Abstract

The effect of irregular hole shape on the spectrum and radiation losses of a photonic crystal waveguide is studied using Bloch-mode expansion. Deviations from a circular hole are characterized by a radius fluctuation amplitude and correlation angle. It is found that the parameter that determines the magnitude of the effect of disorder is the standard deviation of the hole areas. Hence, for a fixed amplitude of the radius fluctuation around the hole, those effects are strongly dependent on the correlation angle of the irregular shape, which suggests how to potentially improve the quality of photonic crystal structures.

© 2012 Optical Society of America

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  1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light(Princeton University, 2008).
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    [CrossRef]
  3. Y. Taguchi, Y. Takahashi, Y. Sato, T. Asano, and S. Noda, Opt. Express 19, 11916 (2011).
    [CrossRef]
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    [CrossRef]
  5. D. Gerace and L. C. Andreani, Opt. Lett. 29, 1897 (2004).
    [CrossRef]
  6. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
    [CrossRef]
  7. M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
    [CrossRef]
  8. S. Mazoyer, J. P. Hugonin, and P. Lalanne, Phys. Rev. Lett. 103, 063903 (2009).
    [CrossRef]
  9. S. John, Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef]
  10. L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
    [CrossRef]
  11. V. Savona, Phys. Rev. B 83, 085301 (2011).
    [CrossRef]
  12. M. Patterson and S. Hughes, Phys. Rev. B 81, 245321 (2010).
    [CrossRef]
  13. N. Le Thomas, Z. Diao, H. Zhang, and R. Houdre, J. Vac. Sci. Technol. B 29, 051601 (2011).
    [CrossRef]
  14. S. Mazoyer, P. Lalanne, J. Rodier, J. Hugonin, M. Spasenovi, L. Kuipers, D. Beggs, and T. Krauss, Opt. Express 18, 14654 (2010).
    [CrossRef]
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    [CrossRef]
  16. M. Skorobogatiy, G. Bégin, and A. Talneau, Opt. Express 13, 2487 (2005).
    [CrossRef]
  17. L. C. Andreani and D. Gerace, Phys. Rev. B 73, 235114 (2006).
    [CrossRef]
  18. J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
    [CrossRef]

2011 (4)

V. Savona, Phys. Rev. B 83, 085301 (2011).
[CrossRef]

N. Le Thomas, Z. Diao, H. Zhang, and R. Houdre, J. Vac. Sci. Technol. B 29, 051601 (2011).
[CrossRef]

S. L. Portalupi, M. Galli, M. Belotti, L. C. Andreani, T. F. Krauss, and L. O’Faolain, Phys. Rev. B 84, 045423 (2011).
[CrossRef]

Y. Taguchi, Y. Takahashi, Y. Sato, T. Asano, and S. Noda, Opt. Express 19, 11916 (2011).
[CrossRef]

2010 (3)

S. Mazoyer, P. Lalanne, J. Rodier, J. Hugonin, M. Spasenovi, L. Kuipers, D. Beggs, and T. Krauss, Opt. Express 18, 14654 (2010).
[CrossRef]

M. Patterson and S. Hughes, Phys. Rev. B 81, 245321 (2010).
[CrossRef]

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef]

2009 (3)

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
[CrossRef]

S. Mazoyer, J. P. Hugonin, and P. Lalanne, Phys. Rev. Lett. 103, 063903 (2009).
[CrossRef]

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, Phys. Rev. B 80, 125332 (2009).
[CrossRef]

2007 (2)

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

L. C. Andreani and D. Gerace, Phys. Status Solidi B 244, 3528 (2007).
[CrossRef]

2006 (1)

L. C. Andreani and D. Gerace, Phys. Rev. B 73, 235114 (2006).
[CrossRef]

2005 (2)

M. Skorobogatiy, G. Bégin, and A. Talneau, Opt. Express 13, 2487 (2005).
[CrossRef]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef]

2004 (1)

1987 (1)

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

Andreani, L. C.

S. L. Portalupi, M. Galli, M. Belotti, L. C. Andreani, T. F. Krauss, and L. O’Faolain, Phys. Rev. B 84, 045423 (2011).
[CrossRef]

L. C. Andreani and D. Gerace, Phys. Status Solidi B 244, 3528 (2007).
[CrossRef]

L. C. Andreani and D. Gerace, Phys. Rev. B 73, 235114 (2006).
[CrossRef]

D. Gerace and L. C. Andreani, Opt. Lett. 29, 1897 (2004).
[CrossRef]

Asano, T.

Beggs, D.

Beggs, D. M.

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
[CrossRef]

Bégin, G.

Belotti, M.

S. L. Portalupi, M. Galli, M. Belotti, L. C. Andreani, T. F. Krauss, and L. O’Faolain, Phys. Rev. B 84, 045423 (2011).
[CrossRef]

Diao, Z.

N. Le Thomas, Z. Diao, H. Zhang, and R. Houdre, J. Vac. Sci. Technol. B 29, 051601 (2011).
[CrossRef]

Galli, M.

S. L. Portalupi, M. Galli, M. Belotti, L. C. Andreani, T. F. Krauss, and L. O’Faolain, Phys. Rev. B 84, 045423 (2011).
[CrossRef]

Garcia, P. D.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef]

Gerace, D.

L. C. Andreani and D. Gerace, Phys. Status Solidi B 244, 3528 (2007).
[CrossRef]

L. C. Andreani and D. Gerace, Phys. Rev. B 73, 235114 (2006).
[CrossRef]

D. Gerace and L. C. Andreani, Opt. Lett. 29, 1897 (2004).
[CrossRef]

Houdre, R.

N. Le Thomas, Z. Diao, H. Zhang, and R. Houdre, J. Vac. Sci. Technol. B 29, 051601 (2011).
[CrossRef]

Houdré, R.

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, Phys. Rev. B 80, 125332 (2009).
[CrossRef]

Hughes, S.

M. Patterson and S. Hughes, Phys. Rev. B 81, 245321 (2010).
[CrossRef]

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
[CrossRef]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef]

Hugonin, J.

Hugonin, J. P.

S. Mazoyer, J. P. Hugonin, and P. Lalanne, Phys. Rev. Lett. 103, 063903 (2009).
[CrossRef]

Ilic, B.

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Jágerská, J.

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, Phys. Rev. B 80, 125332 (2009).
[CrossRef]

Joannopoulos, J. D.

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

John, S.

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

Johnson, S. G.

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

Krauss, T.

Krauss, T. F.

S. L. Portalupi, M. Galli, M. Belotti, L. C. Andreani, T. F. Krauss, and L. O’Faolain, Phys. Rev. B 84, 045423 (2011).
[CrossRef]

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
[CrossRef]

Kuipers, L.

Lalanne, P.

Le Thomas, N.

N. Le Thomas, Z. Diao, H. Zhang, and R. Houdre, J. Vac. Sci. Technol. B 29, 051601 (2011).
[CrossRef]

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, Phys. Rev. B 80, 125332 (2009).
[CrossRef]

Lodahl, P.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef]

Mazoyer, S.

Meade, R. D.

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

Noda, S.

O’Faolain, L.

S. L. Portalupi, M. Galli, M. Belotti, L. C. Andreani, T. F. Krauss, and L. O’Faolain, Phys. Rev. B 84, 045423 (2011).
[CrossRef]

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
[CrossRef]

Patterson, M.

M. Patterson and S. Hughes, Phys. Rev. B 81, 245321 (2010).
[CrossRef]

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
[CrossRef]

Portalupi, S. L.

S. L. Portalupi, M. Galli, M. Belotti, L. C. Andreani, T. F. Krauss, and L. O’Faolain, Phys. Rev. B 84, 045423 (2011).
[CrossRef]

Ramunno, L.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef]

Rodier, J.

Sagnes, I.

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, Phys. Rev. B 80, 125332 (2009).
[CrossRef]

Sapienza, L.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef]

Sato, Y.

Savona, V.

V. Savona, Phys. Rev. B 83, 085301 (2011).
[CrossRef]

Schulz, S.

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
[CrossRef]

Sipe, J. E.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef]

Skorobogatiy, M.

Smolka, S.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef]

Spasenovi, M.

Stobbe, S.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef]

Taguchi, Y.

Takahashi, Y.

Talneau, A.

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, Phys. Rev. B 80, 125332 (2009).
[CrossRef]

M. Skorobogatiy, G. Bégin, and A. Talneau, Opt. Express 13, 2487 (2005).
[CrossRef]

Thyrrestrup, H.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef]

Topolancik, J.

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Vollmer, F.

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

White, T. P.

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
[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).

Young, J. F.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef]

Zabelin, V.

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, Phys. Rev. B 80, 125332 (2009).
[CrossRef]

Zhang, H.

N. Le Thomas, Z. Diao, H. Zhang, and R. Houdre, J. Vac. Sci. Technol. B 29, 051601 (2011).
[CrossRef]

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, Phys. Rev. B 80, 125332 (2009).
[CrossRef]

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

N. Le Thomas, Z. Diao, H. Zhang, and R. Houdre, J. Vac. Sci. Technol. B 29, 051601 (2011).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (6)

S. L. Portalupi, M. Galli, M. Belotti, L. C. Andreani, T. F. Krauss, and L. O’Faolain, Phys. Rev. B 84, 045423 (2011).
[CrossRef]

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, Phys. Rev. B 80, 125332 (2009).
[CrossRef]

L. C. Andreani and D. Gerace, Phys. Rev. B 73, 235114 (2006).
[CrossRef]

V. Savona, Phys. Rev. B 83, 085301 (2011).
[CrossRef]

M. Patterson and S. Hughes, Phys. Rev. B 81, 245321 (2010).
[CrossRef]

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, Phys. Rev. B 80, 195305 (2009).
[CrossRef]

Phys. Rev. Lett. (4)

S. Mazoyer, J. P. Hugonin, and P. Lalanne, Phys. Rev. Lett. 103, 063903 (2009).
[CrossRef]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef]

Phys. Status Solidi B (1)

L. C. Andreani and D. Gerace, Phys. Status Solidi B 244, 3528 (2007).
[CrossRef]

Science (1)

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef]

Other (1)

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

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Figures (3)

Fig. 1.
Fig. 1.

(a) Polar and Cartesian plots of a sample hole shape for two different correlation angles, assuming a fixed radius fluctuation σ=0.006a and (b) the underlying distributions of |Cm|2. (c) and (d) Same, assuming a fixed area fluctuation δA2=0.004a2.

Fig. 2.
Fig. 2.

Computed radiation loss rates. (a) δR2=const model and (b) δA2=const model. Insets: detail of the rates close to the band edge. On the left, the guided bands of the regular structure (solid curves) and the light cone (dashed curve) are displayed for reference.

Fig. 3.
Fig. 3.

DOS histograms close to the band edge (marked by a dashed–dotted line), for (a) σ=0.006a, (b) σ=0.002a, (c) δA2=0.004a2, and (d) δA2=0.001a2.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

ε(g)=ε(g)+2πR0(ε1ε2)Sζeigρζm=imeimθCm,ζJm(gR0),
|Cm|2=σ2ππeϕ22δ2eimϕdϕ.

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