Abstract

We analyze and compare the effect of fabrication disorder on the quality factor of six well-known high-index photonic crystal cavity designs. The theoretical quality factors for the different nominal structures span more than three orders of magnitude, ranging from 5.4 × 104 to 7.5 × 107, and the defect responsible for confining light is introduced in a different way for each structure. Nevertheless, among the different designs we observe similar behavior of the statistics of the disorder-induced light losses. In particular, we show that for high enough disorder, such that the quality factor is mainly determined by the disorder-induced losses, the measured quality factors differ marginally – not only on average as commonly acknowledged, but also in their full statistical distributions. This notably shows that optimizing the theoretical quality factor brings little practical improvement if its value is already much larger than what is typically measured, and if this is the case, there is no way to choose an alternative design more robust to disorder.

© 2013 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  40. N. Descharmes, U. P. Dharanipathy, Z. Diao, M. Tonin, and R. Houdré, “Observation of backaction and self-induced trapping in a planar hollow photonic crystal cavity,” Phys. Rev. Lett.110, 123601 (2013).
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2013 (2)

N. Descharmes, U. P. Dharanipathy, Z. Diao, M. Tonin, and R. Houdré, “Observation of backaction and self-induced trapping in a planar hollow photonic crystal cavity,” Phys. Rev. Lett.110, 123601 (2013).
[CrossRef]

M. Minkov and V. Savona, “Radiative coupling of quantum dots in photonic crystal structures,” Phys. Rev. B87, 125306 (2013).
[CrossRef]

2012 (7)

V. Savona, “Erratum: Electromagnetic modes of a disordered photonic crystal [phys. rev. b 83, 085301 (2011)],” Phys. Rev. B86, 079907 (2012).
[CrossRef]

M. Minkov and V. Savona, “Effect of hole-shape irregularities on photonic crystal waveguides,” Opt. Lett.37, 3108–3110 (2012).
[CrossRef] [PubMed]

K. Welna, S. Portalupi, M. Galli, L. O’Faolain, and T. Krauss, “Novel dispersion-adapted photonic crystal cavity with improved disorder stability,” IEEE J. Quantum Electron.48, 1177–1183 (2012).
[CrossRef]

H. Takagi, Y. Ota, N. Kumagai, S. Ishida, S. Iwamoto, and Y. Arakawa, “High q h1 photonic crystal nanocavities with efficient vertical emission,” Opt. Express20, 28292–28300 (2012).
[CrossRef] [PubMed]

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics6, 605–609 (2012).
[CrossRef]

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics6, 248–252 (2012).
[CrossRef]

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photonics6, 56–61 (2012).
[CrossRef]

2011 (4)

Y. Taguchi, Y. Takahashi, Y. Sato, T. Asano, and S. Noda, “Statistical studies of photonic heterostructure nanocavities with an average q factor of three million,” Opt. Express19, 11916–11921 (2011).
[CrossRef] [PubMed]

S. L. Portalupi, M. Galli, M. Belotti, L. C. Andreani, T. F. Krauss, and L. O’Faolain, “Deliberate versus intrinsic disorder in photonic crystal nanocavities investigated by resonant light scattering,” Phys. Rev. B84, 045423 (2011).
[CrossRef]

V. Savona, “Electromagnetic modes of a disordered photonic crystal,” Phys. Rev. B83, 085301 (2011).
[CrossRef]

N. L. Thomas, Z. Diao, H. Zhang, and R. Houdre, “Statistical analysis of subnanometer residual disorder in photonic crystal waveguides: Correlation between slow light properties and structural properties,” J. Vac. Sci. Technol. B29, 051601 (2011).
[CrossRef]

2010 (7)

J. Jágerská, H. Zhang, Z. Diao, N. L. Thomas, and R. Houdré, “Refractive index sensing with an air-slot photonic crystal nanocavity,” Opt. Lett.35, 2523–2525 (2010).
[CrossRef] [PubMed]

S. Vignolini, F. Riboli, D. S. Wiersma, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, and F. Intonti, “Nanofluidic control of coupled photonic crystal resonators,” Appl. Phys. Lett.96, 141114 (2010).
[CrossRef]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics4, 477–483 (2010).
[CrossRef]

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of gaas photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology21, 065202 (2010).
[CrossRef] [PubMed]

M. Felici, K. A. Atlasov, A. Surrente, and E. Kapon, “Semianalytical approach to the design of photonic crystal cavities,” Phys. Rev. B82, 115118 (2010).
[CrossRef]

M. Nomura, K. Tanabe, S. Iwamoto, and Y. Arakawa, “High-q design of semiconductor-based ultrasmall photonic crystal nanocavity,” Opt. Express18, 8144–8150 (2010).
[CrossRef] [PubMed]

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys.73, 096501 (2010).
[CrossRef]

2009 (4)

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3, 687–695 (2009).
[CrossRef]

C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett.94, 021111 (2009).
[CrossRef]

H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities,” Phys. Rev. B79, 085112 (2009).
[CrossRef]

D. Dorfner, T. Zabel, T. Hrlimann, N. Hauke, L. Frandsen, U. Rant, G. Abstreiter, and J. Finley, “Photonic crystal nanostructures for optical biosensing applications,” Biosens. Bioelectron.24, 3688–3692 (2009).
[CrossRef] [PubMed]

2008 (1)

2007 (2)

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics1, 49–52 (2007).
[CrossRef]

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1, 449–458 (2007).
[CrossRef]

2006 (6)

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett.88, 041112 (2006).
[CrossRef]

G. Khitrova, H. Gibbs, M. Kira, S. Koch, and A. Scherer, “Vacuum rabi splitting in semiconductors,” Nat. Phys.2, 81–90 (2006).
[CrossRef]

T. Asano, B.-S. Song, and S. Noda, “Analysis of the experimental Q factors ( 1 million) of photonic crystal nanocavities,” Opt. Express14, 1996–2002 (2006).
[CrossRef] [PubMed]

L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guied-mode expansion method,” Phys. Rev. B73, 235114 (2006).
[CrossRef]

T. Uesugi, B.-S. Song, T. Asano, and S. Noda, “Investigation of optical nonlinearities in an ultra-high-q si nanocavity in a two-dimensional photonic crystal slab,” Opt. Express14, 377–386 (2006).
[CrossRef] [PubMed]

K. Hennessy, C. Hogerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett.89, 041118 (2006).
[CrossRef]

2005 (3)

D. Gerace and L. C. Andreani, “Effects of disorder on propagation losses and cavity q-factors in photonic crystal slabs,”Photonics Nanostruct. Fundam. Appl.3, 120–128 (2005).
[CrossRef]

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater.4, 207–210 (2005).
[CrossRef]

D. Englund, I. Fushman, and J. Vuckovic, “General recipe for designing photonic crystal cavities,” Opt. Express13, 5961–5975 (2005).
[CrossRef] [PubMed]

2004 (2)

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum rabi splitting with a single quantum dot in a photonic crystal nanocavity,”Nature432, 200–203 (2004).
[CrossRef]

Z. Zhang and M. Qiu, “Small-volume waveguide-section high q microcavities in 2d photonic crystal slabs,” Opt. Express12, 3988–3995 (2004).
[CrossRef] [PubMed]

2003 (2)

Y. Tanaka, T. Asano, Y. Akahane, B.-S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes,” Appl. Phys. Lett.82, 1661–1663 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,”Nature425, 944–947 (2003).
[CrossRef]

Abstreiter, G.

D. Dorfner, T. Zabel, T. Hrlimann, N. Hauke, L. Frandsen, U. Rant, G. Abstreiter, and J. Finley, “Photonic crystal nanostructures for optical biosensing applications,” Biosens. Bioelectron.24, 3688–3692 (2009).
[CrossRef] [PubMed]

Akahane, Y.

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater.4, 207–210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,”Nature425, 944–947 (2003).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B.-S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes,” Appl. Phys. Lett.82, 1661–1663 (2003).
[CrossRef]

Andreani, L. C.

S. L. Portalupi, M. Galli, M. Belotti, L. C. Andreani, T. F. Krauss, and L. O’Faolain, “Deliberate versus intrinsic disorder in photonic crystal nanocavities investigated by resonant light scattering,” Phys. Rev. B84, 045423 (2011).
[CrossRef]

L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guied-mode expansion method,” Phys. Rev. B73, 235114 (2006).
[CrossRef]

D. Gerace and L. C. Andreani, “Effects of disorder on propagation losses and cavity q-factors in photonic crystal slabs,”Photonics Nanostruct. Fundam. Appl.3, 120–128 (2005).
[CrossRef]

Arakawa, Y.

Asano, T.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photonics6, 56–61 (2012).
[CrossRef]

Y. Taguchi, Y. Takahashi, Y. Sato, T. Asano, and S. Noda, “Statistical studies of photonic heterostructure nanocavities with an average q factor of three million,” Opt. Express19, 11916–11921 (2011).
[CrossRef] [PubMed]

H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities,” Phys. Rev. B79, 085112 (2009).
[CrossRef]

Y. Tanaka, T. Asano, and S. Noda, “Design of photonic crystal nanocavity with Q-factor of ∼ 109,” J. Lightwave Technol.26, 1532–1539 (2008).
[CrossRef]

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1, 449–458 (2007).
[CrossRef]

T. Asano, B.-S. Song, and S. Noda, “Analysis of the experimental Q factors ( 1 million) of photonic crystal nanocavities,” Opt. Express14, 1996–2002 (2006).
[CrossRef] [PubMed]

T. Uesugi, B.-S. Song, T. Asano, and S. Noda, “Investigation of optical nonlinearities in an ultra-high-q si nanocavity in a two-dimensional photonic crystal slab,” Opt. Express14, 377–386 (2006).
[CrossRef] [PubMed]

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater.4, 207–210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,”Nature425, 944–947 (2003).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B.-S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes,” Appl. Phys. Lett.82, 1661–1663 (2003).
[CrossRef]

Atlasov, K. A.

M. Felici, K. A. Atlasov, A. Surrente, and E. Kapon, “Semianalytical approach to the design of photonic crystal cavities,” Phys. Rev. B82, 115118 (2010).
[CrossRef]

Badolato, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics6, 605–609 (2012).
[CrossRef]

K. Hennessy, C. Hogerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett.89, 041118 (2006).
[CrossRef]

Balet, L.

S. Vignolini, F. Riboli, D. S. Wiersma, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, and F. Intonti, “Nanofluidic control of coupled photonic crystal resonators,” Appl. Phys. Lett.96, 141114 (2010).
[CrossRef]

Belotti, M.

S. L. Portalupi, M. Galli, M. Belotti, L. C. Andreani, T. F. Krauss, and L. O’Faolain, “Deliberate versus intrinsic disorder in photonic crystal nanocavities investigated by resonant light scattering,” Phys. Rev. B84, 045423 (2011).
[CrossRef]

Carmichael, H.

H. Carmichael, Statistical Methods in Quantum Optics 2: Non-Classical Fields (Springer, 2008).
[CrossRef]

Combrie, S.

C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett.94, 021111 (2009).
[CrossRef]

Deppe, D.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum rabi splitting with a single quantum dot in a photonic crystal nanocavity,”Nature432, 200–203 (2004).
[CrossRef]

Descharmes, N.

N. Descharmes, U. P. Dharanipathy, Z. Diao, M. Tonin, and R. Houdré, “Observation of backaction and self-induced trapping in a planar hollow photonic crystal cavity,” Phys. Rev. Lett.110, 123601 (2013).
[CrossRef]

Dharanipathy, U. P.

N. Descharmes, U. P. Dharanipathy, Z. Diao, M. Tonin, and R. Houdré, “Observation of backaction and self-induced trapping in a planar hollow photonic crystal cavity,” Phys. Rev. Lett.110, 123601 (2013).
[CrossRef]

Diao, Z.

N. Descharmes, U. P. Dharanipathy, Z. Diao, M. Tonin, and R. Houdré, “Observation of backaction and self-induced trapping in a planar hollow photonic crystal cavity,” Phys. Rev. Lett.110, 123601 (2013).
[CrossRef]

N. L. Thomas, Z. Diao, H. Zhang, and R. Houdre, “Statistical analysis of subnanometer residual disorder in photonic crystal waveguides: Correlation between slow light properties and structural properties,” J. Vac. Sci. Technol. B29, 051601 (2011).
[CrossRef]

J. Jágerská, H. Zhang, Z. Diao, N. L. Thomas, and R. Houdré, “Refractive index sensing with an air-slot photonic crystal nanocavity,” Opt. Lett.35, 2523–2525 (2010).
[CrossRef] [PubMed]

Dorfner, D.

D. Dorfner, T. Zabel, T. Hrlimann, N. Hauke, L. Frandsen, U. Rant, G. Abstreiter, and J. Finley, “Photonic crystal nanostructures for optical biosensing applications,” Biosens. Bioelectron.24, 3688–3692 (2009).
[CrossRef] [PubMed]

Ell, C.

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[CrossRef]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics4, 477–483 (2010).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics1, 49–52 (2007).
[CrossRef]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett.88, 041112 (2006).
[CrossRef]

Song, B.

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater.4, 207–210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,”Nature425, 944–947 (2003).
[CrossRef]

Song, B.-S.

Surrente, A.

M. Felici, K. A. Atlasov, A. Surrente, and E. Kapon, “Semianalytical approach to the design of photonic crystal cavities,” Phys. Rev. B82, 115118 (2010).
[CrossRef]

Suzaki, Y.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics6, 248–252 (2012).
[CrossRef]

Sweet, J.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of gaas photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology21, 065202 (2010).
[CrossRef] [PubMed]

Taguchi, Y.

Takagi, H.

Takahashi, R.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics6, 248–252 (2012).
[CrossRef]

Takahashi, Y.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photonics6, 56–61 (2012).
[CrossRef]

Y. Taguchi, Y. Takahashi, Y. Sato, T. Asano, and S. Noda, “Statistical studies of photonic heterostructure nanocavities with an average q factor of three million,” Opt. Express19, 11916–11921 (2011).
[CrossRef] [PubMed]

H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities,” Phys. Rev. B79, 085112 (2009).
[CrossRef]

Tanabe, K.

Tanabe, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics4, 477–483 (2010).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics1, 49–52 (2007).
[CrossRef]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett.88, 041112 (2006).
[CrossRef]

Tanaka, Y.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photonics6, 56–61 (2012).
[CrossRef]

H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities,” Phys. Rev. B79, 085112 (2009).
[CrossRef]

Y. Tanaka, T. Asano, and S. Noda, “Design of photonic crystal nanocavity with Q-factor of ∼ 109,” J. Lightwave Technol.26, 1532–1539 (2008).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B.-S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes,” Appl. Phys. Lett.82, 1661–1663 (2003).
[CrossRef]

Taniyama, H.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics4, 477–483 (2010).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics1, 49–52 (2007).
[CrossRef]

Thomas, N. L.

N. L. Thomas, Z. Diao, H. Zhang, and R. Houdre, “Statistical analysis of subnanometer residual disorder in photonic crystal waveguides: Correlation between slow light properties and structural properties,” J. Vac. Sci. Technol. B29, 051601 (2011).
[CrossRef]

J. Jágerská, H. Zhang, Z. Diao, N. L. Thomas, and R. Houdré, “Refractive index sensing with an air-slot photonic crystal nanocavity,” Opt. Lett.35, 2523–2525 (2010).
[CrossRef] [PubMed]

Tonin, M.

N. Descharmes, U. P. Dharanipathy, Z. Diao, M. Tonin, and R. Houdré, “Observation of backaction and self-induced trapping in a planar hollow photonic crystal cavity,” Phys. Rev. Lett.110, 123601 (2013).
[CrossRef]

Tran, Q. V.

C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett.94, 021111 (2009).
[CrossRef]

Uesugi, T.

Upham, J.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photonics6, 56–61 (2012).
[CrossRef]

Vignolini, S.

S. Vignolini, F. Riboli, D. S. Wiersma, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, and F. Intonti, “Nanofluidic control of coupled photonic crystal resonators,” Appl. Phys. Lett.96, 141114 (2010).
[CrossRef]

Volz, T.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics6, 605–609 (2012).
[CrossRef]

Vuckovic, J.

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3, 687–695 (2009).
[CrossRef]

D. Englund, I. Fushman, and J. Vuckovic, “General recipe for designing photonic crystal cavities,” Opt. Express13, 5961–5975 (2005).
[CrossRef] [PubMed]

Watanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett.88, 041112 (2006).
[CrossRef]

Welna, K.

K. Welna, S. Portalupi, M. Galli, L. O’Faolain, and T. Krauss, “Novel dispersion-adapted photonic crystal cavity with improved disorder stability,” IEEE J. Quantum Electron.48, 1177–1183 (2012).
[CrossRef]

Wiersma, D. S.

S. Vignolini, F. Riboli, D. S. Wiersma, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, and F. Intonti, “Nanofluidic control of coupled photonic crystal resonators,” Appl. Phys. Lett.96, 141114 (2010).
[CrossRef]

Winger, M.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics6, 605–609 (2012).
[CrossRef]

Winn, J. N.

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

Wong, C. W.

C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett.94, 021111 (2009).
[CrossRef]

Yoshie, T.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum rabi splitting with a single quantum dot in a photonic crystal nanocavity,”Nature432, 200–203 (2004).
[CrossRef]

Zabel, T.

D. Dorfner, T. Zabel, T. Hrlimann, N. Hauke, L. Frandsen, U. Rant, G. Abstreiter, and J. Finley, “Photonic crystal nanostructures for optical biosensing applications,” Biosens. Bioelectron.24, 3688–3692 (2009).
[CrossRef] [PubMed]

Zhang, H.

N. L. Thomas, Z. Diao, H. Zhang, and R. Houdre, “Statistical analysis of subnanometer residual disorder in photonic crystal waveguides: Correlation between slow light properties and structural properties,” J. Vac. Sci. Technol. B29, 051601 (2011).
[CrossRef]

J. Jágerská, H. Zhang, Z. Diao, N. L. Thomas, and R. Houdré, “Refractive index sensing with an air-slot photonic crystal nanocavity,” Opt. Lett.35, 2523–2525 (2010).
[CrossRef] [PubMed]

Zhang, Z.

Appl. Phys. Lett. (5)

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett.88, 041112 (2006).
[CrossRef]

C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett.94, 021111 (2009).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B.-S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes,” Appl. Phys. Lett.82, 1661–1663 (2003).
[CrossRef]

K. Hennessy, C. Hogerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett.89, 041118 (2006).
[CrossRef]

S. Vignolini, F. Riboli, D. S. Wiersma, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, and F. Intonti, “Nanofluidic control of coupled photonic crystal resonators,” Appl. Phys. Lett.96, 141114 (2010).
[CrossRef]

Biosens. Bioelectron. (1)

D. Dorfner, T. Zabel, T. Hrlimann, N. Hauke, L. Frandsen, U. Rant, G. Abstreiter, and J. Finley, “Photonic crystal nanostructures for optical biosensing applications,” Biosens. Bioelectron.24, 3688–3692 (2009).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

K. Welna, S. Portalupi, M. Galli, L. O’Faolain, and T. Krauss, “Novel dispersion-adapted photonic crystal cavity with improved disorder stability,” IEEE J. Quantum Electron.48, 1177–1183 (2012).
[CrossRef]

J. Lightwave Technol. (1)

J. Vac. Sci. Technol. B (1)

N. L. Thomas, Z. Diao, H. Zhang, and R. Houdre, “Statistical analysis of subnanometer residual disorder in photonic crystal waveguides: Correlation between slow light properties and structural properties,” J. Vac. Sci. Technol. B29, 051601 (2011).
[CrossRef]

Nanotechnology (1)

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of gaas photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology21, 065202 (2010).
[CrossRef] [PubMed]

Nat. Mater. (1)

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater.4, 207–210 (2005).
[CrossRef]

Nat. Photonics (7)

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics1, 49–52 (2007).
[CrossRef]

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1, 449–458 (2007).
[CrossRef]

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3, 687–695 (2009).
[CrossRef]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics4, 477–483 (2010).
[CrossRef]

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics6, 605–609 (2012).
[CrossRef]

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics6, 248–252 (2012).
[CrossRef]

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photonics6, 56–61 (2012).
[CrossRef]

Nat. Phys. (1)

G. Khitrova, H. Gibbs, M. Kira, S. Koch, and A. Scherer, “Vacuum rabi splitting in semiconductors,” Nat. Phys.2, 81–90 (2006).
[CrossRef]

Nature (2)

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum rabi splitting with a single quantum dot in a photonic crystal nanocavity,”Nature432, 200–203 (2004).
[CrossRef]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,”Nature425, 944–947 (2003).
[CrossRef]

Opt. Express (7)

Opt. Lett. (2)

Photonics Nanostruct. Fundam. Appl. (1)

D. Gerace and L. C. Andreani, “Effects of disorder on propagation losses and cavity q-factors in photonic crystal slabs,”Photonics Nanostruct. Fundam. Appl.3, 120–128 (2005).
[CrossRef]

Phys. Rev. B (7)

H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities,” Phys. Rev. B79, 085112 (2009).
[CrossRef]

V. Savona, “Electromagnetic modes of a disordered photonic crystal,” Phys. Rev. B83, 085301 (2011).
[CrossRef]

L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guied-mode expansion method,” Phys. Rev. B73, 235114 (2006).
[CrossRef]

M. Felici, K. A. Atlasov, A. Surrente, and E. Kapon, “Semianalytical approach to the design of photonic crystal cavities,” Phys. Rev. B82, 115118 (2010).
[CrossRef]

S. L. Portalupi, M. Galli, M. Belotti, L. C. Andreani, T. F. Krauss, and L. O’Faolain, “Deliberate versus intrinsic disorder in photonic crystal nanocavities investigated by resonant light scattering,” Phys. Rev. B84, 045423 (2011).
[CrossRef]

M. Minkov and V. Savona, “Radiative coupling of quantum dots in photonic crystal structures,” Phys. Rev. B87, 125306 (2013).
[CrossRef]

V. Savona, “Erratum: Electromagnetic modes of a disordered photonic crystal [phys. rev. b 83, 085301 (2011)],” Phys. Rev. B86, 079907 (2012).
[CrossRef]

Phys. Rev. Lett. (1)

N. Descharmes, U. P. Dharanipathy, Z. Diao, M. Tonin, and R. Houdré, “Observation of backaction and self-induced trapping in a planar hollow photonic crystal cavity,” Phys. Rev. Lett.110, 123601 (2013).
[CrossRef]

Rep. Prog. Phys. (1)

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys.73, 096501 (2010).
[CrossRef]

Other (2)

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

H. Carmichael, Statistical Methods in Quantum Optics 2: Non-Classical Fields (Springer, 2008).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Designs and profiles (computed with the guided-mode expansion) of the y-component of the electric field, Ey(r), for the different cavities studied here. (a) Improved L3 (see text); (b) A3, where the red holes are shifted outwards; (c) A1 with the red, black, and grey holes correspondingly shifted outwards by dy, 2dy/3 and dy/3; (d) Heterostructure, where the lattice constant is (420/410)a in the region between the dashed lines and (415/410)a in the two regions between a dashed and a dashed-dotted line; (e) Optimized H1: the holes marked in red are shifted outward by 0.12a and their radius is decreased by 0.06a, the ones marked black have a radius decreased by 0.03a, and the ones marked grey are shifted inward by 0.26a. Only the y-polarized of the two degenerate modes is plotted; (f): Optimized H0, where the 8 holes marked in red are shifted symmetrically: the two shifts in the x-direction are 0.14a, and 0.06a, while the two shifts in the y-direction are 0.04a and 0.02a (cf. [12]).

Fig. 2
Fig. 2

For the six different cavities, (a): Dependence of the standard deviation in the resonant mode frequency ω on the disorder magnitude σ; (b) and (c): Dependence of the mean and standard deviation of 1/Qd on σ2. In (a) and (b), the solid lines are determined from a linear interpolation, while in (c) the dashed lines only connect the individual points and serve as a guide for the eye. Inset in (c): zoom-in over the low-σ region.

Fig. 3
Fig. 3

(a)–(c): Histograms showing the occurrence of 1/Qd for the six different cavities, computed using GME for 1000 disorder realizations with (a): σ = 0.0014a, (b): σ = 0.005a, and (c): σ = 0.015a. (d)–(f): Histograms showing the occurrence of Q with the same values of σ as in (a)–(c). The insets in (d) and (e) are a zoom-in over the low-Q range, where the L3, H0 and H1 values are sitting.

Fig. 4
Fig. 4

For the three waveguide-based cavities (A1, A3 and HS), each panel shows 1/Qd in one cavity vs. 1/Qd in another for the same underlying disorder configuration, with 1000 different configurations. First row: HS vs. A1; second row: A1 vs. A3; third row: HS vs. A3. Across columns, σ changes from 0.0014a to 0.005a to 0.015a. The correlation coefficient r is indicated in the top right corner of each panel. Note that the range of the x-axis is twice larger than that of the y-axis due to the larger A3 spread.

Fig. 5
Fig. 5

Convergence of the quality factor with the number of bands included in the BME for four different cavities; thick blue line shows the disorder-less case, while the remaining lines represent 20 different disorder realizations with σ = 0.0014a, a value relevant to state-of-the-art silicon based systems. The FDTD, FEM and GME results for the disorder-less case are also given for reference.

Fig. 6
Fig. 6

Histograms showing the occurrence of Q for the four cavities, computed for 1000 disorder realizations with σ = 0.0014a. On the scale of the main plots, the L3 histogram would appear very narrow, and thus it is shown in an inset. (a) two-band BME results; (b) 100-band BME results; (c) GME results, which correspond to all-band BME.

Equations (2)

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1 Q = 1 Q i + 1 Q d + 1 Q a ,
H k ( r ) = G , α c ( k + G , α ) H k + G , α guided ( r ) ,

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