Abstract

In this paper, we report on the first evidence of guided resonances (GRs) in aperiodically-ordered photonic crystals, tied to the concept of “quasicrystals” in solid-state physics. Via a full-wave numerical study of the transmittance response and the modal structure of a photonic quasicrystal (PQC) slab based on a representative aperiodic geometry (Ammann-Beenker octagonal tiling), we demonstrate the possibility of exciting GR modes, and highlight similarities and differences with the periodic case. In particular, we show that, as for the periodic case, GRs arise from the coupling of the incident plane-wave with degenerate modes of the PQC slab that exhibit a matching symmetry in the spatial distribution, and can still be parameterized via a Fano-like model. Besides the phenomenological implications, our results may provide new degrees of freedom in the engineering of GRs, and pave the way for new developments and applications.

© 2009 Optical Society of America

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2008 (3)

2007 (5)

W. Steurer and D. Sutter-Widmer, "Photonic and phononic quasicrystals," J. Phys. D: Appl. Phys. 40, R229-R247 (2007).
[CrossRef]

T. Prasad, V. L. Colvin, and D. M. Mittleman, "The effect of structural disorder on guided resonances in photonic crystal slabs studied with terahertz time-domain spectroscopy," Opt. Express 15, 16954-16965 (2007) http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-25-16954.
[CrossRef] [PubMed]

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D: Appl. Phys. 40, 2666-2670 (2007).
[CrossRef]

Y. Kanamori, T. Kitani, and K. Hane, "Control of guided resonance in a photonic crystal slab using microelectromechanical actuators," Appl. Phys. Lett. 90, 031911 (2007).
[CrossRef]

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris. "Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing," Proc. SPIE 6447, 2-9 (2007).

2006 (4)

2005 (4)

2004 (4)

2003 (1)

2002 (2)

2001 (1)

T. Ochiai and K. Sakoda, "Dispersion relation and optical transmittance of a hexagonal photonic crystal slab," Phys. Rev. B 63, 125107 (2001).
[CrossRef]

2000 (1)

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)

1995 (1)

K. Sakoda, "Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices," Phys. Rev. B 52, 7982-7986 (1995).
[CrossRef]

1984 (2)

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, "Metallic phase with long-range orientational order and no translation symmetry," Phys. Rev. Lett. 53, 1951-1953 (1984).
[CrossRef]

D. Levine and P. J. Steinhardt, "Quasicrystals: A new class of ordered structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
[CrossRef]

1961 (1)

U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866-1878 (1961).
[CrossRef]

Akahane, Y.

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]

Asano, T.

Astratov, V. N.

Avniel, Y.

A. W. Rodriguez, A. P. McCauley, Y.  Avniel, and S. G. Johnson, "Computation and visualization of photonic quasicrystal spectra via Bloch’s theorem," Phys. Rev. B 77, 104201 (2008).
[CrossRef]

Blech, I.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, "Metallic phase with long-range orientational order and no translation symmetry," Phys. Rev. Lett. 53, 1951-1953 (1984).
[CrossRef]

Brueck, S. R. J.

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris. "Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing," Proc. SPIE 6447, 2-9 (2007).

Bussmann, K.

Cahn, J. W.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, "Metallic phase with long-range orientational order and no translation symmetry," Phys. Rev. Lett. 53, 1951-1953 (1984).
[CrossRef]

Carter, M. W.

Casey, J. A.

Chen, C. H.

Chen, R. T.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, "80-micron interaction length silicon photonic crystal waveguide modulator," Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Chen, X.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, "80-micron interaction length silicon photonic crystal waveguide modulator," Appl. Phys. Lett. 87, 221105 (2005).
[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]

Chutinan, A.

Colvin, V. L.

Crozier, K. B.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, "Air-bridged photonic crystal slab at visible and near-infrared wavelengths," Phys. Rev. B 73, 115126 (2006).
[CrossRef]

Culshaw, I. S.

De la Rue, R. M.

Digonnet, M.

Eddy, C. R.

Eggleton, B. J.

Fan, S.

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris. "Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing," Proc. SPIE 6447, 2-9 (2007).

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, "Air-bridged photonic crystal slab at visible and near-infrared wavelengths," Phys. Rev. B 73, 115126 (2006).
[CrossRef]

W. Suh, O. Solgaard, and S. Fan, "Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs," J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

W. Suh, Z. Wang, and S. Fan, "Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities," IEEE J. Quantum Electron. 40, 1511-1518 (2004).
[CrossRef]

Fan, S. H.

Fano, U.

U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866-1878 (1961).
[CrossRef]

Freeman, D.

Gratias, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, "Metallic phase with long-range orientational order and no translation symmetry," Phys. Rev. Lett. 53, 1951-1953 (1984).
[CrossRef]

Grillet, C.

Gu, L.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, "80-micron interaction length silicon photonic crystal waveguide modulator," Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Hane, K.

Y. Kanamori, T. Kitani, and K. Hane, "Control of guided resonance in a photonic crystal slab using microelectromechanical actuators," Appl. Phys. Lett. 90, 031911 (2007).
[CrossRef]

Harris, J. S.

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris. "Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing," Proc. SPIE 6447, 2-9 (2007).

Henry, R. L.

Holm, R. T.

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]

Imada, M.

Jiang, W.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, "80-micron interaction length silicon photonic crystal waveguide modulator," Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Jiang, Y.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, "80-micron interaction length silicon photonic crystal waveguide modulator," Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Joannopoulos, J. D.

S. H. Fan and J. D. Joannopoulos, "Analysis of guided resonances in photonic crystal slabs," Phys. Rev. B 65, 235112 (2002).
[CrossRef]

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]

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

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]

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Johnson, S. G.

A. W. Rodriguez, A. P. McCauley, Y.  Avniel, and S. G. Johnson, "Computation and visualization of photonic quasicrystal spectra via Bloch’s theorem," Phys. Rev. B 77, 104201 (2008).
[CrossRef]

Kanamori, Y.

Y. Kanamori, T. Kitani, and K. Hane, "Control of guided resonance in a photonic crystal slab using microelectromechanical actuators," Appl. Phys. Lett. 90, 031911 (2007).
[CrossRef]

Kilic, O.

Kim, H.-J.

Kim, M.

Kim, S.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, "Air-bridged photonic crystal slab at visible and near-infrared wavelengths," Phys. Rev. B 73, 115126 (2006).
[CrossRef]

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. H. Fan, "Angular and polarization properties of a photonic crystal slab mirror," Opt. Express 12, 1575-1582 (2004) http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1575.
[CrossRef] [PubMed]

Kino, G.

Kitani, T.

Y. Kanamori, T. Kitani, and K. Hane, "Control of guided resonance in a photonic crystal slab using microelectromechanical actuators," Appl. Phys. Lett. 90, 031911 (2007).
[CrossRef]

Kolodziejski, L. A.

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Krauss, T. F.

Lee, H.-S.

Lee, M. M.

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris. "Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing," Proc. SPIE 6447, 2-9 (2007).

Lee, S.-G.

Levi, O.

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris. "Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing," Proc. SPIE 6447, 2-9 (2007).

Levine, D.

D. Levine and P. J. Steinhardt, "Quasicrystals: A new class of ordered structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
[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]

Lousse, V.

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris. "Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing," Proc. SPIE 6447, 2-9 (2007).

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, "Air-bridged photonic crystal slab at visible and near-infrared wavelengths," Phys. Rev. B 73, 115126 (2006).
[CrossRef]

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. H. Fan, "Angular and polarization properties of a photonic crystal slab mirror," Opt. Express 12, 1575-1582 (2004) http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1575.
[CrossRef] [PubMed]

Luther-Davies, B.

Maciá, E.

E. Maciá, "The role of aperiodic order in science and technology," Rep. Progr. Phys. 69, 397-441 (2006).
[CrossRef]

Madden, S.

McCauley, A. P.

A. W. Rodriguez, A. P. McCauley, Y.  Avniel, and S. G. Johnson, "Computation and visualization of photonic quasicrystal spectra via Bloch’s theorem," Phys. Rev. B 77, 104201 (2008).
[CrossRef]

McPhedran, R.

Mittleman, D. M.

Mochizuki, M.

Moon, K.-M.

Moss, D. J.

Murakowsky, J.

Noda, S.

Ochiai, T.

T. Ochiai and K. Sakoda, "Dispersion relation and optical transmittance of a hexagonal photonic crystal slab," Phys. Rev. B 63, 125107 (2001).
[CrossRef]

Park, I.

Prasad, T.

Prather, D. W.

Pustai, D. M.

Rodriguez, A. W.

A. W. Rodriguez, A. P. McCauley, Y.  Avniel, and S. G. Johnson, "Computation and visualization of photonic quasicrystal spectra via Bloch’s theorem," Phys. Rev. B 77, 104201 (2008).
[CrossRef]

Rosenberg, A.

Sakoda, K.

T. Ochiai and K. Sakoda, "Dispersion relation and optical transmittance of a hexagonal photonic crystal slab," Phys. Rev. B 63, 125107 (2001).
[CrossRef]

K. Sakoda, "Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices," Phys. Rev. B 52, 7982-7986 (1995).
[CrossRef]

Schneider, G. J.

Shamamian, V. A.

Sharkawy, A.

Shechtman, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, "Metallic phase with long-range orientational order and no translation symmetry," Phys. Rev. Lett. 53, 1951-1953 (1984).
[CrossRef]

Shi, S.

Shi, S. Y.

Skolnick, M. S.

Solgaard, O.

Song, B.

Steel, M. J.

Steinhardt, P. J.

D. Levine and P. J. Steinhardt, "Quasicrystals: A new class of ordered structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
[CrossRef]

Steurer, W.

W. Steurer and D. Sutter-Widmer, "Photonic and phononic quasicrystals," J. Phys. D: Appl. Phys. 40, R229-R247 (2007).
[CrossRef]

Stevenson, R. M.

Suh, W.

W. Suh, O. Solgaard, and S. Fan, "Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs," J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

W. Suh, Z. Wang, and S. Fan, "Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities," IEEE J. Quantum Electron. 40, 1511-1518 (2004).
[CrossRef]

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. H. Fan, "Angular and polarization properties of a photonic crystal slab mirror," Opt. Express 12, 1575-1582 (2004) http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1575.
[CrossRef] [PubMed]

W. Suh and S. H. Fan, "Mechanically switchable photonic crystal filter with either all-pass transmission or flat-top reflection characteristics," Opt. Lett. 28, 1763-1765 (2003).
[CrossRef] [PubMed]

Sutter-Widmer, D.

W. Steurer and D. Sutter-Widmer, "Photonic and phononic quasicrystals," J. Phys. D: Appl. Phys. 40, R229-R247 (2007).
[CrossRef]

Tanaka, T.

Tanaka, Y.

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]

Venkataraman, S.

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]

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Wang, Z.

W. Suh, Z. Wang, and S. Fan, "Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities," IEEE J. Quantum Electron. 40, 1511-1518 (2004).
[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]

Whittaker, D. M.

Zhang, J.

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris. "Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing," Proc. SPIE 6447, 2-9 (2007).

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. (2)

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, "80-micron interaction length silicon photonic crystal waveguide modulator," Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Y. Kanamori, T. Kitani, and K. Hane, "Control of guided resonance in a photonic crystal slab using microelectromechanical actuators," Appl. Phys. Lett. 90, 031911 (2007).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. Suh, Z. Wang, and S. Fan, "Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities," IEEE J. Quantum Electron. 40, 1511-1518 (2004).
[CrossRef]

J. Appl. Phys. (1)

W. Suh, O. Solgaard, and S. Fan, "Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs," J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

J. Lightwave Technol. (4)

J. Opt. Soc. Am. B (1)

J. Phys. D: Appl. Phys. (2)

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D: Appl. Phys. 40, 2666-2670 (2007).
[CrossRef]

W. Steurer and D. Sutter-Widmer, "Photonic and phononic quasicrystals," J. Phys. D: Appl. Phys. 40, R229-R247 (2007).
[CrossRef]

Nature (1)

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]

Opt. Express (6)

O. Kilic, M. Digonnet, G. Kino, and O. Solgaard, "Controlling uncoupled resonances in photonic crystals through breaking the mirror symmetry," Opt. Express 16, 13090-13103 (2008) http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13090.
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T. Prasad, V. L. Colvin, and D. M. Mittleman, "The effect of structural disorder on guided resonances in photonic crystal slabs studied with terahertz time-domain spectroscopy," Opt. Express 15, 16954-16965 (2007) http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-25-16954.
[CrossRef] [PubMed]

A. Rosenberg, M. W. Carter, J. A. Casey, M. Kim, R. T. Holm, R. L. Henry, C. R. Eddy, V. A. Shamamian, K. Bussmann, S. Shi, and D. W. Prather, "Guided resonances in asymmetrical GaN photonic crystal slabs observed in the visible spectrum," Opt. Express 13, 6564-6571 (2005) http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-17-6564.
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C. Grillet, D. Freeman, B. Luther-Davies, S. Madden, R. McPhedran, D. J. Moss, M. J. Steel, and B. J. Eggleton, "Characterization and modeling of Fano resonances in chalcogenide photonic crystal membranes," Opt. Express 14, 369-376 (2006) http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-1-369.
[CrossRef] [PubMed]

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. H. Fan, "Angular and polarization properties of a photonic crystal slab mirror," Opt. Express 12, 1575-1582 (2004) http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1575.
[CrossRef] [PubMed]

I. Park, H.-S. Lee, H.-J. Kim, K.-M. Moon, S.-G. Lee, B.-H. O, S.-G. Park, and E.-H. Lee, "Photonic crystal power-splitter based on directional coupling," Opt. Express 12, 3599-3604 (2004) http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-15-3599.
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S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

S. H. Fan and J. D. Joannopoulos, "Analysis of guided resonances in photonic crystal slabs," Phys. Rev. B 65, 235112 (2002).
[CrossRef]

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, "Air-bridged photonic crystal slab at visible and near-infrared wavelengths," Phys. Rev. B 73, 115126 (2006).
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A. W. Rodriguez, A. P. McCauley, Y.  Avniel, and S. G. Johnson, "Computation and visualization of photonic quasicrystal spectra via Bloch’s theorem," Phys. Rev. B 77, 104201 (2008).
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Proc. SPIE (1)

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris. "Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing," Proc. SPIE 6447, 2-9 (2007).

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Figures (8)

Fig. 1.
Fig. 1.

Problem geometry. (a) A portion of the octagonal (Ammann-Beenker, square-rhombus) tiling, from which the supercell (red dashed square) is cut. (b) Detail of the tiling vertices falling inside the supercell, with indication of the lattice constant a and total size L. (c) Final result, in the associated 3-D Cartesian reference system, obtained by placing air holes of radius r in a silicon slab of thickness h at the tiling-vertice positions.

Fig. 2.
Fig. 2.

(a). Full-wave-computed (black solid) and Fano-fitted (red dashed, cf. (1)-(4)) transmittance spectrum (for normal plane-wave incidence, with y-polarized electric field) of the PQC slab (reduced supercell and terminations shown in the inset), with r=0.25a (i.e., air/dielectric fraction ξ ≈ 23.7% ) and h=0.75a. (b), (c) Magnified details around the two GRs.

Fig. 3.
Fig. 3.

Band-structure (even modes) of the PQC slab (supercell as in Fig. 1(c) and parameters as in Fig. 2) along the high symmetry directions of the irreducible Brillouin zone (shown in the inset).

Fig. 4.
Fig. 4.

Electric modal field amplitudes (in the x-y plane, at z=0) for x and y components (Exm and Eym , respectively), at normalized frequency ν 1=0.0785. Indexes m=1,…,4 label the four different modes.

Fig. 5.
Fig. 5.

As in Fig. 4, but at normalized frequency ν 2=0.1013. Indexes m=5,…,8 label the four different modes.

Fig. 6.
Fig. 6.

GR normalized central frequencies (white squares, left axis) and linewidths (blue circles, right axis) for various values of the supercell size.

Fig. 7.
Fig. 7.

As in Fig. 2(a), but for a composite supercell featuring an air layer of thickness ∆ placed around the PQC sample (see inset). Black solid curve: ∆=0 (no air layer); red dashed: ∆=0.88a; blue dotted: ∆=1.5a; magenta dashed-dotted: ∆=2.13a.

Fig. 8.
Fig. 8.

Electric modal field amplitudes (y-component, in the x-y plane, at z=0) for a composite supercell featuring an air layer of thickness ∆=2.13a. Note the resemblance with the y-polarized m=3 mode in Fig. 4, and the significant field decay in the air layer.

Tables (1)

Tables Icon

Table 1. Estimated (via Fano-fit) parameters of the first two GRs for a PQC slab (geometry and parameters as in Fig. 2) and a reference periodic (square) PC slab with same thickness, lattice constant, and air/dielectric fraction.

Equations (4)

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

T ( ν ) = T d ( ν ) k T d ( ν ) ± R d ( ν ) 1 + i Ω k .
R d ( ν ) = i ( 1 n ¯ 2 ) 2 n ¯ sin ( n ¯ ν h a ) cos ( n ¯ ν h a ) i ( 1 + n ¯ 2 ) 2 n ¯ sin ( n ¯ ν h a ) . T d ( ν ) = 1 cos ( n ¯ ν h a ) i ( 1 + n ¯ 2 ) 2 n ¯ sin ( n ¯ ν h a ) ,
n ¯ ( ν ) = 98.361 ν 2 + 1.534 ν + 6.699 .
T GR k ( ν ) = T d ( ν ) ± R d ( ν ) 1 + i Ω k .

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