Abstract

Resonant coupling of light to leaky modes of a photonic crystal slab leads to asymmetric Fano lineshapes in the reflectivity spectra. The generally accepted picture, for a lossless system, is that the sign of the real-valued parameter q controls the asymmetry of a Fano resonance. For the reflectivity of a symmetric slab this situation occurs if the amplitude reflection coefficient of the slab goes through zero. In this article, we show that it is also possible to change the asymmetry of a resonance by angle tuning without reaching a condition of zero amplitude. Moreover, we show that the picture of a real-valued parameter q that controls the asymmetry is incomplete.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866 (1961).
  2. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, "Fano resonances in nanoscale structures," Rev. Mod. Phys. 82, 2257 (2010).
    [CrossRef]
  3. R. K. Adair, C. K. Bockelman, and R. E. Peterson, "Experimental corroboration of the theory of neutron resonance scattering," Phys. Rev. 76, 308 (1949).
    [CrossRef]
  4. K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, "Tuning of the fano effect through a quantum dot in an aharonov-bohm interferometer," Phys. Rev. Lett. 88, 256806 (2002).
    [CrossRef] [PubMed]
  5. M. Mendoza, P. A. Schulz, R. O. Vallejos, and C. H. Lewenkopf, "Fano resonances in the conductance of quantum dots with mixed dynamics," Phys. Rev. B 77, 155307 (2008).
    [CrossRef]
  6. C. Genet, M. P. van Exter, and J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331 (2003).
    [CrossRef]
  7. M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, "Observation of coupling between surface plasmons in index-matched hole arrays," Phys. Rev. B 77, 115437 (2008).
    [CrossRef]
  8. A. Bärnthaler, S. Rotter, F. Libisch, J. Burgdörfer, S. Gehler, U. Kuhl, and H.-J. Stöckmann, "Probing decoherence through fano resonances," Phys. Rev. Lett. 105, 056801 (2010).
    [CrossRef] [PubMed]
  9. M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, "Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice," Appl. Phys. Lett. 70, 1438 (1997).
    [CrossRef]
  10. 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]
  11. 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]
  12. A. A. Clerk, X. Waintal, and P. W. Brouwer, "Fano resonances as a probe of phase coherence in quantum dots," Phys. Rev. Lett. 86, 4636 (2001).
    [CrossRef] [PubMed]
  13. S. Klaiman, N. Moiseyev, and H. R. Sadeghpour, "Interpretation of the fano lineshape reversal in quantum waveguides," Phys. Rev. B 75, 113305 (2007).
    [CrossRef]
  14. S. Fan, and J. D. Joannopoulos, "Analysis of guided resonances in photonic crystal slabs," Phys. Rev. B 65, 235112 (2002).
    [CrossRef]
  15. M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, "Light scattering and fano resonances in high-q photonic crystal nanocavities," Appl. Phys. Lett. 94, 071101 (2009).
    [CrossRef]
  16. S. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80, 908 (2002).
    [CrossRef]
  17. E. Flück, "Local interaction of light with periodic photonic structures," Ph.D. thesis, University of Twente (2003).
  18. E. F. C. Driessen, D. Stolwijk, and M. J. A. de Dood, "Asymmetry reversal in the reflection from a two-dimensional photonic crystal," Opt. Lett. 32, 3137 (2007).
    [CrossRef] [PubMed]
  19. Philips MiPlaza - Cedova, http://www.cedova.com.
  20. Z EON corporation, http://www.zeon.co.jp.
  21. Gel-Pak, http://www.gelpak.com.
  22. Lj. Babić, R. Leijssen, E. Driessen and M. J. A. de Dood, in preparation.
  23. S. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569 (2003).
    [CrossRef]
  24. H. A. Haus, Waves and fields in optoelectronics (Prentice-Hall, New Jersey, 1984).
  25. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751 (1999).
    [CrossRef]
  26. M. Born, and E. Wolf, Principles of Optics (Pergamon Press, 1980), 6th ed.

2010 (2)

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, "Fano resonances in nanoscale structures," Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

A. Bärnthaler, S. Rotter, F. Libisch, J. Burgdörfer, S. Gehler, U. Kuhl, and H.-J. Stöckmann, "Probing decoherence through fano resonances," Phys. Rev. Lett. 105, 056801 (2010).
[CrossRef] [PubMed]

2009 (1)

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

2008 (2)

M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, "Observation of coupling between surface plasmons in index-matched hole arrays," Phys. Rev. B 77, 115437 (2008).
[CrossRef]

M. Mendoza, P. A. Schulz, R. O. Vallejos, and C. H. Lewenkopf, "Fano resonances in the conductance of quantum dots with mixed dynamics," Phys. Rev. B 77, 155307 (2008).
[CrossRef]

2007 (2)

S. Klaiman, N. Moiseyev, and H. R. Sadeghpour, "Interpretation of the fano lineshape reversal in quantum waveguides," Phys. Rev. B 75, 113305 (2007).
[CrossRef]

E. F. C. Driessen, D. Stolwijk, and M. J. A. de Dood, "Asymmetry reversal in the reflection from a two-dimensional photonic crystal," Opt. Lett. 32, 3137 (2007).
[CrossRef] [PubMed]

2003 (2)

S. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569 (2003).
[CrossRef]

C. Genet, M. P. van Exter, and J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331 (2003).
[CrossRef]

2002 (4)

K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, "Tuning of the fano effect through a quantum dot in an aharonov-bohm interferometer," Phys. Rev. Lett. 88, 256806 (2002).
[CrossRef] [PubMed]

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

S. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80, 908 (2002).
[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]

2001 (1)

A. A. Clerk, X. Waintal, and P. W. Brouwer, "Fano resonances as a probe of phase coherence in quantum dots," Phys. Rev. Lett. 86, 4636 (2001).
[CrossRef] [PubMed]

1999 (2)

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. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751 (1999).
[CrossRef]

1997 (1)

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, "Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice," Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

1961 (1)

U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866 (1961).

1949 (1)

R. K. Adair, C. K. Bockelman, and R. E. Peterson, "Experimental corroboration of the theory of neutron resonance scattering," Phys. Rev. 76, 308 (1949).
[CrossRef]

Adair, R. K.

R. K. Adair, C. K. Bockelman, and R. E. Peterson, "Experimental corroboration of the theory of neutron resonance scattering," Phys. Rev. 76, 308 (1949).
[CrossRef]

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]

Aikawa, H.

K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, "Tuning of the fano effect through a quantum dot in an aharonov-bohm interferometer," Phys. Rev. Lett. 88, 256806 (2002).
[CrossRef] [PubMed]

Andreani, L. C.

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

M. 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]

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]

Bärnthaler, A.

A. Bärnthaler, S. Rotter, F. Libisch, J. Burgdörfer, S. Gehler, U. Kuhl, and H.-J. Stöckmann, "Probing decoherence through fano resonances," Phys. Rev. Lett. 105, 056801 (2010).
[CrossRef] [PubMed]

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

M. 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]

Bockelman, C. K.

R. K. Adair, C. K. Bockelman, and R. E. Peterson, "Experimental corroboration of the theory of neutron resonance scattering," Phys. Rev. 76, 308 (1949).
[CrossRef]

Brouwer, P. W.

A. A. Clerk, X. Waintal, and P. W. Brouwer, "Fano resonances as a probe of phase coherence in quantum dots," Phys. Rev. Lett. 86, 4636 (2001).
[CrossRef] [PubMed]

Burgdörfer, J.

A. Bärnthaler, S. Rotter, F. Libisch, J. Burgdörfer, S. Gehler, U. Kuhl, and H.-J. Stöckmann, "Probing decoherence through fano resonances," Phys. Rev. Lett. 105, 056801 (2010).
[CrossRef] [PubMed]

Busch, A.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, "Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice," Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Clerk, A. A.

A. A. Clerk, X. Waintal, and P. W. Brouwer, "Fano resonances as a probe of phase coherence in quantum dots," Phys. Rev. Lett. 86, 4636 (2001).
[CrossRef] [PubMed]

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]

de Dood, M. J. A.

M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, "Observation of coupling between surface plasmons in index-matched hole arrays," Phys. Rev. B 77, 115437 (2008).
[CrossRef]

E. F. C. Driessen, D. Stolwijk, and M. J. A. de Dood, "Asymmetry reversal in the reflection from a two-dimensional photonic crystal," Opt. Lett. 32, 3137 (2007).
[CrossRef] [PubMed]

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]

Driessen, E. F. C.

M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, "Observation of coupling between surface plasmons in index-matched hole arrays," Phys. Rev. B 77, 115437 (2008).
[CrossRef]

E. F. C. Driessen, D. Stolwijk, and M. J. A. de Dood, "Asymmetry reversal in the reflection from a two-dimensional photonic crystal," Opt. Lett. 32, 3137 (2007).
[CrossRef] [PubMed]

Fan, S.

S. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569 (2003).
[CrossRef]

S. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80, 908 (2002).
[CrossRef]

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

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Fano, U.

U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866 (1961).

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, "Fano resonances in nanoscale structures," Rev. Mod. Phys. 82, 2257 (2010).
[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, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, "Light scattering and fano resonances in high-q photonic crystal nanocavities," Appl. Phys. Lett. 94, 071101 (2009).
[CrossRef]

M. 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]

Gehler, S.

A. Bärnthaler, S. Rotter, F. Libisch, J. Burgdörfer, S. Gehler, U. Kuhl, and H.-J. Stöckmann, "Probing decoherence through fano resonances," Phys. Rev. Lett. 105, 056801 (2010).
[CrossRef] [PubMed]

Genet, C.

C. Genet, M. P. van Exter, and J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331 (2003).
[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]

Iye, Y.

K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, "Tuning of the fano effect through a quantum dot in an aharonov-bohm interferometer," Phys. Rev. Lett. 88, 256806 (2002).
[CrossRef] [PubMed]

Joannopoulos, J. D.

S. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569 (2003).
[CrossRef]

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

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Johnson, S. G.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Johnson, S. R.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, "Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice," Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Kanskar, M.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, "Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice," Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Katsumoto, S.

K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, "Tuning of the fano effect through a quantum dot in an aharonov-bohm interferometer," Phys. Rev. Lett. 88, 256806 (2002).
[CrossRef] [PubMed]

Kivshar, Y. S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, "Fano resonances in nanoscale structures," Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

Klaiman, S.

S. Klaiman, N. Moiseyev, and H. R. Sadeghpour, "Interpretation of the fano lineshape reversal in quantum waveguides," Phys. Rev. B 75, 113305 (2007).
[CrossRef]

Kobayashi, K.

K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, "Tuning of the fano effect through a quantum dot in an aharonov-bohm interferometer," Phys. Rev. Lett. 88, 256806 (2002).
[CrossRef] [PubMed]

Kolodziejski, L. A.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Krauss, T. F.

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

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]

Kuhl, U.

A. Bärnthaler, S. Rotter, F. Libisch, J. Burgdörfer, S. Gehler, U. Kuhl, and H.-J. Stöckmann, "Probing decoherence through fano resonances," Phys. Rev. Lett. 105, 056801 (2010).
[CrossRef] [PubMed]

Lewenkopf, C. H.

M. Mendoza, P. A. Schulz, R. O. Vallejos, and C. H. Lewenkopf, "Fano resonances in the conductance of quantum dots with mixed dynamics," Phys. Rev. B 77, 155307 (2008).
[CrossRef]

Libisch, F.

A. Bärnthaler, S. Rotter, F. Libisch, J. Burgdörfer, S. Gehler, U. Kuhl, and H.-J. Stöckmann, "Probing decoherence through fano resonances," Phys. Rev. Lett. 105, 056801 (2010).
[CrossRef] [PubMed]

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]

MacKenzie, J.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, "Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice," Appl. Phys. Lett. 70, 1438 (1997).
[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]

Mendoza, M.

M. Mendoza, P. A. Schulz, R. O. Vallejos, and C. H. Lewenkopf, "Fano resonances in the conductance of quantum dots with mixed dynamics," Phys. Rev. B 77, 155307 (2008).
[CrossRef]

Miroshnichenko, A. E.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, "Fano resonances in nanoscale structures," Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

Moiseyev, N.

S. Klaiman, N. Moiseyev, and H. R. Sadeghpour, "Interpretation of the fano lineshape reversal in quantum waveguides," Phys. Rev. B 75, 113305 (2007).
[CrossRef]

Morin, R.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, "Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice," Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

O’Faolain, L.

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

Pacradouni, V.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, "Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice," Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Paddon, P.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, "Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice," Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

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]

Peterson, R. E.

R. K. Adair, C. K. Bockelman, and R. E. Peterson, "Experimental corroboration of the theory of neutron resonance scattering," Phys. Rev. 76, 308 (1949).
[CrossRef]

Portalupi, S. L.

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

Rotter, S.

A. Bärnthaler, S. Rotter, F. Libisch, J. Burgdörfer, S. Gehler, U. Kuhl, and H.-J. Stöckmann, "Probing decoherence through fano resonances," Phys. Rev. Lett. 105, 056801 (2010).
[CrossRef] [PubMed]

Sadeghpour, H. R.

S. Klaiman, N. Moiseyev, and H. R. Sadeghpour, "Interpretation of the fano lineshape reversal in quantum waveguides," Phys. Rev. B 75, 113305 (2007).
[CrossRef]

Schulz, P. A.

M. Mendoza, P. A. Schulz, R. O. Vallejos, and C. H. Lewenkopf, "Fano resonances in the conductance of quantum dots with mixed dynamics," Phys. Rev. B 77, 155307 (2008).
[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]

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]

Stöckmann, H.-J.

A. Bärnthaler, S. Rotter, F. Libisch, J. Burgdörfer, S. Gehler, U. Kuhl, and H.-J. Stöckmann, "Probing decoherence through fano resonances," Phys. Rev. Lett. 105, 056801 (2010).
[CrossRef] [PubMed]

Stolwijk, D.

M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, "Observation of coupling between surface plasmons in index-matched hole arrays," Phys. Rev. B 77, 115437 (2008).
[CrossRef]

E. F. C. Driessen, D. Stolwijk, and M. J. A. de Dood, "Asymmetry reversal in the reflection from a two-dimensional photonic crystal," Opt. Lett. 32, 3137 (2007).
[CrossRef] [PubMed]

Suh, W.

S. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569 (2003).
[CrossRef]

Tiedje, T.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, "Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice," Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Vallejos, R. O.

M. Mendoza, P. A. Schulz, R. O. Vallejos, and C. H. Lewenkopf, "Fano resonances in the conductance of quantum dots with mixed dynamics," Phys. Rev. B 77, 155307 (2008).
[CrossRef]

van Exter, M. P.

M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, "Observation of coupling between surface plasmons in index-matched hole arrays," Phys. Rev. B 77, 115437 (2008).
[CrossRef]

C. Genet, M. P. van Exter, and J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331 (2003).
[CrossRef]

Villeneuve, P. R.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Waintal, X.

A. A. Clerk, X. Waintal, and P. W. Brouwer, "Fano resonances as a probe of phase coherence in quantum dots," Phys. Rev. Lett. 86, 4636 (2001).
[CrossRef] [PubMed]

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]

Woerdman, J. P.

C. Genet, M. P. van Exter, and J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331 (2003).
[CrossRef]

Young, J. F.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, "Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice," Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Appl. Phys. Lett. (3)

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, "Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice," Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

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

S. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80, 908 (2002).
[CrossRef]

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

S. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569 (2003).
[CrossRef]

Opt. Commun. (1)

C. Genet, M. P. van Exter, and J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331 (2003).
[CrossRef]

Opt. Lett. (1)

E. F. C. Driessen, D. Stolwijk, and M. J. A. de Dood, "Asymmetry reversal in the reflection from a two-dimensional photonic crystal," Opt. Lett. 32, 3137 (2007).
[CrossRef] [PubMed]

Phys. Rev. (2)

U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866 (1961).

R. K. Adair, C. K. Bockelman, and R. E. Peterson, "Experimental corroboration of the theory of neutron resonance scattering," Phys. Rev. 76, 308 (1949).
[CrossRef]

Phys. Rev. B (7)

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]

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]

M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, "Observation of coupling between surface plasmons in index-matched hole arrays," Phys. Rev. B 77, 115437 (2008).
[CrossRef]

S. Klaiman, N. Moiseyev, and H. R. Sadeghpour, "Interpretation of the fano lineshape reversal in quantum waveguides," Phys. Rev. B 75, 113305 (2007).
[CrossRef]

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

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751 (1999).
[CrossRef]

M. Mendoza, P. A. Schulz, R. O. Vallejos, and C. H. Lewenkopf, "Fano resonances in the conductance of quantum dots with mixed dynamics," Phys. Rev. B 77, 155307 (2008).
[CrossRef]

Phys. Rev. Lett. (3)

A. Bärnthaler, S. Rotter, F. Libisch, J. Burgdörfer, S. Gehler, U. Kuhl, and H.-J. Stöckmann, "Probing decoherence through fano resonances," Phys. Rev. Lett. 105, 056801 (2010).
[CrossRef] [PubMed]

A. A. Clerk, X. Waintal, and P. W. Brouwer, "Fano resonances as a probe of phase coherence in quantum dots," Phys. Rev. Lett. 86, 4636 (2001).
[CrossRef] [PubMed]

K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, "Tuning of the fano effect through a quantum dot in an aharonov-bohm interferometer," Phys. Rev. Lett. 88, 256806 (2002).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, "Fano resonances in nanoscale structures," Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

Other (7)

Philips MiPlaza - Cedova, http://www.cedova.com.

Z EON corporation, http://www.zeon.co.jp.

Gel-Pak, http://www.gelpak.com.

Lj. Babić, R. Leijssen, E. Driessen and M. J. A. de Dood, in preparation.

M. Born, and E. Wolf, Principles of Optics (Pergamon Press, 1980), 6th ed.

H. A. Haus, Waves and fields in optoelectronics (Prentice-Hall, New Jersey, 1984).

E. Flück, "Local interaction of light with periodic photonic structures," Ph.D. thesis, University of Twente (2003).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

(color) Measured (blue symbols) and calculated (solid gray lines) reflection spectra for different angles of incidence for a symmetric slab, showing the asymmetry reversal of the p-polarized (−1,±1) mode at Brewster’s angle. The dashed red lines are fits to the data using the Fano model described in the text.

Fig. 2
Fig. 2

(color) Measured (blue symbols) and calculated (solid gray lines) reflection spectra for different angles of incidence for an asymmetric slab, showing the asymmetry flip of the p-polarized (−1,±1) mode. The dashed red lines are fits to the data using the Fano model described in the text.

Fig. 3
Fig. 3

(color) Calculated phase difference between the direct and the resonant contribution for a slab with an effective refractive index of 10, representative for AlGaAs used in the experiment. The plot shows the phase difference as a function of angle of incidence and dimensionless quantity neffd/λ for a symmetric membrane structure (a) and an asymmetric structure on a gel substrate with n3 = 1.4 (b). The solid and dashed lines are explained in the text. The corresponding asymmetry parameter q of the Fano resonance as a function of angle is shown for the symmetric (c) and asymmetric structure (d) for a value of neff d/λ = 0.3. The solid line refers to the real part of q, while the dash-dot line shows the imaginary part of q for the asymmetric structure.

Fig. 4
Fig. 4

(color) Calculated reflection spectra for a symmetric structure (solid lines), for angles of incidence from 68° to 76° in steps of 2°, vertically offset by 0.8 for clarity, showing the asymmetry reversal of the p-polarized (−1,±1) mode. Note that the zero in the amplitude reflection coefficient is indicated by the dash-dot lines, for each reflectivity spectrum. The dashed lines show the fit of the Fano model to the calculated data.

Fig. 5
Fig. 5

Calculated phase difference between the resonant and the non-resonant contribution, as a function of the angle of incidence, for a symmetric structure (solid line). The phase difference is obtained for the p-polarized (−1,±1) mode at the resonance frequency, by fitting a Fano model to the calculated reflection spectra. The asymmetry reversal of the Fano lineshape (Δξ = 0) occurs at Brewster’s angle. The dashed line represents the phase difference calculated using a coupled-mode theory with only two modes, as described in the text. The inset shows the calculated dispersion relation of the leaky mode (solid line), and the folded light line in air (dashed line).

Fig. 6
Fig. 6

(color) Calculated reflection spectra for an asymmetric structure (solid lines), for angles of incidence from 72° to 80° in steps of 2°, vertically offset by 0.2 for clarity, showing the asymmetry reversal of the p-polarized (−1,±1) mode. Note that the zero in the amplitude reflection coefficient is indicated by the dash-dot lines, for each reflectivity spectrum. Dashed lines show the fit of the Fano model to the calculated data.

Fig. 7
Fig. 7

Calculated phase difference between the resonant and the non-resonant contribution, as a function of the angle of incidence, for an asymmetric structure (solid line). The phase difference is obtained for the p-polarized (−1,±1) mode at the resonance frequency, by fitting a Fano model to the calculated reflection spectra. The asymmetry reversal of the Fano lineshape (Δξ = 0) occurs beyond Brewster’s angle for the symmetric structure. The dashed line represents the phase difference calculated using a coupled-mode theory with only two modes, as described in the text. The inset shows the calculated dispersion relation of the leaky mode (solid line), and the folded light lines in both air (dashed line) and gel (dash-dot lines).

Tables (1)

Tables Icon

Table 1 Fitted values of the center frequency, linewidth and phase difference between the resonant and the direct contribution in the reflectivity. Results are given for both measured and calculated spectra, for various angles of incidence for a symmetric slab (top) and an asymmetric slab on a substrate (bottom)

Equations (16)

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

R ( ω ) = | r D exp ( i Δ ξ ) + r R Γ 0 i ( ω ω 0 ) + Γ 0 | 2 .
r D ( ω ) = | r 0 + r 1 ω + r 2 ω 2 | ,
b ± , i = 1 2 k i z k 0 E ± , i ,
b = S b + .
S S = I , S i j = S j i .
S = C + p = 1 N d p d p i ( ω ω p ) + Γ p .
S = ( r t t r ) + Γ 0 i ( ω ω 0 ) + Γ 0 ( ( r ± t ) ( r ± t ) ( r ± t ) ( r ± t ) ) ,
R ( ɛ ) = | S 11 ( ɛ ) | 2 = | r | 2 | q + ɛ | 2 1 + ɛ 2 .
q = ± i t r .
r = r 12 + r 23 exp [ i 2 k 2 z d ] 1 r 21 r 23 exp [ i 2 k 2 z d ] exp [ i 2 k 1 z d ]
t = t 23 t 12 exp [ i ( 2 k 2 z k 1 z k 3 z ) d / 2 ] 1 r 21 r 23 exp [ i 2 k 2 z d ] .
R = | r | 2 = r 12 2 + r 23 2 + 2 r 12 r 23 cos 2 β 1 + r 12 2 r 23 2 + 2 r 12 r 23 cos 2 β ,
cos 2 β = ± 1 .
r 12 = ± r 23 .
| k s | = n s ω 0 > | k || + G | ,
n 2 = 3.118 0.014 ω + 0.029 ω 2 .

Metrics