Abstract

We measure the normal-incidence transmission coefficient of photonic crystal slabs with hexagonal arrays of air holes in silicon. The transmission spectra exhibit sharp resonant features with Fano line shapes. They are produced due to the coupling of the leaky photonic crystal modes, called guided resonances, to the continuum of free-space modes. We investigate the effects of several types of structural disorder on the spectra of these resonances. Our results indicate that guided resonances are very tolerant to disorder in the hole diameter and to interface roughness, but very sensitive to disorder in the lattice periodicity.

© 2007 Optical Society of America

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    [CrossRef]

2007 (6)

Y. Kanamori, T. Kitani, and K. Hane, "Control of guided resonance in a photonic crystal slab using microelectromechanical actuators," Appl. Phys. Lett. 90, 31911 (2007).
[CrossRef]

A. Chakrabarti, "Fano resonance in discrete lattice models: Controlling lineshapes with impurities," Phys. Lett. A 366, 507-512 (2007).
[CrossRef]

R. Harbers, S. Jochim, N. Moll, R. F. Mahrt, D. Erni, J. A. Hoffnagle, and W. D. Hinsberg, "Control of Fano line shapes by means of photonic crystal structures in a dye-doped polymer," Appl. Phys. Lett. 90, 201105 (2007).
[CrossRef]

I. V. Ponomarev, M. Schwab, G. Dasbach, M. Bayer, T. L. Reinecke, J. P. Reithmaier, and A. Forchel, "Influence of geometric disorder on the band structure of a photonic crystal: Experiment and theory," Phys. Rev. B 75, 205434 (2007).
[CrossRef]

R. Meisels and F. Kuchar, "Density-of-states and wave propagation in two-dimensional photonic crystals with positional disorder," J. Opt. A 9, S396-S402 (2007).
[CrossRef]

D. Nau, A. Schonhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, "Correlation effects in disordered metallic photonic crystal slabs," Phys. Rev. Lett. 98, 133902 (2007).
[CrossRef] [PubMed]

2006 (8)

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

Z. P. Jian and D. M. Mittleman, "Characterization of guided resonances in photonic crystal slabs using terahertz time-domain spectroscopy," J. Appl. Phys. 100, 123113 (2006).
[CrossRef]

N. Jukam, C. Yee, M. S. Sherwin, I. Fushman, and J. Vuckovic, "Patterned femtosecond laser excitation of terahertz leaky modes in GaAs photonic crystals," Appl. Phys. Lett. 89, 241112 (2006).
[CrossRef]

K. Dossou, L.C. Botten, C. M. de Sterke, R. McPhedran, A. A. Asatryan, S. Chen, and J. Brnovic, "Efficient couplers for photonic crystal waveguides," Opt. Comm. 265, 207-219 (2006).
[CrossRef]

A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, "Light diffraction from opal-based photonic crystals with growth-induced disorder: Experiment and theory," Phys. Rev. B 73, 205118 (2006).
[CrossRef]

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).
[CrossRef] [PubMed]

R. Ferrini, D. Leuenberger, R. Houdre, H. Benisty, M. Kamp, and A. Forchel, "Disorder-induced losses in planar photonic crystals," Opt. Lett. 31, 1426-1428 (2006).
[CrossRef] [PubMed]

J. F. Song, R. P. Zaccaria, M. B. Yu, and X. W. Sun, "Tunable Fano resonance in photonic crystal slabs," Opt. Express 14, 8812-8826 (2006).
[CrossRef] [PubMed]

2005 (8)

M. Skorobogatiy, G. Bégin, and A. Talneau, "Statistical analysis of geometrical imperfections from the images of 2D photonic crystals," Opt. Express 13, 2487-2502 (2005).
[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).
[CrossRef] [PubMed]

P. Roberts, F. Couny, H. Sabert, B. Mangan, T. Birks, J. Knight, and P. Russell, "Loss in solid-core photonic crystal fibers due to interface roughness scattering," Opt. Express 13, 7779-7793 (2005).
[CrossRef] [PubMed]

Z. Jian, J. Pearce, and D. M. Mittleman, "Two-dimensional photonic crystal slabs in parallel-plate metal waveguides studied with terahertz time-domain spectroscopy," Semiconductor Sci. Tech. 20, S300-S306 (2005).
[CrossRef]

W. Suh, O. Solgaard, and S. Fan, "Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs," J. Appl. Phys. 98, 33102 (2005).
[CrossRef]

R. Rengarajan, D. Mittleman, C. Rich, and V. Colvin, "Effect of disorder on the optical properties of colloidal crystals," Phys. Rev. E 71, 16615 (2005).
[CrossRef]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: Role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94, 33903 (2005).
[CrossRef]

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, "Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap," J. Phys.: Cond. Matter 17, 4049-4055 (2005).
[CrossRef]

2004 (5)

M. H. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

W. R. Frei and H. T. Johnson, "Finite-element analysis of disorder effects in photonic crystals," Phys. Rev. B 70, 165116 (2004).
[CrossRef]

A. R. P. Rau, "Perspectives on the Fano resonance formula," Phys. Scr. 69, C10-C13 (2004).
[CrossRef]

O. Kilic, S. Kim, W. Suh, Y. A. Peter, A. S. Sudbo, M. F. Yanik, S. H. Fan, and O. Solgaard, "Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders," Opt. Lett. 29, 2782-2784 (2004).
[CrossRef] [PubMed]

K. R. Maskaly, G. R. Maskaly, W. C. Carter, and J. L. Maxwell, "Diminished normal reflectivity of one-dimensional photonic crystals due to dielectric interfacial roughness," Opt. Lett. 29, 2791-2793 (2004).
[CrossRef] [PubMed]

2003 (8)

S. H. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the Fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569-572 (2003).
[CrossRef]

W. Bogaerts, P. Bienstman, and R. Baets, "Scattering at sidewall roughness in photonic crystal slabs," Opt. Lett. 28, 689-691 (2003).
[CrossRef] [PubMed]

K.-C. Kwan, X. Zhang, Z.-Q. Zhang, and C. T. Chan, "Effects due to disorder on photonic crystal-based waveguides," Appl. Phys. Lett. 82, 4414-4416 (2003).
[CrossRef]

N. Jukam and M. S. Sherwin, "Two-dimensional terahertz photonic crystals fabricated by deep reactive ion etching in Si," Appl. Phys. Lett. 83, 21-23 (2003).
[CrossRef]

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]

R. Ferrini, B. Lombardet, B. Wild, R. Houdre, and G. H. Duan, "Hole depth- and shape-induced radiation losses in two-dimensional photonic crystals," Appl. Phys. Lett. 82, 1009-1011 (2003).
[CrossRef]

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, "Disorder-induced modification of the attenuation of light in a two-dimensional photonic crystal with complete band gap," Phys. Stat. Sol. A 195, 612-617 (2003).
[CrossRef]

T. N. Langtry, A. A. Asatryan, L. C. Botten, C. M. de Sterke, R. C. McPhedran, and P. A. Robinson, "Effects of disorder in two-dimensional photonic crystal waveguides," Phys. Rev. E 68, 26611 (2003).
[CrossRef]

2002 (1)

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

2001 (2)

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

A. R. Cowan, P. Paddon, V. Pacradouni, and J. F. Young, "Resonant scattering and mode coupling in two-dimensional textured planar waveguides," J. Opt. Soc. Am. A 18, 1160-1170 (2001).
[CrossRef]

2000 (3)

S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[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]

1999 (6)

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]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

H. Y. Ryu, J. K. Hwang, and Y. H. Lee, "Effect of size nonuniformities on the band gap of two-dimensional photonic crystals," Phys. Rev. B 59, 5463-5469 (1999).
[CrossRef]

C. J. Jin, B. Y. Cheng, Z. L. Li, D. Z. Zhang, L. M. Li, and Z. Q. Zhang, "Two dimensional metallic photonic crystal in the THz range," Opt. Commun. 166, 9-13 (1999).
[CrossRef]

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 60, 6118-6127 (1999).
[CrossRef]

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, R. Biswas, and K. M. Ho, "Effect of disorder on photonic band gaps," Phys. Rev. B 59, 12767-12770 (1999).
[CrossRef]

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. H. 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]

1995 (1)

S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Theoretical investigation of fabrication-related disorder on the properties of photonic crystals," J. Appl. Phys. 78, 1415-1418 (1995).
[CrossRef]

1990 (2)

M. van Exter and D. R. Grischkowsky, "Characterization of an optoelectronic terahertz beam system," IEEE Trans. Microwave Theory Tech. 38, 1684-1691 (1990).
[CrossRef]

D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, "Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors," J. Opt. Soc. Am. B 7, 2006-2015 (1990).
[CrossRef]

1987 (2)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of Photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

1961 (1)

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

Abram, R. A.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, "Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap," J. Phys.: Cond. Matter 17, 4049-4055 (2005).
[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]

Albert, J. P.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, "Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap," J. Phys.: Cond. Matter 17, 4049-4055 (2005).
[CrossRef]

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, "Disorder-induced modification of the attenuation of light in a two-dimensional photonic crystal with complete band gap," Phys. Stat. Sol. A 195, 612-617 (2003).
[CrossRef]

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.

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]

Asatryan, A. A.

K. Dossou, L.C. Botten, C. M. de Sterke, R. McPhedran, A. A. Asatryan, S. Chen, and J. Brnovic, "Efficient couplers for photonic crystal waveguides," Opt. Comm. 265, 207-219 (2006).
[CrossRef]

T. N. Langtry, A. A. Asatryan, L. C. Botten, C. M. de Sterke, R. C. McPhedran, and P. A. Robinson, "Effects of disorder in two-dimensional photonic crystal waveguides," Phys. Rev. E 68, 26611 (2003).
[CrossRef]

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 60, 6118-6127 (1999).
[CrossRef]

Baets, R.

Baryshev, A. V.

A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, "Light diffraction from opal-based photonic crystals with growth-induced disorder: Experiment and theory," Phys. Rev. B 73, 205118 (2006).
[CrossRef]

Bauer, C.

D. Nau, A. Schonhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, "Correlation effects in disordered metallic photonic crystal slabs," Phys. Rev. Lett. 98, 133902 (2007).
[CrossRef] [PubMed]

Bayer, M.

I. V. Ponomarev, M. Schwab, G. Dasbach, M. Bayer, T. L. Reinecke, J. P. Reithmaier, and A. Forchel, "Influence of geometric disorder on the band structure of a photonic crystal: Experiment and theory," Phys. Rev. B 75, 205434 (2007).
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Beggs, D. M.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, "Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap," J. Phys.: Cond. Matter 17, 4049-4055 (2005).
[CrossRef]

Bégin, G.

Benisty, H.

Bienstman, P.

Birks, T.

Biswas, R.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, R. Biswas, and K. M. Ho, "Effect of disorder on photonic band gaps," Phys. Rev. B 59, 12767-12770 (1999).
[CrossRef]

Bogaerts, W.

Botten, L. C.

T. N. Langtry, A. A. Asatryan, L. C. Botten, C. M. de Sterke, R. C. McPhedran, and P. A. Robinson, "Effects of disorder in two-dimensional photonic crystal waveguides," Phys. Rev. E 68, 26611 (2003).
[CrossRef]

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 60, 6118-6127 (1999).
[CrossRef]

Botten, L.C.

K. Dossou, L.C. Botten, C. M. de Sterke, R. McPhedran, A. A. Asatryan, S. Chen, and J. Brnovic, "Efficient couplers for photonic crystal waveguides," Opt. Comm. 265, 207-219 (2006).
[CrossRef]

Brand, S.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, "Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap," J. Phys.: Cond. Matter 17, 4049-4055 (2005).
[CrossRef]

Brnovic, J.

K. Dossou, L.C. Botten, C. M. de Sterke, R. McPhedran, A. A. Asatryan, S. Chen, and J. Brnovic, "Efficient couplers for photonic crystal waveguides," Opt. Comm. 265, 207-219 (2006).
[CrossRef]

Bussmann, K.

Carter, M. W.

Carter, W. C.

Casey, J. A.

Cassagne, D.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, "Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap," J. Phys.: Cond. Matter 17, 4049-4055 (2005).
[CrossRef]

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, "Disorder-induced modification of the attenuation of light in a two-dimensional photonic crystal with complete band gap," Phys. Stat. Sol. A 195, 612-617 (2003).
[CrossRef]

Chakrabarti, A.

A. Chakrabarti, "Fano resonance in discrete lattice models: Controlling lineshapes with impurities," Phys. Lett. A 366, 507-512 (2007).
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Chan, C. T.

K.-C. Kwan, X. Zhang, Z.-Q. Zhang, and C. T. Chan, "Effects due to disorder on photonic crystal-based waveguides," Appl. Phys. Lett. 82, 4414-4416 (2003).
[CrossRef]

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, R. Biswas, and K. M. Ho, "Effect of disorder on photonic band gaps," Phys. Rev. B 59, 12767-12770 (1999).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. H. 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, S.

K. Dossou, L.C. Botten, C. M. de Sterke, R. McPhedran, A. A. Asatryan, S. Chen, and J. Brnovic, "Efficient couplers for photonic crystal waveguides," Opt. Comm. 265, 207-219 (2006).
[CrossRef]

Cheng, B. Y.

C. J. Jin, B. Y. Cheng, Z. L. Li, D. Z. Zhang, L. M. Li, and Z. Q. Zhang, "Two dimensional metallic photonic crystal in the THz range," Opt. Commun. 166, 9-13 (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]

Christ, A.

D. Nau, A. Schonhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, "Correlation effects in disordered metallic photonic crystal slabs," Phys. Rev. Lett. 98, 133902 (2007).
[CrossRef] [PubMed]

Chutinan, A.

S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
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Colvin, V.

R. Rengarajan, D. Mittleman, C. Rich, and V. Colvin, "Effect of disorder on the optical properties of colloidal crystals," Phys. Rev. E 71, 16615 (2005).
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Colvin, V. L.

T. Prasad, V. L. Colvin, and D. M. Mittleman, "Dependence of guided resonances on the structural parameters of terahertz photonic crystal slabs," Phys. Rev. B, submitted.

Couny, F.

Cowan, A. R.

Crozier, K. B.

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

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Dasbach, G.

I. V. Ponomarev, M. Schwab, G. Dasbach, M. Bayer, T. L. Reinecke, J. P. Reithmaier, and A. Forchel, "Influence of geometric disorder on the band structure of a photonic crystal: Experiment and theory," Phys. Rev. B 75, 205434 (2007).
[CrossRef]

de Sterke, C. M.

K. Dossou, L.C. Botten, C. M. de Sterke, R. McPhedran, A. A. Asatryan, S. Chen, and J. Brnovic, "Efficient couplers for photonic crystal waveguides," Opt. Comm. 265, 207-219 (2006).
[CrossRef]

T. N. Langtry, A. A. Asatryan, L. C. Botten, C. M. de Sterke, R. C. McPhedran, and P. A. Robinson, "Effects of disorder in two-dimensional photonic crystal waveguides," Phys. Rev. E 68, 26611 (2003).
[CrossRef]

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 60, 6118-6127 (1999).
[CrossRef]

Dossou, K.

K. Dossou, L.C. Botten, C. M. de Sterke, R. McPhedran, A. A. Asatryan, S. Chen, and J. Brnovic, "Efficient couplers for photonic crystal waveguides," Opt. Comm. 265, 207-219 (2006).
[CrossRef]

Duan, G. H.

R. Ferrini, B. Lombardet, B. Wild, R. Houdre, and G. H. Duan, "Hole depth- and shape-induced radiation losses in two-dimensional photonic crystals," Appl. Phys. Lett. 82, 1009-1011 (2003).
[CrossRef]

Eddy, C. R.

Eggleton, B. J.

Erni, D.

R. Harbers, S. Jochim, N. Moll, R. F. Mahrt, D. Erni, J. A. Hoffnagle, and W. D. Hinsberg, "Control of Fano line shapes by means of photonic crystal structures in a dye-doped polymer," Appl. Phys. Lett. 90, 201105 (2007).
[CrossRef]

Fan, S.

W. Suh, O. Solgaard, and S. Fan, "Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs," J. Appl. Phys. 98, 33102 (2005).
[CrossRef]

Fan, S. H.

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

O. Kilic, S. Kim, W. Suh, Y. A. Peter, A. S. Sudbo, M. F. Yanik, S. H. Fan, and O. Solgaard, "Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders," Opt. Lett. 29, 2782-2784 (2004).
[CrossRef] [PubMed]

S. H. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the Fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569-572 (2003).
[CrossRef]

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

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

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]

A. Mekis, J. C. Chen, I. Kurland, S. H. 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]

S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Theoretical investigation of fabrication-related disorder on the properties of photonic crystals," J. Appl. Phys. 78, 1415-1418 (1995).
[CrossRef]

Fano, U.

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

Fattinger, C.

Ferrini, R.

R. Ferrini, D. Leuenberger, R. Houdre, H. Benisty, M. Kamp, and A. Forchel, "Disorder-induced losses in planar photonic crystals," Opt. Lett. 31, 1426-1428 (2006).
[CrossRef] [PubMed]

R. Ferrini, B. Lombardet, B. Wild, R. Houdre, and G. H. Duan, "Hole depth- and shape-induced radiation losses in two-dimensional photonic crystals," Appl. Phys. Lett. 82, 1009-1011 (2003).
[CrossRef]

Forchel, A.

I. V. Ponomarev, M. Schwab, G. Dasbach, M. Bayer, T. L. Reinecke, J. P. Reithmaier, and A. Forchel, "Influence of geometric disorder on the band structure of a photonic crystal: Experiment and theory," Phys. Rev. B 75, 205434 (2007).
[CrossRef]

R. Ferrini, D. Leuenberger, R. Houdre, H. Benisty, M. Kamp, and A. Forchel, "Disorder-induced losses in planar photonic crystals," Opt. Lett. 31, 1426-1428 (2006).
[CrossRef] [PubMed]

Freeman, D.

Frei, W. R.

W. R. Frei and H. T. Johnson, "Finite-element analysis of disorder effects in photonic crystals," Phys. Rev. B 70, 165116 (2004).
[CrossRef]

Fushman, I.

N. Jukam, C. Yee, M. S. Sherwin, I. Fushman, and J. Vuckovic, "Patterned femtosecond laser excitation of terahertz leaky modes in GaAs photonic crystals," Appl. Phys. Lett. 89, 241112 (2006).
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Giessen, H.

D. Nau, A. Schonhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, "Correlation effects in disordered metallic photonic crystal slabs," Phys. Rev. Lett. 98, 133902 (2007).
[CrossRef] [PubMed]

Grillet, C.

Grischkowsky, D.

Grischkowsky, D. R.

M. van Exter and D. R. Grischkowsky, "Characterization of an optoelectronic terahertz beam system," IEEE Trans. Microwave Theory Tech. 38, 1684-1691 (1990).
[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, 31911 (2007).
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Harbers, R.

R. Harbers, S. Jochim, N. Moll, R. F. Mahrt, D. Erni, J. A. Hoffnagle, and W. D. Hinsberg, "Control of Fano line shapes by means of photonic crystal structures in a dye-doped polymer," Appl. Phys. Lett. 90, 201105 (2007).
[CrossRef]

Henry, R. L.

Hinsberg, W. D.

R. Harbers, S. Jochim, N. Moll, R. F. Mahrt, D. Erni, J. A. Hoffnagle, and W. D. Hinsberg, "Control of Fano line shapes by means of photonic crystal structures in a dye-doped polymer," Appl. Phys. Lett. 90, 201105 (2007).
[CrossRef]

Ho, K. M.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, R. Biswas, and K. M. Ho, "Effect of disorder on photonic band gaps," Phys. Rev. B 59, 12767-12770 (1999).
[CrossRef]

Hoffnagle, J. A.

R. Harbers, S. Jochim, N. Moll, R. F. Mahrt, D. Erni, J. A. Hoffnagle, and W. D. Hinsberg, "Control of Fano line shapes by means of photonic crystal structures in a dye-doped polymer," Appl. Phys. Lett. 90, 201105 (2007).
[CrossRef]

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]

Houdre, R.

R. Ferrini, D. Leuenberger, R. Houdre, H. Benisty, M. Kamp, and A. Forchel, "Disorder-induced losses in planar photonic crystals," Opt. Lett. 31, 1426-1428 (2006).
[CrossRef] [PubMed]

R. Ferrini, B. Lombardet, B. Wild, R. Houdre, and G. H. Duan, "Hole depth- and shape-induced radiation losses in two-dimensional photonic crystals," Appl. Phys. Lett. 82, 1009-1011 (2003).
[CrossRef]

Hughes, S.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: Role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94, 33903 (2005).
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Hwang, J. K.

H. Y. Ryu, J. K. Hwang, and Y. H. Lee, "Effect of size nonuniformities on the band gap of two-dimensional photonic crystals," Phys. Rev. B 59, 5463-5469 (1999).
[CrossRef]

Imada, M.

S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Ippen, E. P.

M. H. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Jian, Z.

Z. Jian, J. Pearce, and D. M. Mittleman, "Two-dimensional photonic crystal slabs in parallel-plate metal waveguides studied with terahertz time-domain spectroscopy," Semiconductor Sci. Tech. 20, S300-S306 (2005).
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Jian, Z. P.

Z. P. Jian and D. M. Mittleman, "Characterization of guided resonances in photonic crystal slabs using terahertz time-domain spectroscopy," J. Appl. Phys. 100, 123113 (2006).
[CrossRef]

Jin, C. J.

C. J. Jin, B. Y. Cheng, Z. L. Li, D. Z. Zhang, L. M. Li, and Z. Q. Zhang, "Two dimensional metallic photonic crystal in the THz range," Opt. Commun. 166, 9-13 (1999).
[CrossRef]

Joannopoulos, J. D.

M. H. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

S. H. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the Fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569-572 (2003).
[CrossRef]

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

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[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]

A. Mekis, J. C. Chen, I. Kurland, S. H. 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]

S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Theoretical investigation of fabrication-related disorder on the properties of photonic crystals," J. Appl. Phys. 78, 1415-1418 (1995).
[CrossRef]

Jochim, S.

R. Harbers, S. Jochim, N. Moll, R. F. Mahrt, D. Erni, J. A. Hoffnagle, and W. D. Hinsberg, "Control of Fano line shapes by means of photonic crystal structures in a dye-doped polymer," Appl. Phys. Lett. 90, 201105 (2007).
[CrossRef]

John, S.

S. John, "Strong localization of Photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

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R. Harbers, S. Jochim, N. Moll, R. F. Mahrt, D. Erni, J. A. Hoffnagle, and W. D. Hinsberg, "Control of Fano line shapes by means of photonic crystal structures in a dye-doped polymer," Appl. Phys. Lett. 90, 201105 (2007).
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Figures (9)

Fig. 1.
Fig. 1.

A schematic of the experimental setup. The terahertz radiation propagates in the direction perpendicular to the plane of the photonic crystal slab. The terahertz beam spot size is roughly 8 mm. The samples are all very thin compared to the Rayleigh range of the focused THz beam.

Fig. 2.
Fig. 2.

(a). A top view of the photonic crystal slab. The scale bar is 5 mm. (b) A magnified portion from (a), with a scale bar of 300 µm. The crystal parameters of this sample are r=150 µm, a=400 µm, and t=250 µm. For a hexagonal lattice, the Γ-K direction points along the axis connecting the centers of adjacent (nearest neighbor) holes, while the Γ-M direction points along the axis connecting the centers of next-nearest neighbors.

Fig. 3.
Fig. 3.

Normal-incidence transmission spectrum of a photonic crystal slab with r=150 µm, a=400 µm, and t=250 µm. The open black circles are experimental results, while the solid red curve is obtained from simulations based on the finite elements method (FEM).

Fig. 4.
Fig. 4.

Distribution of the hole diameter for perfect (top) and imperfect (middle and bottom) samples. The perfect sample has a mean hole diameter of 297 µm, which is close to the design parameter of 300 µm. The three samples have hole diameters with standard deviations of 1 µm, 32.0 µm, and 39.6 µm, from top to bottom. The samples in the lower two images have different slab thicknesses. The bin size of each bar in the histogram is 5 µm. Images show sample regions within a 8 mm circular area, roughly equal to the THz beam spot size. All scale bars are 1.5 mm.

Fig. 5.
Fig. 5.

Normal-incidence transmission spectra of photonic crystal slabs with disorder in the hole size. (a) The solid black curve is the transmission spectrum of the ideal crystal with r=150 µm, a=400 µm, and t=250 µm (top picture, Fig. 4), while the dashed red curve is the spectrum of the corresponding imperfect sample (middle picture, Fig. 4). (b) Same as (a) but for a sample with slightly different slab thickness of 275 µm. The corresponding imperfect sample is shown in Fig. 4 (bottom picture).

Fig. 6.
Fig. 6.

Top-view images of photonic crystal slabs showing disorder in the hole shape. Images from left to right increase in magnification. (a) Sample with nominally perfectly circular holes, of diameter 250 µm. (b) Sample with holes of imperfectly circular shape, exhibiting interface roughness.

Fig. 7.
Fig. 7.

Normal-incidence transmission spectra of photonic crystal slabs with r=125 µm, a=400 µm, and t=300 µm. The solid black curve is for the sample with perfectly circular holes [shown in Fig. 6(a)], while the dashed red curve is for a sample with slight disorder in the hole shape [shown in Fig. 6(b)].

Fig. 8.
Fig. 8.

Top-view images of photonic crystal slabs with disorder in the lattice parameter. The holes have a diameter of 250 µm, and the lattice parameter of the nominally perfect sample is 400 µm. (a) Sample with no disorder in the lattice parameter. The first column shows a sample region within a 7 mm circular area. The second column shows a magnified portion of the image in the first column. The last column shows the pair correlation function (red) computed from the image in the first column. The (black) vertical lines depict the pair correlation function of a perfect lattice of infinite size. (b) Same as (a), but for a sample with slight disorder in the lattice parameter. (c) Same as (b), but with a greater degree of disorder in the lattice parameter. All scale bars in the first column are 1.5 mm, while those in the second column are 300 µm.

Fig. 9.
Fig. 9.

Normal-incidence transmission spectra of photonic crystal slabs with r=125 µm, a=400 µm, and t=300 µm. (a) A perfect sample with no disorder in the lattice parameter [shown in Fig. 8(a)]. (b) A sample with slight disorder in the lattice parameter [shown in Fig. 8(b)]. (c) A sample with greater degree of disorder in the lattice parameter [shown in Fig. 8(c)].

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