Abstract

Statistical studies on the scanning electron microscope (SEM) images of two-dimensional photonic crystal (PhC) slab cavities show that fabrication errors in the size and position of etched air holes follow Gaussian distribution. The influences on the characteristics of PhC cavities are then investigated and compared with those caused by fabrication error with widely-accepted uniform distribution through finite-difference time domain (FDTD) simulation. As expected, Gaussian distribution in fabrication error has more significant impact on cavity characteristics than uniform distribution simply by their difference in the fourth moment.

© 2010 IEEE

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  1. A. Rodriguez, M. Ibanescu, J. D. Joannopoulos, S. G. Johnson, "Disorder-immune confinement of light in photonic-crystal cavities," Opt. Lett. 30, 3192-3194 (2005).
  2. T. Asano, B. S. Song, S. Noda, "Analysis of the experimental Q factors (1 million) of photonic crystal nanocavities," Opt. Exp. 14, 1996-2002 (2006).
  3. Y. Tanaka, T. Asano, R. Hatsuta, S. Noda, "Analysis of a line-defect waveguide on a silicon-on-insulator two-dimensional photonic-crystal slab," J. Lightw. Technol. 22, 2787-2792 (2004).
  4. R. Ferrini, D. Leuenberger, R. Houdré, H. Benisty, M. Kamp, A. Forchel, "Disorder-induced losses in planar photonic crystals," Opt. Lett. 31, 1426-1428 (2006).
  5. H. Y. Ryu, J. K. Hwang, Y. H. Lee, "Effect of size nonuniformities on the bandgap of two-dimensional photonic crystals," Phy. Rev. B 59, 5463-5469 (1999).
  6. R. Meisels, F. Kuchar, "Density-of-states and wave propagation in two-dimensional photonic crystals with positional disorder," J. Opt. A 9, 396-402 (2007).
  7. M. A. Kaliteevski, J. M. Martinez, D. Cassagne, J. P. Albert, "Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal," Phy. Rev. B 66, 113101- (2002).
  8. Z. H. Zhu, W. M. Ye, J. R. Ji, X. D. Yuan, C. Zen, "Influence of random errors on the characteristics of typical 2-D photonic crystal microcavity," Appl. Phy. B 88, 231-236 (2007).
  9. C. J. Matthews, R. Seviour, "Effects of disorder on the frequency and field of photonic-crystal cavity resonators," Appl. Phy. B 94, 381-388 (2009).
  10. W. R. Frei, H. T. Johnson, "Finite-element analysis of disorder effects in photonic crystals," Phy. Rev. B 70, 165116- (2004).
  11. H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, S. Noda, "Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities," Phy. Rev. B 79, 85112- (2009).
  12. D. Gerace, L. C. Andreani, "Low-loss guided modes in photonic crystal waveguides," Opt. Exp. 13, 4939-4951 (2005).
  13. Y. Akahane, T. Asano, B. S. Song, S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
  14. R. L. Plackett, "Karl Pearson and the Chi-squared test," Int. Stat. Rev. 51, 59-72 (1983).
  15. R. V. Hogg, A. T. Craig, Introduction to Mathematical Statistics (Macmillan, 1978).
  16. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, "MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method," Comp. Phys. Commun. 181, 687-702 (2010).
  17. V. A. Mandelshtam, H. S. Taylor, "Harmonic inversion of time signals," J. Chem. Phys. 107, 6756-6769 (1997).
  18. R. A. Waldron, "Perturbation formulas for elastic resonators and waveguides," IEEE Trans. Sonics Ultrason. 18, 16-20 (1971).
  19. P. Michler, Single Semiconductor Quantum Dots (2008)9 Springer Book series NanoScience and Technology.
  20. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 2008).

2010 (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, "MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method," Comp. Phys. Commun. 181, 687-702 (2010).

2009 (2)

C. J. Matthews, R. Seviour, "Effects of disorder on the frequency and field of photonic-crystal cavity resonators," Appl. Phy. B 94, 381-388 (2009).

H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, S. Noda, "Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities," Phy. Rev. B 79, 85112- (2009).

2007 (2)

R. Meisels, F. Kuchar, "Density-of-states and wave propagation in two-dimensional photonic crystals with positional disorder," J. Opt. A 9, 396-402 (2007).

Z. H. Zhu, W. M. Ye, J. R. Ji, X. D. Yuan, C. Zen, "Influence of random errors on the characteristics of typical 2-D photonic crystal microcavity," Appl. Phy. B 88, 231-236 (2007).

2006 (2)

T. Asano, B. S. Song, S. Noda, "Analysis of the experimental Q factors (1 million) of photonic crystal nanocavities," Opt. Exp. 14, 1996-2002 (2006).

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

2005 (2)

A. Rodriguez, M. Ibanescu, J. D. Joannopoulos, S. G. Johnson, "Disorder-immune confinement of light in photonic-crystal cavities," Opt. Lett. 30, 3192-3194 (2005).

D. Gerace, L. C. Andreani, "Low-loss guided modes in photonic crystal waveguides," Opt. Exp. 13, 4939-4951 (2005).

2004 (2)

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

Y. Tanaka, T. Asano, R. Hatsuta, S. Noda, "Analysis of a line-defect waveguide on a silicon-on-insulator two-dimensional photonic-crystal slab," J. Lightw. Technol. 22, 2787-2792 (2004).

2003 (1)

Y. Akahane, T. Asano, B. S. Song, S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).

2002 (1)

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, J. P. Albert, "Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal," Phy. Rev. B 66, 113101- (2002).

1999 (1)

H. Y. Ryu, J. K. Hwang, Y. H. Lee, "Effect of size nonuniformities on the bandgap of two-dimensional photonic crystals," Phy. Rev. B 59, 5463-5469 (1999).

1997 (1)

V. A. Mandelshtam, H. S. Taylor, "Harmonic inversion of time signals," J. Chem. Phys. 107, 6756-6769 (1997).

1983 (1)

R. L. Plackett, "Karl Pearson and the Chi-squared test," Int. Stat. Rev. 51, 59-72 (1983).

1971 (1)

R. A. Waldron, "Perturbation formulas for elastic resonators and waveguides," IEEE Trans. Sonics Ultrason. 18, 16-20 (1971).

Appl. Phy. B (2)

Z. H. Zhu, W. M. Ye, J. R. Ji, X. D. Yuan, C. Zen, "Influence of random errors on the characteristics of typical 2-D photonic crystal microcavity," Appl. Phy. B 88, 231-236 (2007).

C. J. Matthews, R. Seviour, "Effects of disorder on the frequency and field of photonic-crystal cavity resonators," Appl. Phy. B 94, 381-388 (2009).

Comp. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, "MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method," Comp. Phys. Commun. 181, 687-702 (2010).

IEEE Trans. Sonics Ultrason. (1)

R. A. Waldron, "Perturbation formulas for elastic resonators and waveguides," IEEE Trans. Sonics Ultrason. 18, 16-20 (1971).

Int. Stat. Rev. (1)

R. L. Plackett, "Karl Pearson and the Chi-squared test," Int. Stat. Rev. 51, 59-72 (1983).

J. Chem. Phys. (1)

V. A. Mandelshtam, H. S. Taylor, "Harmonic inversion of time signals," J. Chem. Phys. 107, 6756-6769 (1997).

J. Lightw. Technol. (1)

Y. Tanaka, T. Asano, R. Hatsuta, S. Noda, "Analysis of a line-defect waveguide on a silicon-on-insulator two-dimensional photonic-crystal slab," J. Lightw. Technol. 22, 2787-2792 (2004).

J. Opt. A (1)

R. Meisels, F. Kuchar, "Density-of-states and wave propagation in two-dimensional photonic crystals with positional disorder," J. Opt. A 9, 396-402 (2007).

Nature (1)

Y. Akahane, T. Asano, B. S. Song, S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).

Opt. Exp. (2)

D. Gerace, L. C. Andreani, "Low-loss guided modes in photonic crystal waveguides," Opt. Exp. 13, 4939-4951 (2005).

T. Asano, B. S. Song, S. Noda, "Analysis of the experimental Q factors (1 million) of photonic crystal nanocavities," Opt. Exp. 14, 1996-2002 (2006).

Opt. Lett. (2)

Phy. Rev. B (4)

H. Y. Ryu, J. K. Hwang, Y. H. Lee, "Effect of size nonuniformities on the bandgap of two-dimensional photonic crystals," Phy. Rev. B 59, 5463-5469 (1999).

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

H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, S. Noda, "Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities," Phy. Rev. B 79, 85112- (2009).

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, J. P. Albert, "Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal," Phy. Rev. B 66, 113101- (2002).

Other (3)

R. V. Hogg, A. T. Craig, Introduction to Mathematical Statistics (Macmillan, 1978).

P. Michler, Single Semiconductor Quantum Dots (2008)9 Springer Book series NanoScience and Technology.

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

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