5)

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Photonic crystals: Imaging by flat lens using negative refraction,” Nature 426(6965), 404 (2003).
[Crossref] [PubMed]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

Y. Taniyasu, M. Kasu, and T. Makimoto, “An aluminium nitride light-emitting diode with a wavelength of 210 nanometres,” Nature 441(7091), 325–328 (2006).
[Crossref] [PubMed]

J. Mikhael, J. Roth, L. Helden, and C. Bechinger, “Archimedean-like tiling on decagonal quasicrystalline surfaces,” Nature 454(7203), 501–504 (2008).
[Crossref] [PubMed]

G. J. Parker, M. E. Zoorob, M. D. B. Charlton, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
[Crossref] [PubMed]

Opt. Commun. (1)

W. J. Hsueh, S. J. Wun, and C. W. Tsao, “Branching features of photonic bandgaps in Fibonacci dielectric heterostructures,” Opt. Commun. 284(7), 1880–1886 (2011).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Phys. Rev. A (1)

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystals with metamaterials using a band-edge formalism,” Phys. Rev. A 78(1), 013836 (2008).
[Crossref]

Phys. Rev. B (1)

K. Ueda, T. Dotera, and T. Gemma, “Photonic band structure calculations of two-dimensional Archimedean tiling patterns,” Phys. Rev. B 75(19), 195122 (2007).
[Crossref]

Phys. Rev. Lett. (8)

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(20), 1951–1953 (1984).
[Crossref]

D. Levine and P. J. Steinhardt, “Quasicrystals: A new class of ordered structures,” Phys. Rev. Lett. 53(26), 2477–2480 (1984).
[Crossref]

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[Crossref] [PubMed]

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[Crossref] [PubMed]

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(5), 055501 (2003).
[Crossref] [PubMed]

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53(22), 2169–2172 (1984).
[Crossref]

J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90(8), 083901 (2003).
[Crossref] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Physica E (1)

A. N. Poddubny and E. L. Ivchenko, “Photonic quasicrystalline and aperiodic structures,” Physica E 42(7), 1871–1895 (2010).
[Crossref]

Science (2)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[Crossref] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

(a) Photonic bandgap of the normal incidence, TE 45°, and TM 45° in the FSL for generation orders v = 2 to 8. The red, blue and green thick lines correspond to the allowed bands for the normal incidence, TE 45°, and TM 45°, respectively. The arrow signs indicate the major gaps. Parameters of the system are nA = 2.0, nB = 4.0, dA = 0.55μm, and dB = 0.45μm. The normalized frequency Ω is defined by Ω=ωD/(2πc), where D = dA + dB. (b) The transmission spectra of a single cell of the FSL with v = 4, 6 and 8 for normal incidence from air. The gray areas correspond to the region of the major gaps shown in (a).

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Fig. 2
Fig. 2

Effective Bragg condition, major gaps and their centers in the gap map of the FSL. (a) The gap map of the normal incidence in the S8 FSL with nA = 2.0, nB = 4.0. The gray areas mark the major gaps. The green lines present the bandedges. The red lines mark the midline of the major gap holes, MMGs, corresponding to the effective Bragg conditions. The x signs indicate the center of the major gaps. The blue and black dashed lines mark the zero-gap lines, LA,m and LB,n, respectively. (b) the thickness filling factor and (c) the normalized frequency, and (d) the gapwidth to gap center ratio of the CLGs in regions (0,0), (1,0), (0,1) and (1,1) of the gap map for nA = 2.0 and 6.0> nB>3.0. The solid and dashed lines correspond to the maximum gaps and the CLGs, respectively.

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Fig. 3
Fig. 3

Omni-gaps and transmission spectra of the FSL. (a) Sketch of the overlap among the major gaps for NI, TM1, and TE1 states and omni-gap in the gap map. The gray region corresponds to the omni-gap. (b) The transmission spectra of the S8 FSL with nA = 2.0, nB = 4.0 at the CFOG for 0°, 45°, 85° of TE and TM polarizations. The gray region corresponds to the omni-gap. (c) The gapwidth to gap center ratios of the CFOG of the S8 FSL for nA = 1.5, 2.0, 3.0, and 3.0< nB<6.0. The dashed and solid lines correspond to the gapwidth to gap center ratio of the CFOG and the maximum omnidirectional gap, respectively.

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Equations (7)

Equations on this page are rendered with MathJax. Learn more.

F= pσ q+pσ , Ω= pσ+q 2 n B cos θ B ,
d A n A cos θ A + τ v−2,v−1 d B n B cos θ B =(m+1+ τ v−2,v−1 n) λ 0 /2,
d A n A cos θ A + τ v−2,v−1 d B n B cos θ B =[m+ τ v−2,v−1 (n+1)] λ 0 /2.
F m,n (CLG) = [1+ (2n+1) n A cos θ A (2m+ τ v−2,v−1 ) n B cos θ B ] −1 ,
Ω m,n (CLG) = 1 4 [ (2m+ τ v−2,v−1 ) n A cos θ A + (2n+1) n B cos θ B ].
F m,n (CHG) = [1+ (2n+1) n A cos θ A (2m+1+ τ v−3,v−1 ) n B cos θ B ] −1 ,
Ω m,n (CHG) = 1 4 [ (2m+1+ τ v−3,v−1 ) n A cos θ A + (2n+1) n B cos θ B ].

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