Abstract

We investigate the influence of structural fluctuations on the Q factor of nanocavities at the surface of 3D photonic crystals with a stacked-stripe structure. We analyze the Q factor of nanocavities by 3D finite-difference time-domain calculations in consideration of the misalignment of the position of the stacked layers and the fluctuation of the patterns in each layer. Misalignment of the order of 50nm has almost no influence on the Q factor, but the pattern fluctuations of the order of nanometers in each layer, especially in the surface layer, seriously impact the decrease of the Q factor.

© 2013 Optical Society of America

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  1. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
    [CrossRef]
  2. S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).
    [CrossRef]
  3. P. Lodahl, a. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
    [CrossRef]
  4. M. 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]
  5. M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
    [CrossRef]
  6. S. A. Rinne, F. García-Santamaría, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52–56 (2007).
    [CrossRef]
  7. K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity,” Nat. Photonics 2, 688–692 (2008).
    [CrossRef]
  8. K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460, 367–370 (2009).
    [CrossRef]
  9. S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
    [CrossRef]
  10. S. Kawashima, K. Ishizaki, and S. Noda, “Light propagation in three-dimensional photonic crystals,” Opt. Express 18, 386–392 (2010).
    [CrossRef]
  11. A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2010).
    [CrossRef]
  12. K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7, 133–137 (2013).
    [CrossRef]
  13. K. Ishizaki, K. Gondaira, Y. Ota, K. Suzuki, and S. Noda, “Nanocavities at the surface of three-dimensional photonic crystals,” Opt. Express 21, 10590–10596 (2013).
    [CrossRef]
  14. A. Chutinan and S. Noda, “Effects of structural fluctuations on the photonic bandgap during fabrication of a photonic crystal: a study of a photonic crystal with a finite number of periods,” J. Opt. Soc. Am. B 16, 1398–1402 (1999).
    [CrossRef]
  15. Z.-Y. Li and Z.-Q. Zhang, “Fragility of photonic band gaps in inverse-opal photonic crystals,” Phys. Rev. B 62, 1516–1519 (2000).
    [CrossRef]
  16. V. Yannopapas, N. Stefanou, and A. Modinos, “Effect of stacking faults on the optical properties of inverted opals,” Phys. Rev. Lett. 86, 4811–4814 (2001).
    [CrossRef]
  17. A. V. Lavrinenko, W. Wohlleben, and R. J. Leyrer, “Influence of imperfections on the insulating and guiding properties of finite Si-inverted opal crystals,” Opt. Express 17, 747–760 (2009).
    [CrossRef]
  18. K. Ishizaki, M. Okano, and S. Noda, “Numerical investigation of emission in finite-sized, three-dimensional photonic crystals with structural fluctuations,” J. Opt. Soc. Am. B 26, 1157–1161 (2009).
    [CrossRef]
  19. A. Rodriguez, M. Ibanescu, J. D. Joannopoulos, and S. G. Johnson, “Disorder-immune confinement of light in photonic-crystal cavities,” Opt. Lett. 30, 3192–3194 (2005).
    [CrossRef]
  20. T. Asano, B.-S. Song, and S. Noda, “Analysis of the experimental Q factors (∼1  million) of photonic crystal nanocavities,” Opt. Express 14, 1996–2002 (2006).
    [CrossRef]
  21. D. Fussell, S. Hughes, and M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B 78, 144201 (2008).
    [CrossRef]
  22. L. Ramunno and S. Hughes, “Disorder-induced resonance shifts in high-index-contrast photonic crystal nanocavities,” Phys. Rev. B 79, 161303 (2009).
    [CrossRef]
  23. 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. B 79, 085112 (2009).
    [CrossRef]
  24. V. Savona, “Electromagnetic modes of a disordered photonic crystal,” Phys. Rev. B 83, 085301 (2011).
    [CrossRef]
  25. 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. B 84, 045423 (2011).
    [CrossRef]
  26. S. Noda, N. Yamamoto, and A. Sasaki, “New realization method of three-dimensional photonic crystal in optical wavelength region,” Jpn. J. Appl. Phys. 35, L909–L912 (1996).
    [CrossRef]
  27. N. Yamamoto and S. Noda, “100 nm-scale alignment using laser beam diffraction pattern observation techniques and wafer fusion for realizing three-dimensional photonic crystal structure,” Jpn. J. Appl. Phys. 37, 3334–3338 (1998).
    [CrossRef]
  28. S. Kawashima, M. Imada, K. Ishizaki, and S. Noda, “High-precision alignment and bonding system for the fabrication of 3-D nanostructures,” J. Microelectromech. Syst. 16, 1140–1144 (2007).
    [CrossRef]

2013 (2)

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7, 133–137 (2013).
[CrossRef]

K. Ishizaki, K. Gondaira, Y. Ota, K. Suzuki, and S. Noda, “Nanocavities at the surface of three-dimensional photonic crystals,” Opt. Express 21, 10590–10596 (2013).
[CrossRef]

2011 (2)

V. Savona, “Electromagnetic modes of a disordered photonic crystal,” Phys. Rev. B 83, 085301 (2011).
[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. B 84, 045423 (2011).
[CrossRef]

2010 (2)

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2010).
[CrossRef]

S. Kawashima, K. Ishizaki, and S. Noda, “Light propagation in three-dimensional photonic crystals,” Opt. Express 18, 386–392 (2010).
[CrossRef]

2009 (6)

A. V. Lavrinenko, W. Wohlleben, and R. J. Leyrer, “Influence of imperfections on the insulating and guiding properties of finite Si-inverted opal crystals,” Opt. Express 17, 747–760 (2009).
[CrossRef]

K. Ishizaki, M. Okano, and S. Noda, “Numerical investigation of emission in finite-sized, three-dimensional photonic crystals with structural fluctuations,” J. Opt. Soc. Am. B 26, 1157–1161 (2009).
[CrossRef]

L. Ramunno and S. Hughes, “Disorder-induced resonance shifts in high-index-contrast photonic crystal nanocavities,” Phys. Rev. B 79, 161303 (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. B 79, 085112 (2009).
[CrossRef]

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460, 367–370 (2009).
[CrossRef]

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

2008 (2)

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity,” Nat. Photonics 2, 688–692 (2008).
[CrossRef]

D. Fussell, S. Hughes, and M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B 78, 144201 (2008).
[CrossRef]

2007 (2)

S. A. Rinne, F. García-Santamaría, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52–56 (2007).
[CrossRef]

S. Kawashima, M. Imada, K. Ishizaki, and S. Noda, “High-precision alignment and bonding system for the fabrication of 3-D nanostructures,” J. Microelectromech. Syst. 16, 1140–1144 (2007).
[CrossRef]

2006 (2)

T. Asano, B.-S. Song, and S. Noda, “Analysis of the experimental Q factors (∼1  million) of photonic crystal nanocavities,” Opt. Express 14, 1996–2002 (2006).
[CrossRef]

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
[CrossRef]

2005 (1)

2004 (3)

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).
[CrossRef]

P. Lodahl, a. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef]

M. 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]

2001 (1)

V. Yannopapas, N. Stefanou, and A. Modinos, “Effect of stacking faults on the optical properties of inverted opals,” Phys. Rev. Lett. 86, 4811–4814 (2001).
[CrossRef]

2000 (2)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

Z.-Y. Li and Z.-Q. Zhang, “Fragility of photonic band gaps in inverse-opal photonic crystals,” Phys. Rev. B 62, 1516–1519 (2000).
[CrossRef]

1999 (1)

1998 (1)

N. Yamamoto and S. Noda, “100 nm-scale alignment using laser beam diffraction pattern observation techniques and wafer fusion for realizing three-dimensional photonic crystal structure,” Jpn. J. Appl. Phys. 37, 3334–3338 (1998).
[CrossRef]

1996 (1)

S. Noda, N. Yamamoto, and A. Sasaki, “New realization method of three-dimensional photonic crystal in optical wavelength region,” Jpn. J. Appl. Phys. 35, L909–L912 (1996).
[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. B 84, 045423 (2011).
[CrossRef]

Aoki, K.

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity,” Nat. Photonics 2, 688–692 (2008).
[CrossRef]

Arakawa, Y.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2010).
[CrossRef]

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity,” Nat. Photonics 2, 688–692 (2008).
[CrossRef]

Asano, T.

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. B 79, 085112 (2009).
[CrossRef]

T. Asano, B.-S. Song, and S. Noda, “Analysis of the experimental Q factors (∼1  million) of photonic crystal nanocavities,” Opt. Express 14, 1996–2002 (2006).
[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. B 84, 045423 (2011).
[CrossRef]

Braun, P. V.

S. A. Rinne, F. García-Santamaría, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52–56 (2007).
[CrossRef]

Chutinan, A.

Dignam, M.

D. Fussell, S. Hughes, and M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B 78, 144201 (2008).
[CrossRef]

Fussell, D.

D. Fussell, S. Hughes, and M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B 78, 144201 (2008).
[CrossRef]

Galli, 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. B 84, 045423 (2011).
[CrossRef]

García-Santamaría, F.

S. A. Rinne, F. García-Santamaría, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52–56 (2007).
[CrossRef]

Gondaira, K.

K. Ishizaki, K. Gondaira, Y. Ota, K. Suzuki, and S. Noda, “Nanocavities at the surface of three-dimensional photonic crystals,” Opt. Express 21, 10590–10596 (2013).
[CrossRef]

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7, 133–137 (2013).
[CrossRef]

Guimard, D.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2010).
[CrossRef]

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity,” Nat. Photonics 2, 688–692 (2008).
[CrossRef]

Hagino, H.

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. B 79, 085112 (2009).
[CrossRef]

Hughes, S.

L. Ramunno and S. Hughes, “Disorder-induced resonance shifts in high-index-contrast photonic crystal nanocavities,” Phys. Rev. B 79, 161303 (2009).
[CrossRef]

D. Fussell, S. Hughes, and M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B 78, 144201 (2008).
[CrossRef]

Ibanescu, M.

Imada, M.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

S. Kawashima, M. Imada, K. Ishizaki, and S. Noda, “High-precision alignment and bonding system for the fabrication of 3-D nanostructures,” J. Microelectromech. Syst. 16, 1140–1144 (2007).
[CrossRef]

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
[CrossRef]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).
[CrossRef]

Ippen, E. P.

M. 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]

Irman, A.

P. Lodahl, a. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef]

Ishida, S.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2010).
[CrossRef]

Ishizaki, K.

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7, 133–137 (2013).
[CrossRef]

K. Ishizaki, K. Gondaira, Y. Ota, K. Suzuki, and S. Noda, “Nanocavities at the surface of three-dimensional photonic crystals,” Opt. Express 21, 10590–10596 (2013).
[CrossRef]

S. Kawashima, K. Ishizaki, and S. Noda, “Light propagation in three-dimensional photonic crystals,” Opt. Express 18, 386–392 (2010).
[CrossRef]

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460, 367–370 (2009).
[CrossRef]

K. Ishizaki, M. Okano, and S. Noda, “Numerical investigation of emission in finite-sized, three-dimensional photonic crystals with structural fluctuations,” J. Opt. Soc. Am. B 26, 1157–1161 (2009).
[CrossRef]

S. Kawashima, M. Imada, K. Ishizaki, and S. Noda, “High-precision alignment and bonding system for the fabrication of 3-D nanostructures,” J. Microelectromech. Syst. 16, 1140–1144 (2007).
[CrossRef]

Iwamoto, S.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2010).
[CrossRef]

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity,” Nat. Photonics 2, 688–692 (2008).
[CrossRef]

Joannopoulos, J. D.

A. Rodriguez, M. Ibanescu, J. D. Joannopoulos, and S. G. Johnson, “Disorder-immune confinement of light in photonic-crystal cavities,” Opt. Lett. 30, 3192–3194 (2005).
[CrossRef]

M. 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]

Johnson, S. G.

A. Rodriguez, M. Ibanescu, J. D. Joannopoulos, and S. G. Johnson, “Disorder-immune confinement of light in photonic-crystal cavities,” Opt. Lett. 30, 3192–3194 (2005).
[CrossRef]

M. 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]

Kawashima, S.

S. Kawashima, K. Ishizaki, and S. Noda, “Light propagation in three-dimensional photonic crystals,” Opt. Express 18, 386–392 (2010).
[CrossRef]

S. Kawashima, M. Imada, K. Ishizaki, and S. Noda, “High-precision alignment and bonding system for the fabrication of 3-D nanostructures,” J. Microelectromech. Syst. 16, 1140–1144 (2007).
[CrossRef]

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
[CrossRef]

Koumura, M.

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7, 133–137 (2013).
[CrossRef]

Krauss, T. F.

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. B 84, 045423 (2011).
[CrossRef]

Lavrinenko, A. V.

Lee, L. H.

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
[CrossRef]

Leyrer, R. J.

Li, Z.-Y.

Z.-Y. Li and Z.-Q. Zhang, “Fragility of photonic band gaps in inverse-opal photonic crystals,” Phys. Rev. B 62, 1516–1519 (2000).
[CrossRef]

Lidorikis, E.

M. 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]

Lodahl, P.

P. Lodahl, a. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef]

Modinos, A.

V. Yannopapas, N. Stefanou, and A. Modinos, “Effect of stacking faults on the optical properties of inverted opals,” Phys. Rev. Lett. 86, 4811–4814 (2001).
[CrossRef]

Nakamori, T.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

Nikolaev, I. S.

P. Lodahl, a. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef]

Nishioka, M.

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity,” Nat. Photonics 2, 688–692 (2008).
[CrossRef]

Noda, S.

K. Ishizaki, K. Gondaira, Y. Ota, K. Suzuki, and S. Noda, “Nanocavities at the surface of three-dimensional photonic crystals,” Opt. Express 21, 10590–10596 (2013).
[CrossRef]

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7, 133–137 (2013).
[CrossRef]

S. Kawashima, K. Ishizaki, and S. Noda, “Light propagation in three-dimensional photonic crystals,” Opt. Express 18, 386–392 (2010).
[CrossRef]

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460, 367–370 (2009).
[CrossRef]

K. Ishizaki, M. Okano, and S. Noda, “Numerical investigation of emission in finite-sized, three-dimensional photonic crystals with structural fluctuations,” J. Opt. Soc. Am. B 26, 1157–1161 (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. B 79, 085112 (2009).
[CrossRef]

S. Kawashima, M. Imada, K. Ishizaki, and S. Noda, “High-precision alignment and bonding system for the fabrication of 3-D nanostructures,” J. Microelectromech. Syst. 16, 1140–1144 (2007).
[CrossRef]

T. Asano, B.-S. Song, and S. Noda, “Analysis of the experimental Q factors (∼1  million) of photonic crystal nanocavities,” Opt. Express 14, 1996–2002 (2006).
[CrossRef]

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
[CrossRef]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).
[CrossRef]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

A. Chutinan and S. Noda, “Effects of structural fluctuations on the photonic bandgap during fabrication of a photonic crystal: a study of a photonic crystal with a finite number of periods,” J. Opt. Soc. Am. B 16, 1398–1402 (1999).
[CrossRef]

N. Yamamoto and S. Noda, “100 nm-scale alignment using laser beam diffraction pattern observation techniques and wafer fusion for realizing three-dimensional photonic crystal structure,” Jpn. J. Appl. Phys. 37, 3334–3338 (1998).
[CrossRef]

S. Noda, N. Yamamoto, and A. Sasaki, “New realization method of three-dimensional photonic crystal in optical wavelength region,” Jpn. J. Appl. Phys. 35, L909–L912 (1996).
[CrossRef]

Nomura, M.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2010).
[CrossRef]

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity,” Nat. Photonics 2, 688–692 (2008).
[CrossRef]

O’Faolain, L.

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. B 84, 045423 (2011).
[CrossRef]

Ogawa, S.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).
[CrossRef]

Okano, M.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

K. Ishizaki, M. Okano, and S. Noda, “Numerical investigation of emission in finite-sized, three-dimensional photonic crystals with structural fluctuations,” J. Opt. Soc. Am. B 26, 1157–1161 (2009).
[CrossRef]

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
[CrossRef]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).
[CrossRef]

Ota, Y.

K. Ishizaki, K. Gondaira, Y. Ota, K. Suzuki, and S. Noda, “Nanocavities at the surface of three-dimensional photonic crystals,” Opt. Express 21, 10590–10596 (2013).
[CrossRef]

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

Overgaag, K.

P. Lodahl, a. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef]

Portalupi, S. L.

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. B 84, 045423 (2011).
[CrossRef]

Qi, M.

M. 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]

Rakich, P. T.

M. 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]

Ramunno, L.

L. Ramunno and S. Hughes, “Disorder-induced resonance shifts in high-index-contrast photonic crystal nanocavities,” Phys. Rev. B 79, 161303 (2009).
[CrossRef]

Rinne, S. A.

S. A. Rinne, F. García-Santamaría, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52–56 (2007).
[CrossRef]

Rodriguez, A.

Sasaki, A.

S. Noda, N. Yamamoto, and A. Sasaki, “New realization method of three-dimensional photonic crystal in optical wavelength region,” Jpn. J. Appl. Phys. 35, L909–L912 (1996).
[CrossRef]

Savona, V.

V. Savona, “Electromagnetic modes of a disordered photonic crystal,” Phys. Rev. B 83, 085301 (2011).
[CrossRef]

Smith, H. I.

M. 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]

Song, B.-S.

Stefanou, N.

V. Yannopapas, N. Stefanou, and A. Modinos, “Effect of stacking faults on the optical properties of inverted opals,” Phys. Rev. Lett. 86, 4811–4814 (2001).
[CrossRef]

Suzuki, K.

K. Ishizaki, K. Gondaira, Y. Ota, K. Suzuki, and S. Noda, “Nanocavities at the surface of three-dimensional photonic crystals,” Opt. Express 21, 10590–10596 (2013).
[CrossRef]

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7, 133–137 (2013).
[CrossRef]

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

Takahashi, S.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

Takahashi, Y.

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. B 79, 085112 (2009).
[CrossRef]

Tanaka, Y.

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. B 79, 085112 (2009).
[CrossRef]

Tandaechanurat, A.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2010).
[CrossRef]

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

Van Driel, a. Floris

P. Lodahl, a. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef]

Vanmaekelbergh, D.

P. Lodahl, a. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef]

Vos, W. L.

P. Lodahl, a. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef]

Wohlleben, W.

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

N. Yamamoto and S. Noda, “100 nm-scale alignment using laser beam diffraction pattern observation techniques and wafer fusion for realizing three-dimensional photonic crystal structure,” Jpn. J. Appl. Phys. 37, 3334–3338 (1998).
[CrossRef]

S. Noda, N. Yamamoto, and A. Sasaki, “New realization method of three-dimensional photonic crystal in optical wavelength region,” Jpn. J. Appl. Phys. 35, L909–L912 (1996).
[CrossRef]

Yannopapas, V.

V. Yannopapas, N. Stefanou, and A. Modinos, “Effect of stacking faults on the optical properties of inverted opals,” Phys. Rev. Lett. 86, 4811–4814 (2001).
[CrossRef]

Yoshimoto, S.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).
[CrossRef]

Zhang, Z.-Q.

Z.-Y. Li and Z.-Q. Zhang, “Fragility of photonic band gaps in inverse-opal photonic crystals,” Phys. Rev. B 62, 1516–1519 (2000).
[CrossRef]

Appl. Phys. Lett. (1)

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
[CrossRef]

J. Microelectromech. Syst. (1)

S. Kawashima, M. Imada, K. Ishizaki, and S. Noda, “High-precision alignment and bonding system for the fabrication of 3-D nanostructures,” J. Microelectromech. Syst. 16, 1140–1144 (2007).
[CrossRef]

J. Opt. Soc. Am. B (2)

Jpn. J. Appl. Phys. (2)

S. Noda, N. Yamamoto, and A. Sasaki, “New realization method of three-dimensional photonic crystal in optical wavelength region,” Jpn. J. Appl. Phys. 35, L909–L912 (1996).
[CrossRef]

N. Yamamoto and S. Noda, “100 nm-scale alignment using laser beam diffraction pattern observation techniques and wafer fusion for realizing three-dimensional photonic crystal structure,” Jpn. J. Appl. Phys. 37, 3334–3338 (1998).
[CrossRef]

Nat. Mater. (1)

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009).
[CrossRef]

Nat. Photonics (4)

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2010).
[CrossRef]

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7, 133–137 (2013).
[CrossRef]

S. A. Rinne, F. García-Santamaría, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52–56 (2007).
[CrossRef]

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic-crystal nanocavity,” Nat. Photonics 2, 688–692 (2008).
[CrossRef]

Nature (3)

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460, 367–370 (2009).
[CrossRef]

P. Lodahl, a. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef]

M. 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]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. B (6)

D. Fussell, S. Hughes, and M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B 78, 144201 (2008).
[CrossRef]

L. Ramunno and S. Hughes, “Disorder-induced resonance shifts in high-index-contrast photonic crystal nanocavities,” Phys. Rev. B 79, 161303 (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. B 79, 085112 (2009).
[CrossRef]

V. Savona, “Electromagnetic modes of a disordered photonic crystal,” Phys. Rev. B 83, 085301 (2011).
[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. B 84, 045423 (2011).
[CrossRef]

Z.-Y. Li and Z.-Q. Zhang, “Fragility of photonic band gaps in inverse-opal photonic crystals,” Phys. Rev. B 62, 1516–1519 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

V. Yannopapas, N. Stefanou, and A. Modinos, “Effect of stacking faults on the optical properties of inverted opals,” Phys. Rev. Lett. 86, 4811–4814 (2001).
[CrossRef]

Science (2)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Nanocavity at the surface of a 3D photonic crystal with a stacked-stripe structure. (a) Overhead view of a schematic structure of a surface nanocavity. Blue (light gray in black and white version) shows the dielectric region. (b) Top view of a schematic structure of a cavity.

Fig. 2.
Fig. 2.

Influence of the misalignment of the position of the surface layer. (a) Schematic of the misalignment of the surface layer. (b) Calculated Q factors under existence of the misalignments on the surface layer.

Fig. 3.
Fig. 3.

Influence of the misalignment of the position of the surface layer on the band diagram of a surface mode and cavity-mode frequency. (a) Band diagram without misalignment. Insets show representative directions in real and reciprocal spaces. (b)–(e) Band diagrams with x-directional misalignments of 25, 50, 75, and 100 nm. (f)–(i) Band diagrams for y-directional misalignments of 25, 50, 75, and 100 nm. Surface-mode gap vanished in (i), and the cavity mode is not obtained within the surface-mode gap range in (e), (h), or (i).

Fig. 4.
Fig. 4.

Influence of the misalignment of the positions of striped layers. (a) Schematic of the misalignment of striped layers. (b) Calculated Q factors under the existence of misalignments in striped layers.

Fig. 5.
Fig. 5.

Influence of the fluctuation of pattern in the surface layer with cross-geometric pattern. (a) Modeled fluctuations in the cross-geometric layer. (b) Calculation result of the Q factor under the existence of the fluctuation of patterns.

Fig. 6.
Fig. 6.

Influence of the fluctuation of pattern in the stripe layer between the 2nd and 18th layers. (a) Modeled fluctuations in the striped layer. (b) Calculation result of the Q factor under the existence of the fluctuation of patterns.

Fig. 7.
Fig. 7.

Influence of the fluctuation of pattern by considering simultaneous occurrence of various fluctuations.

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