Abstract

We show that modes in a photonic crystal slab that are uncoupled to outside radiation in a symmetric structure can be excited by breaking the mirror symmetry through introducing a protrusion on the side of the photonic crystal holes. We show that coupling to these resonances can be controlled by the strength of this asymmetry, and that it is also possible to choose among modes to couple to, through the shape of the asymmetry introduced. We provide simple theoretical arguments that explain the effect, and present eigenmode simulations and time-domain simulations. We confirm this predicted behavior with measurements on a photonic crystal with a broken mirror symmetry that exhibits an additional sharp resonant feature with a linewidth of 0.5 nm, in agreement with both calculated and simulated predictions.

© 2008 Optical Society of America

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  1. V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, "Photonic band-structure effects in the reflectivity of periodically patterned waveguides," Phys. Rev. B 60, R16255 (1999).
    [CrossRef]
  2. S. Fan and J. D. Joannopoulos, "Analysis of guided resonances in photonic crystal slabs," Phys. Rev. B 65, 235112 (2002).
    [CrossRef]
  3. O. Kilic, S. Kim, W. Suh, Y. Peter, A. Sudbø, M. Yanik, S. Fan, and O. Solgaard, "Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders," Opt. Lett. 29, 2782 (2004).
    [CrossRef] [PubMed]
  4. K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, "Air-bridged photonic crystal slabs at visible and near-infrared wavelength," Phys. Rev. B 73, 115126 (2006).
    [CrossRef]
  5. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of photonic band structure in a two-dimensional periodic dielectric array," Phys. Rev. Lett. 68, 2023 (1992).
    [CrossRef] [PubMed]
  6. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of the photon dispersion relation in two-dimensional ordered dielectric arrays," J. Opt. Soc. Am. B 10, 322 (1993).
    [CrossRef]
  7. M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
    [CrossRef]
  8. K. Sakoda, "Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices," Phys. Rev. B 52, 7982 (1995).
    [CrossRef]
  9. K. Ohtaka and Y. Tanabe, "Photonic bands using vector spherical waves. III. Group-theoretical treatment," J. Phys. Soc. Jpn. 65, 2670 (1996).
    [CrossRef]
  10. V. Karathanos, "Inactive frequency bands in photonic crystals," J. Mod. Opt. 45, 1751 (1998).
    [CrossRef]
  11. V. Pacradouni, W. J. Mandeville, A. R. Crown, P. Paddon, J. F. Young, and S. R. Johnson, "Photonic band structure of dielectric membranes periodically textured in two dimensions," Phys. Rev. B 62, 4204 (2000).
    [CrossRef]
  12. P. Paddon and J. F. Young, "Two-dimensional vector-coupled-mode theory for textured planar waveguides," Phys. Rev. B 61, 2090 (2000).
    [CrossRef]
  13. T. Ochiai and K. Sakoda, "Dispersion relation and optical transmittance of a hexagonal photonic crystal slab," Phys. Rev. B 63, 125107 (2001).
    [CrossRef]
  14. K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, M. Troccoli, and F. Capasso, "Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser," Appl. Phys. Lett. 84, 4146 (2004).
    [CrossRef]
  15. A.-L. Fehrembach and A. Sentenac, "Unpolarized narrow-band filtering with resonant gratings," Appl. Phys. Lett. 86, 121105 (2005).
    [CrossRef]
  16. O. Painter and K. Srinivasan, "Localized defect states in two-dimensional photonic crystal slab waveguides: A simple model based upon symmetry analysis," Phys. Rev. B 68, 035110 (2003).
    [CrossRef]
  17. K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670 (2002).
    [PubMed]
  18. T. Ito and K. Sakoda, "Photonic bands of metallic systems. II. Features of surface plasmon polaritons," Phys. Rev. B 64, 045117 (2001).
    [CrossRef]
  19. R. Wang, X-H. Wang, B-Y. Gu, and G-Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307 (2001).
    [CrossRef]
  20. R. Padjen, J. M. Gerard, and J. Y. Marzin, "Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems," J. Mod. Opt. 41, 295 (1994).
    [CrossRef]
  21. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173 (2001).
    [CrossRef] [PubMed]
  22. W. Hergert and M. Däne, "Group theoretical investigations of photonic band structures," Phys. Status Solidi A 197, 620 (2003).
    [CrossRef]
  23. O. Kilic, M. Digonnet, G. Kino, and O. Solgaard, "External fibre Fabry-Perot acoustic sensor based on a photonic-crystal mirror," Meas. Sci. Technol. 18, 3049 (2007).
    [CrossRef]
  24. H. Takeda and K. Yoshino, "Disappearances of uncoupled modes in two-dimensional photonic crystals due to anisotropies of liquid crystals," Phys. Rev. E 67, 056612 (2003).
    [CrossRef]

2007 (1)

O. Kilic, M. Digonnet, G. Kino, and O. Solgaard, "External fibre Fabry-Perot acoustic sensor based on a photonic-crystal mirror," Meas. Sci. Technol. 18, 3049 (2007).
[CrossRef]

2006 (1)

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, "Air-bridged photonic crystal slabs at visible and near-infrared wavelength," Phys. Rev. B 73, 115126 (2006).
[CrossRef]

2005 (1)

A.-L. Fehrembach and A. Sentenac, "Unpolarized narrow-band filtering with resonant gratings," Appl. Phys. Lett. 86, 121105 (2005).
[CrossRef]

2004 (2)

O. Kilic, S. Kim, W. Suh, Y. Peter, A. Sudbø, M. Yanik, S. Fan, and O. Solgaard, "Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders," Opt. Lett. 29, 2782 (2004).
[CrossRef] [PubMed]

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, M. Troccoli, and F. Capasso, "Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser," Appl. Phys. Lett. 84, 4146 (2004).
[CrossRef]

2003 (3)

W. Hergert and M. Däne, "Group theoretical investigations of photonic band structures," Phys. Status Solidi A 197, 620 (2003).
[CrossRef]

H. Takeda and K. Yoshino, "Disappearances of uncoupled modes in two-dimensional photonic crystals due to anisotropies of liquid crystals," Phys. Rev. E 67, 056612 (2003).
[CrossRef]

O. Painter and K. Srinivasan, "Localized defect states in two-dimensional photonic crystal slab waveguides: A simple model based upon symmetry analysis," Phys. Rev. B 68, 035110 (2003).
[CrossRef]

2002 (3)

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670 (2002).
[PubMed]

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

S. Fan and J. D. Joannopoulos, "Analysis of guided resonances in photonic crystal slabs," Phys. Rev. B 65, 235112 (2002).
[CrossRef]

2001 (4)

T. Ito and K. Sakoda, "Photonic bands of metallic systems. II. Features of surface plasmon polaritons," Phys. Rev. B 64, 045117 (2001).
[CrossRef]

R. Wang, X-H. Wang, B-Y. Gu, and G-Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307 (2001).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

T. Ochiai and K. Sakoda, "Dispersion relation and optical transmittance of a hexagonal photonic crystal slab," Phys. Rev. B 63, 125107 (2001).
[CrossRef]

2000 (2)

V. Pacradouni, W. J. Mandeville, A. R. Crown, P. Paddon, J. F. Young, and S. R. Johnson, "Photonic band structure of dielectric membranes periodically textured in two dimensions," Phys. Rev. B 62, 4204 (2000).
[CrossRef]

P. Paddon and J. F. Young, "Two-dimensional vector-coupled-mode theory for textured planar waveguides," Phys. Rev. B 61, 2090 (2000).
[CrossRef]

1999 (1)

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, "Photonic band-structure effects in the reflectivity of periodically patterned waveguides," Phys. Rev. B 60, R16255 (1999).
[CrossRef]

1998 (1)

V. Karathanos, "Inactive frequency bands in photonic crystals," J. Mod. Opt. 45, 1751 (1998).
[CrossRef]

1996 (1)

K. Ohtaka and Y. Tanabe, "Photonic bands using vector spherical waves. III. Group-theoretical treatment," J. Phys. Soc. Jpn. 65, 2670 (1996).
[CrossRef]

1995 (1)

K. Sakoda, "Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices," Phys. Rev. B 52, 7982 (1995).
[CrossRef]

1994 (1)

R. Padjen, J. M. Gerard, and J. Y. Marzin, "Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems," J. Mod. Opt. 41, 295 (1994).
[CrossRef]

1993 (1)

1992 (1)

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of photonic band structure in a two-dimensional periodic dielectric array," Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

Agio, M.

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

Andreani, L. C.

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

Arjavalingam, G.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of the photon dispersion relation in two-dimensional ordered dielectric arrays," J. Opt. Soc. Am. B 10, 322 (1993).
[CrossRef]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of photonic band structure in a two-dimensional periodic dielectric array," Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

Astratov, V. N.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, "Photonic band-structure effects in the reflectivity of periodically patterned waveguides," Phys. Rev. B 60, R16255 (1999).
[CrossRef]

Bellutti, P.

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

Belotti, M.

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

Bettotti, P.

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

Brommer, K. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of the photon dispersion relation in two-dimensional ordered dielectric arrays," J. Opt. Soc. Am. B 10, 322 (1993).
[CrossRef]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of photonic band structure in a two-dimensional periodic dielectric array," Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

Capasso, F.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, M. Troccoli, and F. Capasso, "Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser," Appl. Phys. Lett. 84, 4146 (2004).
[CrossRef]

Colombelli, R.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, M. Troccoli, and F. Capasso, "Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser," Appl. Phys. Lett. 84, 4146 (2004).
[CrossRef]

Crown, A. R.

V. Pacradouni, W. J. Mandeville, A. R. Crown, P. Paddon, J. F. Young, and S. R. Johnson, "Photonic band structure of dielectric membranes periodically textured in two dimensions," Phys. Rev. B 62, 4204 (2000).
[CrossRef]

Crozier, K. B.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, "Air-bridged photonic crystal slabs at visible and near-infrared wavelength," Phys. Rev. B 73, 115126 (2006).
[CrossRef]

Culshaw, I. S.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, "Photonic band-structure effects in the reflectivity of periodically patterned waveguides," Phys. Rev. B 60, R16255 (1999).
[CrossRef]

Dal Negro, L.

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

Däne, M.

W. Hergert and M. Däne, "Group theoretical investigations of photonic band structures," Phys. Status Solidi A 197, 620 (2003).
[CrossRef]

De La Rue, R. M.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, "Photonic band-structure effects in the reflectivity of periodically patterned waveguides," Phys. Rev. B 60, R16255 (1999).
[CrossRef]

Digonnet, M.

O. Kilic, M. Digonnet, G. Kino, and O. Solgaard, "External fibre Fabry-Perot acoustic sensor based on a photonic-crystal mirror," Meas. Sci. Technol. 18, 3049 (2007).
[CrossRef]

Fan, S.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, "Air-bridged photonic crystal slabs at visible and near-infrared wavelength," Phys. Rev. B 73, 115126 (2006).
[CrossRef]

O. Kilic, S. Kim, W. Suh, Y. Peter, A. Sudbø, M. Yanik, S. Fan, and O. Solgaard, "Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders," Opt. Lett. 29, 2782 (2004).
[CrossRef] [PubMed]

S. Fan and J. D. Joannopoulos, "Analysis of guided resonances in photonic crystal slabs," Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Fehrembach, A.-L.

A.-L. Fehrembach and A. Sentenac, "Unpolarized narrow-band filtering with resonant gratings," Appl. Phys. Lett. 86, 121105 (2005).
[CrossRef]

Gaburro, Z.

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

Galli, M.

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

Gerard, J. M.

R. Padjen, J. M. Gerard, and J. Y. Marzin, "Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems," J. Mod. Opt. 41, 295 (1994).
[CrossRef]

Gmachl, C.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, M. Troccoli, and F. Capasso, "Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser," Appl. Phys. Lett. 84, 4146 (2004).
[CrossRef]

Gu, B-Y.

R. Wang, X-H. Wang, B-Y. Gu, and G-Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307 (2001).
[CrossRef]

Guizzetti, G.

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

Hergert, W.

W. Hergert and M. Däne, "Group theoretical investigations of photonic band structures," Phys. Status Solidi A 197, 620 (2003).
[CrossRef]

Ito, T.

T. Ito and K. Sakoda, "Photonic bands of metallic systems. II. Features of surface plasmon polaritons," Phys. Rev. B 64, 045117 (2001).
[CrossRef]

Joannopoulos, J. D.

S. Fan and J. D. Joannopoulos, "Analysis of guided resonances in photonic crystal slabs," Phys. Rev. B 65, 235112 (2002).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of the photon dispersion relation in two-dimensional ordered dielectric arrays," J. Opt. Soc. Am. B 10, 322 (1993).
[CrossRef]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of photonic band structure in a two-dimensional periodic dielectric array," Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

Johnson, S. G.

Johnson, S. R.

V. Pacradouni, W. J. Mandeville, A. R. Crown, P. Paddon, J. F. Young, and S. R. Johnson, "Photonic band structure of dielectric membranes periodically textured in two dimensions," Phys. Rev. B 62, 4204 (2000).
[CrossRef]

Karathanos, V.

V. Karathanos, "Inactive frequency bands in photonic crystals," J. Mod. Opt. 45, 1751 (1998).
[CrossRef]

Kilic, O.

O. Kilic, M. Digonnet, G. Kino, and O. Solgaard, "External fibre Fabry-Perot acoustic sensor based on a photonic-crystal mirror," Meas. Sci. Technol. 18, 3049 (2007).
[CrossRef]

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, "Air-bridged photonic crystal slabs at visible and near-infrared wavelength," Phys. Rev. B 73, 115126 (2006).
[CrossRef]

O. Kilic, S. Kim, W. Suh, Y. Peter, A. Sudbø, M. Yanik, S. Fan, and O. Solgaard, "Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders," Opt. Lett. 29, 2782 (2004).
[CrossRef] [PubMed]

Kim, S.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, "Air-bridged photonic crystal slabs at visible and near-infrared wavelength," Phys. Rev. B 73, 115126 (2006).
[CrossRef]

O. Kilic, S. Kim, W. Suh, Y. Peter, A. Sudbø, M. Yanik, S. Fan, and O. Solgaard, "Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders," Opt. Lett. 29, 2782 (2004).
[CrossRef] [PubMed]

Kino, G.

O. Kilic, M. Digonnet, G. Kino, and O. Solgaard, "External fibre Fabry-Perot acoustic sensor based on a photonic-crystal mirror," Meas. Sci. Technol. 18, 3049 (2007).
[CrossRef]

Krauss, T. F.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, "Photonic band-structure effects in the reflectivity of periodically patterned waveguides," Phys. Rev. B 60, R16255 (1999).
[CrossRef]

Lousse, V.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, "Air-bridged photonic crystal slabs at visible and near-infrared wavelength," Phys. Rev. B 73, 115126 (2006).
[CrossRef]

Lui, A.

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

Mandeville, W. J.

V. Pacradouni, W. J. Mandeville, A. R. Crown, P. Paddon, J. F. Young, and S. R. Johnson, "Photonic band structure of dielectric membranes periodically textured in two dimensions," Phys. Rev. B 62, 4204 (2000).
[CrossRef]

Marabelli, F.

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

Marzin, J. Y.

R. Padjen, J. M. Gerard, and J. Y. Marzin, "Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems," J. Mod. Opt. 41, 295 (1994).
[CrossRef]

Meade, R. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of the photon dispersion relation in two-dimensional ordered dielectric arrays," J. Opt. Soc. Am. B 10, 322 (1993).
[CrossRef]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of photonic band structure in a two-dimensional periodic dielectric array," Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

Ochiai, T.

T. Ochiai and K. Sakoda, "Dispersion relation and optical transmittance of a hexagonal photonic crystal slab," Phys. Rev. B 63, 125107 (2001).
[CrossRef]

Ohtaka, K.

K. Ohtaka and Y. Tanabe, "Photonic bands using vector spherical waves. III. Group-theoretical treatment," J. Phys. Soc. Jpn. 65, 2670 (1996).
[CrossRef]

Pacradouni, V.

V. Pacradouni, W. J. Mandeville, A. R. Crown, P. Paddon, J. F. Young, and S. R. Johnson, "Photonic band structure of dielectric membranes periodically textured in two dimensions," Phys. Rev. B 62, 4204 (2000).
[CrossRef]

Paddon, P.

V. Pacradouni, W. J. Mandeville, A. R. Crown, P. Paddon, J. F. Young, and S. R. Johnson, "Photonic band structure of dielectric membranes periodically textured in two dimensions," Phys. Rev. B 62, 4204 (2000).
[CrossRef]

P. Paddon and J. F. Young, "Two-dimensional vector-coupled-mode theory for textured planar waveguides," Phys. Rev. B 61, 2090 (2000).
[CrossRef]

Padjen, R.

R. Padjen, J. M. Gerard, and J. Y. Marzin, "Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems," J. Mod. Opt. 41, 295 (1994).
[CrossRef]

Painter, O.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, M. Troccoli, and F. Capasso, "Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser," Appl. Phys. Lett. 84, 4146 (2004).
[CrossRef]

O. Painter and K. Srinivasan, "Localized defect states in two-dimensional photonic crystal slab waveguides: A simple model based upon symmetry analysis," Phys. Rev. B 68, 035110 (2003).
[CrossRef]

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670 (2002).
[PubMed]

Patrini, M.

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

Pavesi, L.

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

Peter, Y.

Rappe, A. M.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of the photon dispersion relation in two-dimensional ordered dielectric arrays," J. Opt. Soc. Am. B 10, 322 (1993).
[CrossRef]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of photonic band structure in a two-dimensional periodic dielectric array," Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

Robertson, W. M.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of the photon dispersion relation in two-dimensional ordered dielectric arrays," J. Opt. Soc. Am. B 10, 322 (1993).
[CrossRef]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of photonic band structure in a two-dimensional periodic dielectric array," Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

Sakoda, K.

T. Ito and K. Sakoda, "Photonic bands of metallic systems. II. Features of surface plasmon polaritons," Phys. Rev. B 64, 045117 (2001).
[CrossRef]

T. Ochiai and K. Sakoda, "Dispersion relation and optical transmittance of a hexagonal photonic crystal slab," Phys. Rev. B 63, 125107 (2001).
[CrossRef]

K. Sakoda, "Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices," Phys. Rev. B 52, 7982 (1995).
[CrossRef]

Sentenac, A.

A.-L. Fehrembach and A. Sentenac, "Unpolarized narrow-band filtering with resonant gratings," Appl. Phys. Lett. 86, 121105 (2005).
[CrossRef]

Sergent, A. M.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, M. Troccoli, and F. Capasso, "Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser," Appl. Phys. Lett. 84, 4146 (2004).
[CrossRef]

Skolnick, M. S.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, "Photonic band-structure effects in the reflectivity of periodically patterned waveguides," Phys. Rev. B 60, R16255 (1999).
[CrossRef]

Solgaard, O.

O. Kilic, M. Digonnet, G. Kino, and O. Solgaard, "External fibre Fabry-Perot acoustic sensor based on a photonic-crystal mirror," Meas. Sci. Technol. 18, 3049 (2007).
[CrossRef]

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, "Air-bridged photonic crystal slabs at visible and near-infrared wavelength," Phys. Rev. B 73, 115126 (2006).
[CrossRef]

O. Kilic, S. Kim, W. Suh, Y. Peter, A. Sudbø, M. Yanik, S. Fan, and O. Solgaard, "Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders," Opt. Lett. 29, 2782 (2004).
[CrossRef] [PubMed]

Srinivasan, K.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, M. Troccoli, and F. Capasso, "Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser," Appl. Phys. Lett. 84, 4146 (2004).
[CrossRef]

O. Painter and K. Srinivasan, "Localized defect states in two-dimensional photonic crystal slab waveguides: A simple model based upon symmetry analysis," Phys. Rev. B 68, 035110 (2003).
[CrossRef]

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670 (2002).
[PubMed]

Stevenson, R. M.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, "Photonic band-structure effects in the reflectivity of periodically patterned waveguides," Phys. Rev. B 60, R16255 (1999).
[CrossRef]

Sudbø, A.

Suh, W.

Takeda, H.

H. Takeda and K. Yoshino, "Disappearances of uncoupled modes in two-dimensional photonic crystals due to anisotropies of liquid crystals," Phys. Rev. E 67, 056612 (2003).
[CrossRef]

Tanabe, Y.

K. Ohtaka and Y. Tanabe, "Photonic bands using vector spherical waves. III. Group-theoretical treatment," J. Phys. Soc. Jpn. 65, 2670 (1996).
[CrossRef]

Tennant, D. M.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, M. Troccoli, and F. Capasso, "Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser," Appl. Phys. Lett. 84, 4146 (2004).
[CrossRef]

Troccoli, M.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, M. Troccoli, and F. Capasso, "Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser," Appl. Phys. Lett. 84, 4146 (2004).
[CrossRef]

Wang, R.

R. Wang, X-H. Wang, B-Y. Gu, and G-Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307 (2001).
[CrossRef]

Wang, X-H.

R. Wang, X-H. Wang, B-Y. Gu, and G-Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307 (2001).
[CrossRef]

Whittaker, D. M.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, "Photonic band-structure effects in the reflectivity of periodically patterned waveguides," Phys. Rev. B 60, R16255 (1999).
[CrossRef]

Yang, G-Z.

R. Wang, X-H. Wang, B-Y. Gu, and G-Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307 (2001).
[CrossRef]

Yanik, M.

Yoshino, K.

H. Takeda and K. Yoshino, "Disappearances of uncoupled modes in two-dimensional photonic crystals due to anisotropies of liquid crystals," Phys. Rev. E 67, 056612 (2003).
[CrossRef]

Young, J. F.

V. Pacradouni, W. J. Mandeville, A. R. Crown, P. Paddon, J. F. Young, and S. R. Johnson, "Photonic band structure of dielectric membranes periodically textured in two dimensions," Phys. Rev. B 62, 4204 (2000).
[CrossRef]

P. Paddon and J. F. Young, "Two-dimensional vector-coupled-mode theory for textured planar waveguides," Phys. Rev. B 61, 2090 (2000).
[CrossRef]

Appl. Phys. Lett. (2)

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, M. Troccoli, and F. Capasso, "Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser," Appl. Phys. Lett. 84, 4146 (2004).
[CrossRef]

A.-L. Fehrembach and A. Sentenac, "Unpolarized narrow-band filtering with resonant gratings," Appl. Phys. Lett. 86, 121105 (2005).
[CrossRef]

J. Appl. Phys. (1)

R. Wang, X-H. Wang, B-Y. Gu, and G-Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307 (2001).
[CrossRef]

J. Mod. Opt. (2)

R. Padjen, J. M. Gerard, and J. Y. Marzin, "Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems," J. Mod. Opt. 41, 295 (1994).
[CrossRef]

V. Karathanos, "Inactive frequency bands in photonic crystals," J. Mod. Opt. 45, 1751 (1998).
[CrossRef]

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

J. Phys. Soc. Jpn. (1)

K. Ohtaka and Y. Tanabe, "Photonic bands using vector spherical waves. III. Group-theoretical treatment," J. Phys. Soc. Jpn. 65, 2670 (1996).
[CrossRef]

Meas. Sci. Technol. (1)

O. Kilic, M. Digonnet, G. Kino, and O. Solgaard, "External fibre Fabry-Perot acoustic sensor based on a photonic-crystal mirror," Meas. Sci. Technol. 18, 3049 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (10)

T. Ito and K. Sakoda, "Photonic bands of metallic systems. II. Features of surface plasmon polaritons," Phys. Rev. B 64, 045117 (2001).
[CrossRef]

M. Galli, M. Agio, L. C. Andreani, M. Belotti, G. Guizzetti, F. Marabelli, M. Patrini, P. Bettotti, L. Dal Negro, Z. Gaburro, L. Pavesi, A. Lui, and P. Bellutti, "Spectroscopy of photonic bands in macroporous silicon photonic crystals," Phys. Rev. B 65, 113111 (2002).
[CrossRef]

K. Sakoda, "Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices," Phys. Rev. B 52, 7982 (1995).
[CrossRef]

V. Pacradouni, W. J. Mandeville, A. R. Crown, P. Paddon, J. F. Young, and S. R. Johnson, "Photonic band structure of dielectric membranes periodically textured in two dimensions," Phys. Rev. B 62, 4204 (2000).
[CrossRef]

P. Paddon and J. F. Young, "Two-dimensional vector-coupled-mode theory for textured planar waveguides," Phys. Rev. B 61, 2090 (2000).
[CrossRef]

T. Ochiai and K. Sakoda, "Dispersion relation and optical transmittance of a hexagonal photonic crystal slab," Phys. Rev. B 63, 125107 (2001).
[CrossRef]

O. Painter and K. Srinivasan, "Localized defect states in two-dimensional photonic crystal slab waveguides: A simple model based upon symmetry analysis," Phys. Rev. B 68, 035110 (2003).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, "Photonic band-structure effects in the reflectivity of periodically patterned waveguides," Phys. Rev. B 60, R16255 (1999).
[CrossRef]

S. Fan and J. D. Joannopoulos, "Analysis of guided resonances in photonic crystal slabs," Phys. Rev. B 65, 235112 (2002).
[CrossRef]

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, "Air-bridged photonic crystal slabs at visible and near-infrared wavelength," Phys. Rev. B 73, 115126 (2006).
[CrossRef]

Phys. Rev. E (1)

H. Takeda and K. Yoshino, "Disappearances of uncoupled modes in two-dimensional photonic crystals due to anisotropies of liquid crystals," Phys. Rev. E 67, 056612 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of photonic band structure in a two-dimensional periodic dielectric array," Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

Phys. Status Solidi A (1)

W. Hergert and M. Däne, "Group theoretical investigations of photonic band structures," Phys. Status Solidi A 197, 620 (2003).
[CrossRef]

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Figures (13)

Fig. 1.
Fig. 1.

(a) Mirror symmetries in a square-lattice PCS unit cell. (b) A square-lattice PCS with broken mirror symmetry.

Fig. 2.
Fig. 2.

The six modes of a square-lattice PCS classified with respect to their mirror symmetries, along with the symmetries of polarized plane waves at normal incidence for reference (after Ref. [18]).

Fig. 3.
Fig. 3.

Demonstration of how the perturbed non-degenerate modes A1 (a) and B2 (b) can couple to plane waves due to their mixed symmetries. The arrows are illustrative electric fields, while the colors depict the symmetries of the modes that are related to the directions of the fields.

Fig. 4.
Fig. 4.

Simulated mode profiles of six different modes of the PCS, showing the symmetries, the power in the displacement field, and the mode number. The power is normalized to the peak power. The color scale is linear as shown in the color bar. The coloring is in the same convention used in Figs. 2 and 3.

Fig. 5.
Fig. 5.

Simulated mode profiles of the perturbed modes A1 and B2, showing the symmetric and antisymmetric parts. The power is normalized to the peak power. The color scale is linear as shown in the color bar. The symmetry coloring is in the same convention used in Fig. 4, while the non-symmetric perturbed modes are shown in a single color (purple).

Fig. 6.
Fig. 6.

Transmission spectra of three PCS with the three different hole shapes, circular (dotted and blue), keyhole (solid and red), and double-keyhole (dashed and green). The spectra were plotted for two different polarizations to see the different non-degenerate resonances in each polarization. The arrows are pointing to non-degenerate resonances of the keyhole PCS.

Fig. 7.
Fig. 7.

Simulated spectra showing how the linewidth of the non-degenerate resonance changes for different protrusion sizes, which are (a) 1.5%, (b) 2.3%, and (c) 3.0% of the hole size respectively. The arrows are pointing to the non-degenerate resonances of the keyhole PCS.

Fig. 8.
Fig. 8.

Scanning-electron micrographs (SEMs) of the fabricated PCS with three different hole shapes. Colored circles are overlaid on the SEMs for reference. The scale bar on the SEMs and the pitch are 1000 nm, and the hole diameter and slab thickness are 450 nm.

Fig. 9.
Fig. 9.

Measured spectra of the three different PCS with SEMs shown in Fig. 8. This measurement shows only the polarization. The arrow is pointing to the non-degenerate resonance of the keyhole PCS.

Fig. 10.
Fig. 10.

Comparison of the measured and simulated spectra of the keyhole PCS.

Fig. 11.
Fig. 11.

A gradual increase in the distance of the protrusion or its size does not necessarily mean that the asymmetry is increased. When we gradually increase the distance of the protrusion from the center through (a), (b), and (c), we observe that although it appears that the asymmetry increases, we end up with a structure that is symmetric. Similarly, when we gradually increase the size of the protrusion through (d), (e), and (f), we end up with a symmetric structure (although the symmetry axis is shifted upwards to the middle of the holes).

Fig. 12.
Fig. 12.

Comparison of four modes perturbed by two different protrusions. (a), (b), (c), and (d) correspond to the 21st odd, the 24th odd, the 15th odd, and the 28th even modes respectively. (a1), (b1), (c1), and (d1) show the unperturbed modes. (a2), (b2), (c2), and (d2) show the modes perturbed with a circular protrusion close to the PCS hole. (a3), (b3), (c3), and (d3) show the modes perturbed with a circular protrusion away from the PCS hole. The amount of normalized power in the respective degenerate part of the perturbed mode is given below each mode profile.

Fig. 13.
Fig. 13.

Comparison of two perturbed non-degenerate modes in the keyhole PCS. These two modes have the strongest degenerate parts, i.e. are perturbed most out of the five non-degenerate modes in our wavelength range and polarization.

Equations (4)

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

e x | A 1 = e x σ ̂ x σ ̂ x A 1 = ( e x ) ( + A 1 ) = e x | A 1 e x A 1 = 0
e y A 1 = e y σ ̂ y σ ̂ y A 1 = ( e y ) ( + A 1 ) = e y A 1 e y A 1 = 0
A 1 = 1 2 ( A 1 + σ ̂ y A 1 ) + 1 2 ( A 1 + σ ̂ y A 1 ) = A 1 s + A 1 as
S = max ( ε * ε ε | ε )

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