Abstract

Different types of planar photonic crystal cavities aimed at optimizing the far-field emission pattern are designed and experimentally assessed by resonant scattering measurements. We systematically investigate the interplay between achieving the highest possible quality (Q) factor and maximizing the in- and out-coupling efficiency into a narrow emission cone. Cavities operate at telecommunications wavelengths, i.e. around ~ 1.55 µm, and are realized in silicon membranes. A strong modification of the far-field emission pattern, and therefore a substantial increase of the coupling efficiency in the vertical direction, is obtained by properly modifying the holes around L3, L5 and L7 type PhC cavities, as we predict theoretically and show experimentally. An optimal compromise yielding simultaneously a high Q-factor and a large coupling to the fundamental cavity mode is found for a L7-type cavity with a measured Q ≃ 62000, whose resonant scattering efficiency is improved by about two orders of magnitude with respect to the unmodified structure. These results are especially useful for prospective applications in light emitting devices, such as nano-lasers or single-photon sources, in which vertical in- and out-coupling of the electromagnetic field is necessarily required.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  25. . M. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frédéric, P. J. Poole, G. C. Aers, and R. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  28. . D. Gerace and L. C. Andreani, “Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs,” Photon. Nanostruct. Fundam. Appl. 3, 120–128 (2005).
    [CrossRef]
  29. . L. C. Andreani and D. Gerace, “Photonic crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).
    [CrossRef]
  30. . Commercial FDTD software from Lumerical Solutions Inc. has been partly used for the 3D FDTD simulations reported in this work.
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    [CrossRef]
  32. . A. Witvrouwa, B. Du Bois, P. De Moor, A. Verbist, C. Van Hoof, H. Bender, K. Baert, “A comparison between wet HF etching and vapor HF etching for sacrificial oxide removal,” Proc. SPIE 4174130–141 (2000).
    [CrossRef]
  33. . D. Gerace, H. E. Türeci, A. Imamoğlu, V. Giovannetti, and R. Fazio, “The quantum optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
    [CrossRef]

2009 (7)

. M. Larque, T. Karle, I. Robert-Philipp, and A. Beveratos, “Optimizing H1 cavities for the generation of entangled photon pairs,” New J. Phys. 11, 033022 (2009).
[CrossRef]

. N.-V.-Q. Tran, S. Combrié, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101(R) (2009).
[CrossRef]

. M. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frédéric, P. J. Poole, G. C. Aers, and R. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2009).
[CrossRef]

. M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett. 94, 071101 (2009).
[CrossRef]

. P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

. D. Gerace, H. E. Türeci, A. Imamoğlu, V. Giovannetti, and R. Fazio, “The quantum optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

. M. Toishi, D. Englund, A. Faraon, and J. Vučković, “High-brightness single photon source from a quantum dot in a directional emission nanocavity,” Opt. Express 17, 14618–14626 (2009).
[CrossRef] [PubMed]

2008 (3)

2007 (1)

. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photon. 1, 449–458 (2007).
[CrossRef]

2006 (5)

. S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96, 127404 (2006).
[CrossRef] [PubMed]

. 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]

. S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006).
[CrossRef]

. L. C. Andreani and D. Gerace, “Photonic crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).
[CrossRef]

. L. O’Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42, 1454–1455 (2006).
[CrossRef]

2005 (8)

. P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal micresonators excited via an integrated waveguide and fiber taper,” Opt. Express,  13801–820 (2005).
[CrossRef] [PubMed]

. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[CrossRef] [PubMed]

. D. Englund, I. Fushman, and J. Vučković, “General recipe for designing photonic crystal cavities,” Opt. Express 13, 5961–5975 (2005).
[CrossRef] [PubMed]

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

. A. Badolato, K. Hennessy,M. Atatüre, J. Dreiser, E. Hu, P.M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[CrossRef] [PubMed]

. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[CrossRef] [PubMed]

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

. C. Sauvan, Ph. Lalanne, and J. P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B 71, 165118 (2005).
[CrossRef]

2004 (3)

. K. Srinivasan, P. E. Barclay, M. Borselli, O. Painter, “Optical-fiber-based measurement of an ultra-small volume high-Q photonic crystal microcavity,” Phys. Rev. B 70, 081306(R) (2004).
[CrossRef]

. L. C. Andreani, D. Gerace, and M. Agio, “Gap maps, diffraction losses, and exciton-polaritons in photonic crystal slabs,” Photon. Nanostruct. Fundam. Appl. 2, 103–110 (2004).
[CrossRef]

. M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H. Ryu, “Waveguides, resonators and their coupled elements in photonic crystal slabs,” Opt. Express 12, 1551–1561 (2004).
[CrossRef] [PubMed]

2003 (1)

. 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]

2002 (1)

2001 (1)

. S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[CrossRef]

2000 (1)

. A. Witvrouwa, B. Du Bois, P. De Moor, A. Verbist, C. Van Hoof, H. Bender, K. Baert, “A comparison between wet HF etching and vapor HF etching for sacrificial oxide removal,” Proc. SPIE 4174130–141 (2000).
[CrossRef]

Aers, G. C.

. M. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frédéric, P. J. Poole, G. C. Aers, and R. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2009).
[CrossRef]

Agio, M.

. L. C. Andreani, D. Gerace, and M. Agio, “Gap maps, diffraction losses, and exciton-polaritons in photonic crystal slabs,” Photon. Nanostruct. Fundam. Appl. 2, 103–110 (2004).
[CrossRef]

Akahane, Y.

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

Andreani, L. C.

. M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett. 94, 071101 (2009).
[CrossRef]

. M. Belotti, J. Galisteo-Lopez, S. De Angelis, M. Galli, I. Maksymov, L. C. Andreani, D. Peyrade, and Y. Chen, “All-optical switching in 2D silicon photonic crystals with low loss waveguides and optical cavities,” Opt. Express 16, 11624–11636 (2008).
[PubMed]

. L. C. Andreani and D. Gerace, “Photonic crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).
[CrossRef]

. S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96, 127404 (2006).
[CrossRef] [PubMed]

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

. L. C. Andreani, D. Gerace, and M. Agio, “Gap maps, diffraction losses, and exciton-polaritons in photonic crystal slabs,” Photon. Nanostruct. Fundam. Appl. 2, 103–110 (2004).
[CrossRef]

Arakawa, Y.

. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[CrossRef] [PubMed]

Asano, T.

. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photon. 1, 449–458 (2007).
[CrossRef]

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

Atatüre, M.

. A. Badolato, K. Hennessy,M. Atatüre, J. Dreiser, E. Hu, P.M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[CrossRef] [PubMed]

Badolato, A.

. S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96, 127404 (2006).
[CrossRef] [PubMed]

. A. Badolato, K. Hennessy,M. Atatüre, J. Dreiser, E. Hu, P.M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[CrossRef] [PubMed]

Baert, K.

. A. Witvrouwa, B. Du Bois, P. De Moor, A. Verbist, C. Van Hoof, H. Bender, K. Baert, “A comparison between wet HF etching and vapor HF etching for sacrificial oxide removal,” Proc. SPIE 4174130–141 (2000).
[CrossRef]

Barclay, P. E.

. P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal micresonators excited via an integrated waveguide and fiber taper,” Opt. Express,  13801–820 (2005).
[CrossRef] [PubMed]

. K. Srinivasan, P. E. Barclay, M. Borselli, O. Painter, “Optical-fiber-based measurement of an ultra-small volume high-Q photonic crystal microcavity,” Phys. Rev. B 70, 081306(R) (2004).
[CrossRef]

Belotti, M.

. M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett. 94, 071101 (2009).
[CrossRef]

. M. Belotti, J. Galisteo-Lopez, S. De Angelis, M. Galli, I. Maksymov, L. C. Andreani, D. Peyrade, and Y. Chen, “All-optical switching in 2D silicon photonic crystals with low loss waveguides and optical cavities,” Opt. Express 16, 11624–11636 (2008).
[PubMed]

Bender, H.

. A. Witvrouwa, B. Du Bois, P. De Moor, A. Verbist, C. Van Hoof, H. Bender, K. Baert, “A comparison between wet HF etching and vapor HF etching for sacrificial oxide removal,” Proc. SPIE 4174130–141 (2000).
[CrossRef]

Benisty, H.

Beveratos, A.

. M. Larque, T. Karle, I. Robert-Philipp, and A. Beveratos, “Optimizing H1 cavities for the generation of entangled photon pairs,” New J. Phys. 11, 033022 (2009).
[CrossRef]

Borselli, M.

. K. Srinivasan, P. E. Barclay, M. Borselli, O. Painter, “Optical-fiber-based measurement of an ultra-small volume high-Q photonic crystal microcavity,” Phys. Rev. B 70, 081306(R) (2004).
[CrossRef]

Bouwmeester, D.

. S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96, 127404 (2006).
[CrossRef] [PubMed]

Chen, Y.

Cheung, I. W.

. M. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frédéric, P. J. Poole, G. C. Aers, and R. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2009).
[CrossRef]

Choi, Y.-S.

. S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96, 127404 (2006).
[CrossRef] [PubMed]

Chong, H.

. L. O’Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42, 1454–1455 (2006).
[CrossRef]

Combrié, S.

. N.-V.-Q. Tran, S. Combrié, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101(R) (2009).
[CrossRef]

. S. Combrié, A. De Rossi, Q. V. Tran, and H. Benisty, “GaAs photonic crystal cavity with ultra-high Q: microwatt nonlinearity at 1.55 μm,” Opt. Lett. 33, 1908–1910 (2008).
[CrossRef]

Dalacu, D.

. M. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frédéric, P. J. Poole, G. C. Aers, and R. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2009).
[CrossRef]

De Angelis, S.

De La Rue, R. M.

. L. O’Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42, 1454–1455 (2006).
[CrossRef]

De Moor, P.

. A. Witvrouwa, B. Du Bois, P. De Moor, A. Verbist, C. Van Hoof, H. Bender, K. Baert, “A comparison between wet HF etching and vapor HF etching for sacrificial oxide removal,” Proc. SPIE 4174130–141 (2000).
[CrossRef]

De Rossi, A.

. N.-V.-Q. Tran, S. Combrié, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101(R) (2009).
[CrossRef]

. S. Combrié, A. De Rossi, Q. V. Tran, and H. Benisty, “GaAs photonic crystal cavity with ultra-high Q: microwatt nonlinearity at 1.55 μm,” Opt. Lett. 33, 1908–1910 (2008).
[CrossRef]

Deotare, P.

. P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Dreiser, J.

. A. Badolato, K. Hennessy,M. Atatüre, J. Dreiser, E. Hu, P.M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[CrossRef] [PubMed]

Du Bois, B.

. A. Witvrouwa, B. Du Bois, P. De Moor, A. Verbist, C. Van Hoof, H. Bender, K. Baert, “A comparison between wet HF etching and vapor HF etching for sacrificial oxide removal,” Proc. SPIE 4174130–141 (2000).
[CrossRef]

Englund, D.

. M. Toishi, D. Englund, A. Faraon, and J. Vučković, “High-brightness single photon source from a quantum dot in a directional emission nanocavity,” Opt. Express 17, 14618–14626 (2009).
[CrossRef] [PubMed]

. D. Englund, I. Fushman, and J. Vučković, “General recipe for designing photonic crystal cavities,” Opt. Express 13, 5961–5975 (2005).
[CrossRef] [PubMed]

. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[CrossRef] [PubMed]

Fan, S.

. S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[CrossRef]

Faraon, A.

Fattal, D.

. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[CrossRef] [PubMed]

Fazio, R.

. D. Gerace, H. E. Türeci, A. Imamoğlu, V. Giovannetti, and R. Fazio, “The quantum optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

Frank, I.

. P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Frédéric, S.

. M. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frédéric, P. J. Poole, G. C. Aers, and R. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2009).
[CrossRef]

Fujita, M.

. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photon. 1, 449–458 (2007).
[CrossRef]

Fushman, I.

Galisteo-Lopez, J.

Galli, M.

. M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett. 94, 071101 (2009).
[CrossRef]

. M. Belotti, J. Galisteo-Lopez, S. De Angelis, M. Galli, I. Maksymov, L. C. Andreani, D. Peyrade, and Y. Chen, “All-optical switching in 2D silicon photonic crystals with low loss waveguides and optical cavities,” Opt. Express 16, 11624–11636 (2008).
[PubMed]

Gerace, D.

. D. Gerace, H. E. Türeci, A. Imamoğlu, V. Giovannetti, and R. Fazio, “The quantum optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

. L. C. Andreani and D. Gerace, “Photonic crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).
[CrossRef]

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

. L. C. Andreani, D. Gerace, and M. Agio, “Gap maps, diffraction losses, and exciton-polaritons in photonic crystal slabs,” Photon. Nanostruct. Fundam. Appl. 2, 103–110 (2004).
[CrossRef]

Giovannetti, V.

. D. Gerace, H. E. Türeci, A. Imamoğlu, V. Giovannetti, and R. Fazio, “The quantum optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

Hennessy, K.

. S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96, 127404 (2006).
[CrossRef] [PubMed]

. A. Badolato, K. Hennessy,M. Atatüre, J. Dreiser, E. Hu, P.M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[CrossRef] [PubMed]

Hu, E.

. A. Badolato, K. Hennessy,M. Atatüre, J. Dreiser, E. Hu, P.M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[CrossRef] [PubMed]

Hu, E. L.

. S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96, 127404 (2006).
[CrossRef] [PubMed]

Hugonin, J. P.

. C. Sauvan, Ph. Lalanne, and J. P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B 71, 165118 (2005).
[CrossRef]

Imamoglu, A.

. D. Gerace, H. E. Türeci, A. Imamoğlu, V. Giovannetti, and R. Fazio, “The quantum optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

. A. Badolato, K. Hennessy,M. Atatüre, J. Dreiser, E. Hu, P.M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[CrossRef] [PubMed]

Joannopoulos, J. D.

. S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[CrossRef]

Johnson, S. G.

. S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[CrossRef]

Karle, T.

. M. Larque, T. Karle, I. Robert-Philipp, and A. Beveratos, “Optimizing H1 cavities for the generation of entangled photon pairs,” New J. Phys. 11, 033022 (2009).
[CrossRef]

Khan, M.

. P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Kim, S.-H.

. S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006).
[CrossRef]

Kim, S.-K.

. S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006).
[CrossRef]

Kira, G.

Krauss, T. F.

. M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett. 94, 071101 (2009).
[CrossRef]

. L. O’Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42, 1454–1455 (2006).
[CrossRef]

Kuramochi, E.

Lalanne, Ph.

. C. Sauvan, Ph. Lalanne, and J. P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B 71, 165118 (2005).
[CrossRef]

Larque, M.

. M. Larque, T. Karle, I. Robert-Philipp, and A. Beveratos, “Optimizing H1 cavities for the generation of entangled photon pairs,” New J. Phys. 11, 033022 (2009).
[CrossRef]

Lee, Y.-H.

. S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006).
[CrossRef]

Loncar, M.

. P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Maksymov, I.

McCutcheon, M.

. P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

. M. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frédéric, P. J. Poole, G. C. Aers, and R. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2009).
[CrossRef]

McIntyre, D.

. L. O’Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42, 1454–1455 (2006).
[CrossRef]

Mekis, A.

. S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[CrossRef]

Mitsugi, S.

Nakaoka, T.

. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[CrossRef] [PubMed]

Noda, S.

. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photon. 1, 449–458 (2007).
[CrossRef]

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

Notomi, M.

O’Faolain, L.

. M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett. 94, 071101 (2009).
[CrossRef]

. L. O’Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42, 1454–1455 (2006).
[CrossRef]

Painter, O.

Petroff, P. M.

. S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96, 127404 (2006).
[CrossRef] [PubMed]

Petroff, P.M.

. A. Badolato, K. Hennessy,M. Atatüre, J. Dreiser, E. Hu, P.M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[CrossRef] [PubMed]

Peyrade, D.

Poole, P. J.

. M. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frédéric, P. J. Poole, G. C. Aers, and R. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2009).
[CrossRef]

Portalupi, S. L.

. M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett. 94, 071101 (2009).
[CrossRef]

Rakher, M. T.

. S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96, 127404 (2006).
[CrossRef] [PubMed]

Rieger, G. W.

. M. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frédéric, P. J. Poole, G. C. Aers, and R. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2009).
[CrossRef]

Robert-Philipp, I.

. M. Larque, T. Karle, I. Robert-Philipp, and A. Beveratos, “Optimizing H1 cavities for the generation of entangled photon pairs,” New J. Phys. 11, 033022 (2009).
[CrossRef]

Römer, F.

Ryu, H.

Sauvan, C.

. C. Sauvan, Ph. Lalanne, and J. P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B 71, 165118 (2005).
[CrossRef]

Shinya, A.

Solomon, G.

. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[CrossRef] [PubMed]

Song, B. S.

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

Srinivasan, K.

Strauf, S.

. S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96, 127404 (2006).
[CrossRef] [PubMed]

Tanabe, 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]

. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[CrossRef] [PubMed]

Thoms, S.

. L. O’Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42, 1454–1455 (2006).
[CrossRef]

Toishi, M.

Tran, N.-V.-Q.

. N.-V.-Q. Tran, S. Combrié, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101(R) (2009).
[CrossRef]

Tran, Q. V.

Türeci, H. E.

. D. Gerace, H. E. Türeci, A. Imamoğlu, V. Giovannetti, and R. Fazio, “The quantum optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

Van Hoof, C.

. A. Witvrouwa, B. Du Bois, P. De Moor, A. Verbist, C. Van Hoof, H. Bender, K. Baert, “A comparison between wet HF etching and vapor HF etching for sacrificial oxide removal,” Proc. SPIE 4174130–141 (2000).
[CrossRef]

Verbist, A.

. A. Witvrouwa, B. Du Bois, P. De Moor, A. Verbist, C. Van Hoof, H. Bender, K. Baert, “A comparison between wet HF etching and vapor HF etching for sacrificial oxide removal,” Proc. SPIE 4174130–141 (2000).
[CrossRef]

Vuckovic, J.

. M. Toishi, D. Englund, A. Faraon, and J. Vučković, “High-brightness single photon source from a quantum dot in a directional emission nanocavity,” Opt. Express 17, 14618–14626 (2009).
[CrossRef] [PubMed]

. D. Englund, I. Fushman, and J. Vučković, “General recipe for designing photonic crystal cavities,” Opt. Express 13, 5961–5975 (2005).
[CrossRef] [PubMed]

. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[CrossRef] [PubMed]

Waks, E.

. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (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]

Williams, R.

. M. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frédéric, P. J. Poole, G. C. Aers, and R. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2009).
[CrossRef]

Witvrouwa, A.

. A. Witvrouwa, B. Du Bois, P. De Moor, A. Verbist, C. Van Hoof, H. Bender, K. Baert, “A comparison between wet HF etching and vapor HF etching for sacrificial oxide removal,” Proc. SPIE 4174130–141 (2000).
[CrossRef]

Witzigmann, B.

Yamamoto, Y.

. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[CrossRef] [PubMed]

Young, J. F.

. M. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frédéric, P. J. Poole, G. C. Aers, and R. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2009).
[CrossRef]

Yuan, X.

. L. O’Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42, 1454–1455 (2006).
[CrossRef]

Zhang, B.

. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (5)

. M. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frédéric, P. J. Poole, G. C. Aers, and R. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2009).
[CrossRef]

. M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett. 94, 071101 (2009).
[CrossRef]

. P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[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]

. S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[CrossRef]

Electron. Lett. (1)

. L. O’Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42, 1454–1455 (2006).
[CrossRef]

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

Nat. Mater. (1)

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

Nat. Photon. (1)

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. Commercial FDTD software from Lumerical Solutions Inc. has been partly used for the 3D FDTD simulations reported in this work.

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Figures (6)

Fig. 1.
Fig. 1.

(a) Schematic of far-field optimized PPhC cavity of the L3-type. Holes with red edge are shrunk and shifted to optimize the Q-factor. Dark holes are modified to increase the vertical out-coupling. (b) Calculated Q-factor and out-coupling efficiency (η out) as a function of the filled holes’ radius enlargement. Parameters of the basic PPhC structure are: membrane thickness d = 220 nm, lattice constant a = 420 nm, photonic crystal holes’ radius r/a = 0.265, refractive index of dielectric slab n diel = 3.46, red holes shift Δx/a = 0.16, shrink Δr′/a = −0.06. (c) A selection of calculated far-field patterns (electric field intensity profile, ∣E2) corresponding to the labeled numbers on the efficiency plot (see numbers in panel b). Field intensities are normalized to the total emitted power in the vertical half-space. Concentric circles correspond to θ = 20°,30°,40°,50°,60°,90° from the inner to the outer one, respectively.

Fig. 2.
Fig. 2.

(a) Schematic pictures of the fabricated PPhC devices: 3, 5, and 7 missing holes define the L3, L5 and L7-type cavities, respectively. Red holes are shifted (Δx/a = 0.16) and shrunk (Δr′/a = −0.06) for Q-factor optimization, while dark holes are modified for far-field optimization. (b) SEM images of 3 fabricated devices on silicon membranes. Holes corresponding to the filled circles in (a) are enlarged by Δr″ = 21 nm in these images. Lattice constant is a = 420 nm for all the investigated PPhC devices.

Fig. 3.
Fig. 3.

(a) Schematic illustration of the resonant scattering technique. (b) Resonant scattering signal from a L7 cavity with Δr″ = 0, showing the largest Q-factor. (c) Measured Q-factor as a function of holes’ enlargement for L3, L5, and L7 PPhC devices. (d) Calculated Q-factor (by GME) as a function of holes’ enlargement for L3, L5, and L7 PPhC devices.

Fig. 4.
Fig. 4.

(a) Sample spectra from resonant scattering measurements on the fundamental mode of L3-type PPhC. (b) The extracted Q-factors and RS efficiencies extracted from the measured data in (a) and plotted as a function of Δr″, to be compared to Fig. 1(b).

Fig. 5.
Fig. 5.

(a) Experimentally determined RS efficiencies (η RS), for L3, L5, and L7 cavities, respectively, as a function of Δr″, as measured with a focussing objective having NA=0.5; (b) corresponding figures of merit, given by the product Q × η RS.

Fig. 6.
Fig. 6.

(a) Modelling of the collection efficiency for L3, L5, and L7 devices (as obtained from 3D FDTD simulations) for an objective with NA=0.5, which has been filtered with a normalized gaussian spot propagated in the far-field whose divergence angle corresponds to the nominal NA (the result is defined η FDTD); (b) the corresponding figures of merit (Q × η FDTD) obtained from the calculated Q-factors (Fig. 3d) for the experimentally realized values of Δr″.

Equations (1)

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F ( ω ) = A 0 + F 0 [ q + 2 ( ω ω 0 ) Γ ] 2 1 + [ 2 ( ω ω 0 ) Γ ] 2 ,

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