Abstract

A finite two-dimensional photonic crystal with a triangular lattice of air columns in a dielectric background is designed with a waveguide and a resonant cavity. By a time-domain solution of Maxwell’s equations we observe the existence of impurity modes inside the photonic bandgap. An electromagnetic wave launched through the waveguide, with an appropriate frequency, can enhance the field inside the cavity and yield a peak in the transmission. Considering a manufactured structure, in which the columns are not perfectly equal, we repeat our calculations and analyze how the impurity modes are modified. For both cases, periodic and real, we measure the quality factor of the cavity.

© 2000 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  17. D. Labilloy, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional pho-tonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
    [CrossRef]
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  23. The four digits diameters’ values, shown in Fig. 2, are determined by the Halle group from the analysis of the SEM picture. Because of the fluctuations along the pores and the method used to obtain the diameters, only the first three digits are reliable. However, the fourth digit does not significantly affect the results and can be neglected in the calculations.
  24. When the source is suddenly switched off, all frequencies are introduced. However, they rapidly fade away, and the frequency of the cavity mode is the only one surviving.

1999

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional pho-tonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
[CrossRef]

1998

A. Birner, U. Grüning, S. Ottow, A. Schneider, F. Müller, V. Lehmann, H. Föll, and U. Gösele, “Macroporous silicon: a two-dimensional photonic bandgap material suitable for the near-infrared spectral range,” Phys. Status Solidi A 165, 111–117 (1998).
[CrossRef]

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

B. D’Urso, O. Painter, J. O’Brien, T. Tombrello, A. Yariv, and A. Scherer, “Modal reflectivity in finite-depth two-dimensional photonic-crystal microcavities,” J. Opt. Soc. Am. B 15, 1155–1159 (1998).
[CrossRef]

1997

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

1996

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–701 (1996).
[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

1994

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[CrossRef]

1987

E. Yablonovich, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

1984

Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sinica A 27, 1063–1076 (1984).

1966

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic me-dia,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

Alerhand, O. L.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[CrossRef]

Bardinal, V.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Benisty, H.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional pho-tonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Birner, A.

A. Birner, U. Grüning, S. Ottow, A. Schneider, F. Müller, V. Lehmann, H. Föll, and U. Gösele, “Macroporous silicon: a two-dimensional photonic bandgap material suitable for the near-infrared spectral range,” Phys. Status Solidi A 165, 111–117 (1998).
[CrossRef]

Brand, S.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–701 (1996).
[CrossRef]

Cassagne, D.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Chow, E.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

D’Urso, B.

De La Rue, R. M.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–701 (1996).
[CrossRef]

Devenyi, A.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[CrossRef]

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Ferrera, J.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Föll, H.

A. Birner, U. Grüning, S. Ottow, A. Schneider, F. Müller, V. Lehmann, H. Föll, and U. Gösele, “Macroporous silicon: a two-dimensional photonic bandgap material suitable for the near-infrared spectral range,” Phys. Status Solidi A 165, 111–117 (1998).
[CrossRef]

Foresi, J. S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Gösele, U.

A. Birner, U. Grüning, S. Ottow, A. Schneider, F. Müller, V. Lehmann, H. Föll, and U. Gösele, “Macroporous silicon: a two-dimensional photonic bandgap material suitable for the near-infrared spectral range,” Phys. Status Solidi A 165, 111–117 (1998).
[CrossRef]

Grüning, U.

A. Birner, U. Grüning, S. Ottow, A. Schneider, F. Müller, V. Lehmann, H. Föll, and U. Gösele, “Macroporous silicon: a two-dimensional photonic bandgap material suitable for the near-infrared spectral range,” Phys. Status Solidi A 165, 111–117 (1998).
[CrossRef]

Hietala, V.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

Houdré, R.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional pho-tonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Ippen, E. P.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Joannopoulos, J. D.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[CrossRef]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

Jouanin, C.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Kash, K.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[CrossRef]

Kimerling, L. C.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Krauss, T. F.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional pho-tonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–701 (1996).
[CrossRef]

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Labilloy, D.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional pho-tonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Lehmann, V.

A. Birner, U. Grüning, S. Ottow, A. Schneider, F. Müller, V. Lehmann, H. Föll, and U. Gösele, “Macroporous silicon: a two-dimensional photonic bandgap material suitable for the near-infrared spectral range,” Phys. Status Solidi A 165, 111–117 (1998).
[CrossRef]

Liao, Z. P.

Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sinica A 27, 1063–1076 (1984).

Lin, S.-Y.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

Meade, R. D.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[CrossRef]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Müller, F.

A. Birner, U. Grüning, S. Ottow, A. Schneider, F. Müller, V. Lehmann, H. Föll, and U. Gösele, “Macroporous silicon: a two-dimensional photonic bandgap material suitable for the near-infrared spectral range,” Phys. Status Solidi A 165, 111–117 (1998).
[CrossRef]

O’Brien, J.

Oesterle, U.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional pho-tonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Ottow, S.

A. Birner, U. Grüning, S. Ottow, A. Schneider, F. Müller, V. Lehmann, H. Föll, and U. Gösele, “Macroporous silicon: a two-dimensional photonic bandgap material suitable for the near-infrared spectral range,” Phys. Status Solidi A 165, 111–117 (1998).
[CrossRef]

Painter, O.

Rattier, M.

Scherer, A.

Schneider, A.

A. Birner, U. Grüning, S. Ottow, A. Schneider, F. Müller, V. Lehmann, H. Föll, and U. Gösele, “Macroporous silicon: a two-dimensional photonic bandgap material suitable for the near-infrared spectral range,” Phys. Status Solidi A 165, 111–117 (1998).
[CrossRef]

Smith, C. J. M.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional pho-tonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
[CrossRef]

Smith, D. A.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[CrossRef]

Smith, H. I.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Steinmeyer, G.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Thoen, E. R.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Tombrello, T.

Villeneuve, P. R.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Weisbuch, C.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional pho-tonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Wong, H. L.

Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sinica A 27, 1063–1076 (1984).

Yablonovich, E.

E. Yablonovich, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

Yang, B. P.

Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sinica A 27, 1063–1076 (1984).

Yariv, A.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic me-dia,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

Yuan, Y. F.

Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sinica A 27, 1063–1076 (1984).

IEEE Trans. Antennas Propag.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic me-dia,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

J. Appl. Phys.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Nature

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–701 (1996).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Phys. Rev. B

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional pho-tonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
[CrossRef]

Phys. Rev. Lett.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

E. Yablonovich, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

Phys. Status Solidi A

A. Birner, U. Grüning, S. Ottow, A. Schneider, F. Müller, V. Lehmann, H. Föll, and U. Gösele, “Macroporous silicon: a two-dimensional photonic bandgap material suitable for the near-infrared spectral range,” Phys. Status Solidi A 165, 111–117 (1998).
[CrossRef]

Sci. Sinica A

Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sinica A 27, 1063–1076 (1984).

Science

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

Other

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C. M. Soukoulis, ed., Photonic Band Gaps Materials, Vol. 315 of NATO ASI Ser., Ser. E Applied Sciences (Kluwer Academic, Dortrecht, The Netherlands, 1996).

C. Weisbuch and J. Rarity, eds., Microcavities and Photonic Band Gaps: Physics and Applications, Vol. 324 of NATO ASI Ser., Ser. E Applied Sciences (Kluwer Academic, Dortrecht, The Netherlands, 1996).

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The four digits diameters’ values, shown in Fig. 2, are determined by the Halle group from the analysis of the SEM picture. Because of the fluctuations along the pores and the method used to obtain the diameters, only the first three digits are reliable. However, the fourth digit does not significantly affect the results and can be neglected in the calculations.

When the source is suddenly switched off, all frequencies are introduced. However, they rapidly fade away, and the frequency of the cavity mode is the only one surviving.

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Figures (6)

Fig. 1
Fig. 1

Two-dimensional photonic crystal with a triangular lattice. The missing columns yield a waveguide and a resonant cavity in the middle. There are 18×11 unit cells with lattice constant a=1.5 µm; air columns have diameter d=1.28 µm. The dielectric background is silicon, d=11.9. The source is put at the left side of the structure, in front of the WG.

Fig. 2
Fig. 2

SEM picture of the sample manufactured at Halle. The numbers inside the holes represent the real diameter in micrometers. The average diameter of the marked holes is dav=1.23 µm. For the other holes we chose d=1.28 µm, as it is in the ideal structure. The depth of column etching is 100 µm.

Fig. 3
Fig. 3

Transmission for λ between 3.0 and 6.0 µm. The solid (dashed) curve refers to the ideal (real) structure. Each impurity mode is marked with an italic (Greek) letter for the ideal (real) case. The corresponding wavelengths are a (3.564 µm), b (3.830 µm), c (4.074 µm), d (5.147 µm), α (3.585 µm), β (3.848 µm), γ (4.095 µm), and δ (5.198 µm).

Fig. 4
Fig. 4

Normalized amplitude of the electric field for the impurity modes of the ideal structure: (a) hexapole λ=3.564 µm, (b) monopole λ=3.830 µm, (c) decapole λ=4.074 µm, and (d) so-called pentapole λ=5.147 µm.

Fig. 5
Fig. 5

Normalized amplitude of the electric field for the impurity modes of the real structure: (α) hexapole λ=3.585 µm, (β) monopole λ=3.848 µm, (γ) decapole λ=4.095 µm, and (δ) pentapole λ=5.198 µm.

Fig. 6
Fig. 6

Normalized amplitude of the electric field for the modes (d) λ=5.147 µm (top panel) and (δ) λ=5.198 µm (bottom panel). The snapshots, which are contour plots in log scale, cover the whole structure.

Tables (1)

Tables Icon

Table 1 Quality Factor for the Impurity Modes

Equations (3)

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

t H(r, t)=-×E(r, t),
(r)t E(r, t)=×H(r, t),
dEdt=-2πcλ0QE,

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