Abstract

Based on the infrared optical material germanium, in the basic structural unit of a two-dimensional decagonal photonic quasi-crystal, photonic bandgaps of four square unit cells with a scattering radius in the range of [0,0.3a] have been calculated within two cases of construction (i.e., air cylinders arranged in germanium and germanium cylinders arranged in air) by using the plane wave expansion method. In considering the Bragg-like scattering effect in two-dimensional photonic quasi-crystals as the elastic collision in physics, we put forward the photonic bandgap impact function F=q1q2q3επr2 for the first time, to the best of our knowledge. A certain unit cell structure shares some similar photonic bandgap properties with a periodic structure. For a certain structure of the unit cell, the center frequency change trends of the photonic bandgap and the type of photonic bandgap generated are not related with the period of the photonic crystal, but with the relative dielectric constant and the construction, respectively. Different unit cell structures own different photonic bandgap structures. This occurs because the high degree of rotational symmetry of the quasi-periodic structure and weak long-range order of the basic structural unit lead to different Bragg-like scattering effects within the unit cell structures.

© 2011 Optical Society of America

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  1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ. Press, 2008).
  2. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
    [CrossRef] [PubMed]
  3. E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
    [CrossRef] [PubMed]
  4. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
    [CrossRef] [PubMed]
  5. 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]
  6. P. Russell, “Photonic crystal fibers,” Science 299, 358–362(2003).
    [CrossRef] [PubMed]
  7. S. A. Cerqueira, “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys. 73, 024401 (2010).
    [CrossRef]
  8. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
    [CrossRef] [PubMed]
  9. H. G. Park, S. H. Kim, S. H. Kwon, G. J. Young, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
    [CrossRef] [PubMed]
  10. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
    [CrossRef] [PubMed]
  11. X. Y. Chen, P. Shum, and J. J. Hu, “Special control of the cutoff frequencies in a 2D photonic crystal coupled-cavity waveguide,” Opt. Commun. 276, 93–96 (2007).
    [CrossRef]
  12. C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75, 1848–1850 (1999).
    [CrossRef]
  13. J. L. Yin, X. G. Huang, S. H. Liu, and S. J. Hu, “Photonic bandgap properties of 8-fold symmetric photonic quasicrystals,” Opt. Commun. 269, 385–388 (2007).
    [CrossRef]
  14. Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).
    [CrossRef]
  15. M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740–743 (2000).
    [CrossRef] [PubMed]
  16. M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S.-I. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals,” Phys. Rev. B 66, 214205 (2002).
    [CrossRef]
  17. M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B 80, 155112 (2009).
    [CrossRef]
  18. D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand, and R. A. Abram, “Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells,” J. Mod. Opt. 53, 407–416 (2006).
    [CrossRef]
  19. K. Wang, “Light localization in photonic band gaps of quasiperiodic dielectric structures,” Phys. Rev. B 82, 045119 (2010).
    [CrossRef]
  20. K. Wang, “Structural effects on light wave behavior in quasiperiodic regular and decagonal Penrose-tiling dielectric media: a comparative study,” Phys. Rev. B 76, 085107 (2007).
    [CrossRef]
  21. Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006).
    [CrossRef]
  22. A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
    [CrossRef] [PubMed]
  23. Y. Q. Wang, X. Y. Hu, X. S. Xu, B. Y. Chen, and D. Z. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
    [CrossRef]
  24. A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14, 1–7 (2006).
    [CrossRef]

2010 (2)

S. A. Cerqueira, “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys. 73, 024401 (2010).
[CrossRef]

K. Wang, “Light localization in photonic band gaps of quasiperiodic dielectric structures,” Phys. Rev. B 82, 045119 (2010).
[CrossRef]

2009 (1)

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B 80, 155112 (2009).
[CrossRef]

2007 (3)

X. Y. Chen, P. Shum, and J. J. Hu, “Special control of the cutoff frequencies in a 2D photonic crystal coupled-cavity waveguide,” Opt. Commun. 276, 93–96 (2007).
[CrossRef]

J. L. Yin, X. G. Huang, S. H. Liu, and S. J. Hu, “Photonic bandgap properties of 8-fold symmetric photonic quasicrystals,” Opt. Commun. 269, 385–388 (2007).
[CrossRef]

K. Wang, “Structural effects on light wave behavior in quasiperiodic regular and decagonal Penrose-tiling dielectric media: a comparative study,” Phys. Rev. B 76, 085107 (2007).
[CrossRef]

2006 (3)

Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006).
[CrossRef]

A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14, 1–7 (2006).
[CrossRef]

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand, and R. A. Abram, “Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells,” J. Mod. Opt. 53, 407–416 (2006).
[CrossRef]

2005 (1)

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

2004 (2)

H. G. Park, S. H. Kim, S. H. Kwon, G. J. Young, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef] [PubMed]

2003 (3)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef] [PubMed]

P. Russell, “Photonic crystal fibers,” Science 299, 358–362(2003).
[CrossRef] [PubMed]

Y. Q. Wang, X. Y. Hu, X. S. Xu, B. Y. Chen, and D. Z. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[CrossRef]

2002 (1)

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S.-I. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals,” Phys. Rev. B 66, 214205 (2002).
[CrossRef]

2000 (2)

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

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

1999 (2)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef] [PubMed]

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75, 1848–1850 (1999).
[CrossRef]

1998 (2)

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (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]

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Abram, R. A.

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand, and R. A. Abram, “Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells,” J. Mod. Opt. 53, 407–416 (2006).
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef] [PubMed]

Allan, D. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef] [PubMed]

Alleman, A.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef] [PubMed]

Asano, T.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef] [PubMed]

Baek, J. H.

H. G. Park, S. H. Kim, S. H. Kwon, G. J. Young, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef] [PubMed]

Baumberg, J. J.

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

Beggs, D. M.

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand, and R. A. Abram, “Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells,” J. Mod. Opt. 53, 407–416 (2006).
[CrossRef]

Birks, T. A.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef] [PubMed]

Brand, S.

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand, and R. A. Abram, “Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells,” J. Mod. Opt. 53, 407–416 (2006).
[CrossRef]

Capolino, F.

A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14, 1–7 (2006).
[CrossRef]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Cerqueira, S. A.

S. A. Cerqueira, “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys. 73, 024401 (2010).
[CrossRef]

Chan, C. H.

Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006).
[CrossRef]

Chan, C. T.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).
[CrossRef]

Chan, Y. S.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).
[CrossRef]

Charlton, M. D. B.

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

Chen, B. Y.

Y. Q. Wang, X. Y. Hu, X. S. Xu, B. Y. Chen, and D. Z. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[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, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Chen, X. Y.

X. Y. Chen, P. Shum, and J. J. Hu, “Special control of the cutoff frequencies in a 2D photonic crystal coupled-cavity waveguide,” Opt. Commun. 276, 93–96 (2007).
[CrossRef]

Cheng, B. Y.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75, 1848–1850 (1999).
[CrossRef]

Chow, E.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef] [PubMed]

Della Villa, A.

A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14, 1–7 (2006).
[CrossRef]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Egashira, M.

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S.-I. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals,” Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Enoch, S.

A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14, 1–7 (2006).
[CrossRef]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[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, 1679–1682 (1998).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[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, 1679–1682 (1998).
[CrossRef] [PubMed]

Florescu, M.

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B 80, 155112 (2009).
[CrossRef]

Galdi, V.

A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14, 1–7 (2006).
[CrossRef]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Hase, M.

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S.-I. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals,” Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Hou, H.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Hu, J. J.

X. Y. Chen, P. Shum, and J. J. Hu, “Special control of the cutoff frequencies in a 2D photonic crystal coupled-cavity waveguide,” Opt. Commun. 276, 93–96 (2007).
[CrossRef]

Hu, S. J.

J. L. Yin, X. G. Huang, S. H. Liu, and S. J. Hu, “Photonic bandgap properties of 8-fold symmetric photonic quasicrystals,” Opt. Commun. 269, 385–388 (2007).
[CrossRef]

Hu, X. Y.

Y. Q. Wang, X. Y. Hu, X. S. Xu, B. Y. Chen, and D. Z. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[CrossRef]

Huang, X. G.

J. L. Yin, X. G. Huang, S. H. Liu, and S. J. Hu, “Photonic bandgap properties of 8-fold symmetric photonic quasicrystals,” Opt. Commun. 269, 385–388 (2007).
[CrossRef]

Jin, C. J.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75, 1848–1850 (1999).
[CrossRef]

Joannopoulos, J. D.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

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. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ. Press, 2008).

Johnson, S. G.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ. Press, 2008).

Kaliteevski, M. A.

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand, and R. A. Abram, “Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells,” J. Mod. Opt. 53, 407–416 (2006).
[CrossRef]

Kim, S. B.

H. G. Park, S. H. Kim, S. H. Kwon, G. J. Young, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Kim, S. H.

H. G. Park, S. H. Kim, S. H. Kwon, G. J. Young, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Knight, J. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef] [PubMed]

Kojima, K. M.

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S.-I. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals,” Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Kwon, S. H.

H. G. Park, S. H. Kim, S. H. Kwon, G. J. Young, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Lai, Y.

Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006).
[CrossRef]

Lee, Y. H.

H. G. Park, S. H. Kim, S. H. Kwon, G. J. Young, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Li, Z. L.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75, 1848–1850 (1999).
[CrossRef]

Lin, S. Y.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Lipson, M.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef] [PubMed]

Liu, S. H.

J. L. Yin, X. G. Huang, S. H. Liu, and S. J. Hu, “Photonic bandgap properties of 8-fold symmetric photonic quasicrystals,” Opt. Commun. 269, 385–388 (2007).
[CrossRef]

Liu, Z. Y.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).
[CrossRef]

Man, B. Y.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75, 1848–1850 (1999).
[CrossRef]

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef] [PubMed]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ. Press, 2008).

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[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, 1679–1682 (1998).
[CrossRef] [PubMed]

Miyazaki, H.

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S.-I. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals,” Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Netti, M. C.

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

Noda, S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef] [PubMed]

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef] [PubMed]

Park, H. G.

H. G. Park, S. H. Kim, S. H. Kwon, G. J. Young, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Parker, G. J.

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

Pierro, V.

A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14, 1–7 (2006).
[CrossRef]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Roberts, P. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef] [PubMed]

Roper, D. T.

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand, and R. A. Abram, “Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells,” J. Mod. Opt. 53, 407–416 (2006).
[CrossRef]

Russell, P.

P. Russell, “Photonic crystal fibers,” Science 299, 358–362(2003).
[CrossRef] [PubMed]

Russell, P. St. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef] [PubMed]

Shinya, N.

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S.-I. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals,” Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Shum, P.

X. Y. Chen, P. Shum, and J. J. Hu, “Special control of the cutoff frequencies in a 2D photonic crystal coupled-cavity waveguide,” Opt. Commun. 276, 93–96 (2007).
[CrossRef]

Song, B. S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef] [PubMed]

Steinhardt, P. J.

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B 80, 155112 (2009).
[CrossRef]

Tayeb, G.

A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14, 1–7 (2006).
[CrossRef]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[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, 1679–1682 (1998).
[CrossRef] [PubMed]

Torquato, S.

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B 80, 155112 (2009).
[CrossRef]

Tsang, L.

Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006).
[CrossRef]

Uchida, S.-I.

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S.-I. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals,” Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Vawter, G. A.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Villeneuve, P. R.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Wang, K.

K. Wang, “Light localization in photonic band gaps of quasiperiodic dielectric structures,” Phys. Rev. B 82, 045119 (2010).
[CrossRef]

K. Wang, “Structural effects on light wave behavior in quasiperiodic regular and decagonal Penrose-tiling dielectric media: a comparative study,” Phys. Rev. B 76, 085107 (2007).
[CrossRef]

Wang, Y. Q.

Y. Q. Wang, X. Y. Hu, X. S. Xu, B. Y. Chen, and D. Z. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[CrossRef]

Wendt, J. R.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

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, 1679–1682 (1998).
[CrossRef] [PubMed]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ. Press, 2008).

Xu, X. S.

Y. Q. Wang, X. Y. Hu, X. S. Xu, B. Y. Chen, and D. Z. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[CrossRef]

Yang, J. K.

H. G. Park, S. H. Kim, S. H. Kwon, G. J. Young, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Yin, J. L.

J. L. Yin, X. G. Huang, S. H. Liu, and S. J. Hu, “Photonic bandgap properties of 8-fold symmetric photonic quasicrystals,” Opt. Commun. 269, 385–388 (2007).
[CrossRef]

Young, G. J.

H. G. Park, S. H. Kim, S. H. Kwon, G. J. Young, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Zhang, D. Z.

Y. Q. Wang, X. Y. Hu, X. S. Xu, B. Y. Chen, and D. Z. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[CrossRef]

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75, 1848–1850 (1999).
[CrossRef]

Zhang, Z. Q.

Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006).
[CrossRef]

Zoorob, M. E.

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

Zubrzycki, W.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75, 1848–1850 (1999).
[CrossRef]

J. Mod. Opt. (1)

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand, and R. A. Abram, “Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells,” J. Mod. Opt. 53, 407–416 (2006).
[CrossRef]

Nature (4)

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef] [PubMed]

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

Opt. Commun. (2)

X. Y. Chen, P. Shum, and J. J. Hu, “Special control of the cutoff frequencies in a 2D photonic crystal coupled-cavity waveguide,” Opt. Commun. 276, 93–96 (2007).
[CrossRef]

J. L. Yin, X. G. Huang, S. H. Liu, and S. J. Hu, “Photonic bandgap properties of 8-fold symmetric photonic quasicrystals,” Opt. Commun. 269, 385–388 (2007).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (6)

Y. Q. Wang, X. Y. Hu, X. S. Xu, B. Y. Chen, and D. Z. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[CrossRef]

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S.-I. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals,” Phys. Rev. B 66, 214205 (2002).
[CrossRef]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B 80, 155112 (2009).
[CrossRef]

K. Wang, “Light localization in photonic band gaps of quasiperiodic dielectric structures,” Phys. Rev. B 82, 045119 (2010).
[CrossRef]

K. Wang, “Structural effects on light wave behavior in quasiperiodic regular and decagonal Penrose-tiling dielectric media: a comparative study,” Phys. Rev. B 76, 085107 (2007).
[CrossRef]

Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

S. A. Cerqueira, “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys. 73, 024401 (2010).
[CrossRef]

Science (4)

H. G. Park, S. H. Kim, S. H. Kwon, G. J. Young, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef] [PubMed]

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]

P. Russell, “Photonic crystal fibers,” Science 299, 358–362(2003).
[CrossRef] [PubMed]

Other (1)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ. Press, 2008).

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Figures (3)

Fig. 1
Fig. 1

Structure of a two-dimensional decagonal photonic quasi-crystal and its basic structural unit and square unit cells.

Fig. 2
Fig. 2

Photonic bandgaps of the different unit cells of the basic structural unit and radius of scatterers in the [ 0 , 0.3 a ] range changed for the case of air cylinders arranged in germanium.

Fig. 3
Fig. 3

Photonic bandgaps of different unit cells of the basic structural unit and radius of scatterers in the [ 0 , 0.3 a ] range changed for the case of germanium cylinders arranged in air.

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