Abstract

This work investigates the resonant modes of a 12-fold symmetric defect free photonic quasicrystal (PQC) nanorod array using finite difference time domain (FDTD) simulation. Localized modes can exist in PQC without introducing defects due to the lack of translational symmetry. The resonant modes of the unit cell PQC and the one time expanded PQC from unit cell are systematically examined. The resonant spectrum is that of a single rod modified by the interaction among PQC nanorods. The mode confinement is contributed by guided resonance and destructive interference scattering. The self-scaling similarity of resonant spectrum and mode profile are also investigated.

© 2014 Optical Society of America

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  1. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
    [Crossref] [PubMed]
  2. 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]
  3. T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B Condens. Matter 50(6), 4220–4223 (1994).
    [Crossref] [PubMed]
  4. 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]
  5. W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436(7053), 993–996 (2005).
    [Crossref] [PubMed]
  6. A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
    [Crossref] [PubMed]
  7. T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
    [Crossref] [PubMed]
  8. S. Walter and S.-W. Daniel, “Photonic and phononic quasicrystals,” J. Phys. D Appl. Phys. 40(13), R229–R247 (2007).
    [Crossref]
  9. K. Mnaymneh and R. C. Gauthier, “Mode localization and band-gap formation in defect-free photonic quasicrystals,” Opt. Express 15(8), 5089–5099 (2007).
    [Crossref] [PubMed]
  10. G. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. 60(11), 1081–1084 (1988).
    [Crossref] [PubMed]
  11. M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing Action due to the Two-Dimensional Quasiperiodicity of Photonic Quasicrystals with a Penrose Lattice,” Phys. Rev. Lett. 92(12), 123906 (2004).
    [Crossref] [PubMed]
  12. 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(6779), 740–743 (2000).
    [Crossref] [PubMed]
  13. K. Nozaki and T. Baba, “Lasing Characteristics of 12-Fold Symmetric Quasi-periodic Photonic Crystal Slab Nanolasers,” Jpn. J. Appl. Phys. 45(8A), 6087–6090 (2006).
    [Crossref]
  14. K. Nozaki and T. Baba, “Quasiperiodic photonic crystal microcavity lasers,” Appl. Phys. Lett. 84(24), 4875–4877 (2004).
    [Crossref]
  15. J. Hendrickson, B. C. Richards, J. Sweet, G. Khitrova, A. N. Poddubny, E. L. Ivchenko, M. Wegener, and H. M. Gibbs, “Excitonic polaritons in Fibonacci quasicrystals,” Opt. Express 16(20), 15382–15387 (2008).
    [Crossref] [PubMed]
  16. L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4(3), 165–169 (2010).
    [Crossref]
  17. S.-K. Kim, J.-H. Lee, S.-H. Kim, I.-K. Hwang, Y.-H. Lee, and S.-B. Kim, “Photonic quasicrystal single-cell cavity mode,” Appl. Phys. Lett. 86(3), 031101 (2005).
    [Crossref]
  18. S. P. Chang, K. P. Sou, C. H. Chen, Y. J. Cheng, J. K. Huang, C. H. Lin, H. C. Kuo, C. Y. Chang, and W. F. Hsieh, “Lasing action in gallium nitride quasicrystal nanorod arrays,” Opt. Express 20(11), 12457–12462 (2012).
    [Crossref] [PubMed]
  19. M. Oxborrow and C. L. Henley, “Random square-triangle tilings: A model for twelvefold-symmetric quasicrystals,” Phys. Rev. B Condens. Matter 48(10), 6966–6998 (1993).
    [Crossref] [PubMed]
  20. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
    [Crossref]

2012 (1)

2010 (1)

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4(3), 165–169 (2010).
[Crossref]

2008 (1)

2007 (3)

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[Crossref] [PubMed]

S. Walter and S.-W. Daniel, “Photonic and phononic quasicrystals,” J. Phys. D Appl. Phys. 40(13), R229–R247 (2007).
[Crossref]

K. Mnaymneh and R. C. Gauthier, “Mode localization and band-gap formation in defect-free photonic quasicrystals,” Opt. Express 15(8), 5089–5099 (2007).
[Crossref] [PubMed]

2006 (2)

K. Nozaki and T. Baba, “Lasing Characteristics of 12-Fold Symmetric Quasi-periodic Photonic Crystal Slab Nanolasers,” Jpn. J. Appl. Phys. 45(8A), 6087–6090 (2006).
[Crossref]

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[Crossref] [PubMed]

2005 (2)

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436(7053), 993–996 (2005).
[Crossref] [PubMed]

S.-K. Kim, J.-H. Lee, S.-H. Kim, I.-K. Hwang, Y.-H. Lee, and S.-B. Kim, “Photonic quasicrystal single-cell cavity mode,” Appl. Phys. Lett. 86(3), 031101 (2005).
[Crossref]

2004 (2)

K. Nozaki and T. Baba, “Quasiperiodic photonic crystal microcavity lasers,” Appl. Phys. Lett. 84(24), 4875–4877 (2004).
[Crossref]

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing Action due to the Two-Dimensional Quasiperiodicity of Photonic Quasicrystals with a Penrose Lattice,” Phys. Rev. Lett. 92(12), 123906 (2004).
[Crossref] [PubMed]

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

2000 (1)

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(6779), 740–743 (2000).
[Crossref] [PubMed]

1999 (1)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[Crossref]

1994 (2)

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]

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B Condens. Matter 50(6), 4220–4223 (1994).
[Crossref] [PubMed]

1993 (1)

M. Oxborrow and C. L. Henley, “Random square-triangle tilings: A model for twelvefold-symmetric quasicrystals,” Phys. Rev. B Condens. Matter 48(10), 6966–6998 (1993).
[Crossref] [PubMed]

1988 (1)

G. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. 60(11), 1081–1084 (1988).
[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]

Agrawal, A.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[Crossref] [PubMed]

Ali, M. K.

G. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. 60(11), 1081–1084 (1988).
[Crossref] [PubMed]

Baba, T.

K. Nozaki and T. Baba, “Lasing Characteristics of 12-Fold Symmetric Quasi-periodic Photonic Crystal Slab Nanolasers,” Jpn. J. Appl. Phys. 45(8A), 6087–6090 (2006).
[Crossref]

K. Nozaki and T. Baba, “Quasiperiodic photonic crystal microcavity lasers,” Appl. Phys. Lett. 84(24), 4875–4877 (2004).
[Crossref]

Baumberg, J. J.

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

Beere, H. E.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4(3), 165–169 (2010).
[Crossref]

Beltram, F.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4(3), 165–169 (2010).
[Crossref]

Cademartiri, L.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[Crossref] [PubMed]

Chaikin, P. M.

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436(7053), 993–996 (2005).
[Crossref] [PubMed]

Chang, C. Y.

Chang, S. P.

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(6779), 740–743 (2000).
[Crossref] [PubMed]

Chen, C. H.

Cheng, Y. 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]

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]

Daniel, S.-W.

S. Walter and S.-W. Daniel, “Photonic and phononic quasicrystals,” J. Phys. D Appl. Phys. 40(13), R229–R247 (2007).
[Crossref]

Edagawa, K.

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing Action due to the Two-Dimensional Quasiperiodicity of Photonic Quasicrystals with a Penrose Lattice,” Phys. Rev. Lett. 92(12), 123906 (2004).
[Crossref] [PubMed]

Faist, J.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4(3), 165–169 (2010).
[Crossref]

Fan, S.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[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(5), 055501 (2003).
[Crossref] [PubMed]

Gauthier, R. C.

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]

Gibbs, H. M.

Gumbs, G.

G. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. 60(11), 1081–1084 (1988).
[Crossref] [PubMed]

Hattori, T.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B Condens. Matter 50(6), 4220–4223 (1994).
[Crossref] [PubMed]

Hendrickson, J.

Henley, C. L.

M. Oxborrow and C. L. Henley, “Random square-triangle tilings: A model for twelvefold-symmetric quasicrystals,” Phys. Rev. B Condens. Matter 48(10), 6966–6998 (1993).
[Crossref] [PubMed]

Hermatschweiler, M.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[Crossref] [PubMed]

Hsieh, W. F.

Huang, J. K.

Hwang, I.-K.

S.-K. Kim, J.-H. Lee, S.-H. Kim, I.-K. Hwang, Y.-H. Lee, and S.-B. Kim, “Photonic quasicrystal single-cell cavity mode,” Appl. Phys. Lett. 86(3), 031101 (2005).
[Crossref]

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.

Joannopoulos, J. D.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[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]

Johnson, S. G.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[Crossref]

Kawato, S.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B Condens. Matter 50(6), 4220–4223 (1994).
[Crossref] [PubMed]

Khitrova, G.

Kim, S.-B.

S.-K. Kim, J.-H. Lee, S.-H. Kim, I.-K. Hwang, Y.-H. Lee, and S.-B. Kim, “Photonic quasicrystal single-cell cavity mode,” Appl. Phys. Lett. 86(3), 031101 (2005).
[Crossref]

Kim, S.-H.

S.-K. Kim, J.-H. Lee, S.-H. Kim, I.-K. Hwang, Y.-H. Lee, and S.-B. Kim, “Photonic quasicrystal single-cell cavity mode,” Appl. Phys. Lett. 86(3), 031101 (2005).
[Crossref]

Kim, S.-K.

S.-K. Kim, J.-H. Lee, S.-H. Kim, I.-K. Hwang, Y.-H. Lee, and S.-B. Kim, “Photonic quasicrystal single-cell cavity mode,” Appl. Phys. Lett. 86(3), 031101 (2005).
[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(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]

Kolodziejski, L.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[Crossref]

Kuo, H. C.

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]

Ledermann, A.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[Crossref] [PubMed]

Lee, J.-H.

S.-K. Kim, J.-H. Lee, S.-H. Kim, I.-K. Hwang, Y.-H. Lee, and S.-B. Kim, “Photonic quasicrystal single-cell cavity mode,” Appl. Phys. Lett. 86(3), 031101 (2005).
[Crossref]

Lee, Y.-H.

S.-K. Kim, J.-H. Lee, S.-H. Kim, I.-K. Hwang, Y.-H. Lee, and S.-B. Kim, “Photonic quasicrystal single-cell cavity mode,” Appl. Phys. Lett. 86(3), 031101 (2005).
[Crossref]

Lin, C. H.

Mahler, L.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4(3), 165–169 (2010).
[Crossref]

Man, W.

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436(7053), 993–996 (2005).
[Crossref] [PubMed]

Matsui, T.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[Crossref] [PubMed]

Megens, M.

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436(7053), 993–996 (2005).
[Crossref] [PubMed]

Mnaymneh, K.

Nahata, A.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[Crossref] [PubMed]

Nakatsuka, H.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B Condens. Matter 50(6), 4220–4223 (1994).
[Crossref] [PubMed]

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(6779), 740–743 (2000).
[Crossref] [PubMed]

Notomi, M.

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing Action due to the Two-Dimensional Quasiperiodicity of Photonic Quasicrystals with a Penrose Lattice,” Phys. Rev. Lett. 92(12), 123906 (2004).
[Crossref] [PubMed]

Nozaki, K.

K. Nozaki and T. Baba, “Lasing Characteristics of 12-Fold Symmetric Quasi-periodic Photonic Crystal Slab Nanolasers,” Jpn. J. Appl. Phys. 45(8A), 6087–6090 (2006).
[Crossref]

K. Nozaki and T. Baba, “Quasiperiodic photonic crystal microcavity lasers,” Appl. Phys. Lett. 84(24), 4875–4877 (2004).
[Crossref]

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]

Oxborrow, M.

M. Oxborrow and C. L. Henley, “Random square-triangle tilings: A model for twelvefold-symmetric quasicrystals,” Phys. Rev. B Condens. Matter 48(10), 6966–6998 (1993).
[Crossref] [PubMed]

Ozin, G. A.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[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(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]

Poddubny, A. N.

Richards, B. C.

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]

Ritchie, D. A.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4(3), 165–169 (2010).
[Crossref]

Sou, K. P.

Steinhardt, P. J.

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436(7053), 993–996 (2005).
[Crossref] [PubMed]

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]

Suzuki, H.

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing Action due to the Two-Dimensional Quasiperiodicity of Photonic Quasicrystals with a Penrose Lattice,” Phys. Rev. Lett. 92(12), 123906 (2004).
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Sweet, J.

Tamamura, T.

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing Action due to the Two-Dimensional Quasiperiodicity of Photonic Quasicrystals with a Penrose Lattice,” Phys. Rev. Lett. 92(12), 123906 (2004).
[Crossref] [PubMed]

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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).
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A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
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Tsurumachi, N.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B Condens. Matter 50(6), 4220–4223 (1994).
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T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
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S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[Crossref]

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A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
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S. Walter and S.-W. Daniel, “Photonic and phononic quasicrystals,” J. Phys. D Appl. Phys. 40(13), R229–R247 (2007).
[Crossref]

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L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4(3), 165–169 (2010).
[Crossref]

Wegener, M.

J. Hendrickson, B. C. Richards, J. Sweet, G. Khitrova, A. N. Poddubny, E. L. Ivchenko, M. Wegener, and H. M. Gibbs, “Excitonic polaritons in Fibonacci quasicrystals,” Opt. Express 16(20), 15382–15387 (2008).
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A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
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Wiersma, D. S.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4(3), 165–169 (2010).
[Crossref]

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
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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).
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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(6779), 740–743 (2000).
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K. Nozaki and T. Baba, “Quasiperiodic photonic crystal microcavity lasers,” Appl. Phys. Lett. 84(24), 4875–4877 (2004).
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J. Phys. D Appl. Phys. (1)

S. Walter and S.-W. Daniel, “Photonic and phononic quasicrystals,” J. Phys. D Appl. Phys. 40(13), R229–R247 (2007).
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Jpn. J. Appl. Phys. (1)

K. Nozaki and T. Baba, “Lasing Characteristics of 12-Fold Symmetric Quasi-periodic Photonic Crystal Slab Nanolasers,” Jpn. J. Appl. Phys. 45(8A), 6087–6090 (2006).
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Nat. Mater. (1)

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[Crossref] [PubMed]

Nat. Photonics (1)

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4(3), 165–169 (2010).
[Crossref]

Nature (3)

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
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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(6779), 740–743 (2000).
[Crossref] [PubMed]

Opt. Express (3)

Phys. Rev. B (1)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[Crossref]

Phys. Rev. B Condens. Matter (2)

M. Oxborrow and C. L. Henley, “Random square-triangle tilings: A model for twelvefold-symmetric quasicrystals,” Phys. Rev. B Condens. Matter 48(10), 6966–6998 (1993).
[Crossref] [PubMed]

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[Crossref] [PubMed]

Phys. Rev. Lett. (5)

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

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[Crossref] [PubMed]

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[Crossref] [PubMed]

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing Action due to the Two-Dimensional Quasiperiodicity of Photonic Quasicrystals with a Penrose Lattice,” Phys. Rev. Lett. 92(12), 123906 (2004).
[Crossref] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

(a) Construction of the 12 fold symmetric PQC structure. (b) Illustration of hexagonal rods placed at the PQC unit cell lattice vertices (blue line). Different source locations are used to excite resonant modes. (c) SEM plane view image of the fabricated sample with the PQC lattice pattern overlaid to show its PQC structure.

Fig. 2
Fig. 2

The reciprocal pattern of (a) a unit cell, (b) the first off-spring cell, and (c) the second off-spring cell.

Fig. 3
Fig. 3

The calculated resonant spectra of the unit cell obtained from (a) various source locations and (b) various lattice constants. (c) The resonant spectrum of a single rod.

Fig. 4
Fig. 4

(a)-(d) The mode patterns of resonant peaks 458, 494, 538, and 455 nm of the unit PQC cell. (e)-(f) The mode patterns of resonant peaks 460 and 543 nm of a single rod.

Fig. 5
Fig. 5

(a) Resonant spectrum of the first off-spring cell. Unit cell spectrum is also included for comparison. (b) Resonant spectra of the first off-spring cell for various excitation sources. (c) Lasing spectrum when a PQC sample was pumped by a pulsed laser.

Fig. 6
Fig. 6

(a) and (c) are the 458 nm and 494 nm resonant mode profiles of the first off-spring cells, respectively. (b) and (d) are respectively the enlarged center portion of (a) and (c). The overlaid dashed red line circles are the unit cells for visual guidance.

Fig. 7
Fig. 7

(a) The calculated spectrum from 1100 to 1700 nm. (b) The calculated mode profile. The large hexagons represent the locations of unit cells.

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