Abstract

The effect of having a finite number of layers on the design of omnidirectional reflectors was investigated. It was shown that the structure should be finished with a low-index layer having a thickness larger than a quarter-wave to increase reflectivity, whereas layers below may remain of quarter-wave optical thickness at normal incidence angle. This general trend has been used for designing and realizing two a-Si–SiO2 (amorphous silicon and silicon dioxide) omnidirectional reflectors in the near-infrared range on a silicon and a silica substrate, respectively. Owing to the decrease of absorption of recrystallized silicon as compared with a-Si in the visible range, the transmissivity of the structure realized on silica substrate was dramatically increased in the visible range upon annealing, whereas the high reflectivity and the omnidirectional effect were maintained in the near-infrared range.

© 2001 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. D. Labilloy, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional photonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
    [CrossRef]
  4. S. Kawakami, “Fabrication of submicrometer 3D periodic structures composed of Si/SiO2,” Electron. Lett. 33, 1260–1261 (1997).
    [CrossRef]
  5. Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
    [CrossRef] [PubMed]
  6. D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
    [CrossRef]
  7. K. M. Chen, A. W. Sparks, S.-C. Luan, D. R. Lim, K. Wada, L. C. Kimerling, “SiO2/TiO2 omnidirectional reflector and microcavity resonator via the sol-gel method,” Appl. Phys. Lett. 75, 3805–3807 (1999).
    [CrossRef]
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    [CrossRef]
  9. D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, S. V. Gaponenko, “All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control,” J. Lightwave Technol. 17, 2018–2024 (1999).
    [CrossRef]
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    [CrossRef]
  11. D. C. Diaz, C. L. Schow, J. Qi, J. C. Campbell, J. C. Bean, L. J. Peticolas, “Si/SiO2 resonant cavity detector,” Appl. Phys. Lett. 69, 2798–2800 (1996).
    [CrossRef]
  12. F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés,” Ann. Phys. (Paris) 5, 596–640 and 706–784 (1950).
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    [CrossRef] [PubMed]
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    [CrossRef]
  16. W. Fukato, K. Yoshino, C. M. Fortmann, I. Shimizu, “Wide band gap amorphous silicon thin films prepared by chemical annealing,” J. Appl. Phys. 85, 812–818 (1999).
    [CrossRef]
  17. D. Souche, A. Brunet-Bruneau, S. Fisson, V. Nguyen Van, G. Vuye, F. Abelès, J. Rivory, “Visible and infrared ellipsometry study of ion assisted SiO2 films,” Thin Solid Films 313–314, 676–681 (1998).

1999 (6)

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

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
[CrossRef]

K. M. Chen, A. W. Sparks, S.-C. Luan, D. R. Lim, K. Wada, L. C. Kimerling, “SiO2/TiO2 omnidirectional reflector and microcavity resonator via the sol-gel method,” Appl. Phys. Lett. 75, 3805–3807 (1999).
[CrossRef]

W. H. Southwell, “Omnidirectional mirror design with quarter-wave dielectric stacks,” Appl. Opt. 38, 5464–5467 (1999).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, S. V. Gaponenko, “All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control,” J. Lightwave Technol. 17, 2018–2024 (1999).
[CrossRef]

W. Fukato, K. Yoshino, C. M. Fortmann, I. Shimizu, “Wide band gap amorphous silicon thin films prepared by chemical annealing,” J. Appl. Phys. 85, 812–818 (1999).
[CrossRef]

1998 (2)

D. Souche, A. Brunet-Bruneau, S. Fisson, V. Nguyen Van, G. Vuye, F. Abelès, J. Rivory, “Visible and infrared ellipsometry study of ion assisted SiO2 films,” Thin Solid Films 313–314, 676–681 (1998).

Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

1997 (2)

1996 (2)

Y. Ishikawa, N. Shibata, S. Fukatsu, “Epitaxy-ready Si/SiO2 Bragg reflectors by multiple separation-by-implantation oxygen,” Appl. Phys. Lett. 69, 3881–3883 (1996).
[CrossRef]

D. C. Diaz, C. L. Schow, J. Qi, J. C. Campbell, J. C. Bean, L. J. Peticolas, “Si/SiO2 resonant cavity detector,” Appl. Phys. Lett. 69, 2798–2800 (1996).
[CrossRef]

1987 (1)

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

1986 (1)

A. R. Forouhi, I. Bloomer, “Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,” Phys. Rev. B 34, 7018–7026 (1986).
[CrossRef]

1966 (1)

1950 (1)

F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés,” Ann. Phys. (Paris) 5, 596–640 and 706–784 (1950).

Abelès, F.

D. Souche, A. Brunet-Bruneau, S. Fisson, V. Nguyen Van, G. Vuye, F. Abelès, J. Rivory, “Visible and infrared ellipsometry study of ion assisted SiO2 films,” Thin Solid Films 313–314, 676–681 (1998).

F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés,” Ann. Phys. (Paris) 5, 596–640 and 706–784 (1950).

Bean, J. C.

D. C. Diaz, C. L. Schow, J. Qi, J. C. Campbell, J. C. Bean, L. J. Peticolas, “Si/SiO2 resonant cavity detector,” Appl. Phys. Lett. 69, 2798–2800 (1996).
[CrossRef]

Benisty, H.

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

Bloomer, I.

A. R. Forouhi, I. Bloomer, “Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,” Phys. Rev. B 34, 7018–7026 (1986).
[CrossRef]

Brunet-Bruneau, A.

D. Souche, A. Brunet-Bruneau, S. Fisson, V. Nguyen Van, G. Vuye, F. Abelès, J. Rivory, “Visible and infrared ellipsometry study of ion assisted SiO2 films,” Thin Solid Films 313–314, 676–681 (1998).

Campbell, J. C.

D. C. Diaz, C. L. Schow, J. Qi, J. C. Campbell, J. C. Bean, L. J. Peticolas, “Si/SiO2 resonant cavity detector,” Appl. Phys. Lett. 69, 2798–2800 (1996).
[CrossRef]

Chen, K. M.

K. M. Chen, A. W. Sparks, S.-C. Luan, D. R. Lim, K. Wada, L. C. Kimerling, “SiO2/TiO2 omnidirectional reflector and microcavity resonator via the sol-gel method,” Appl. Phys. Lett. 75, 3805–3807 (1999).
[CrossRef]

Chigrin, D. N.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, S. V. Gaponenko, “All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control,” J. Lightwave Technol. 17, 2018–2024 (1999).
[CrossRef]

Chiping, C.

Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Diaz, D. C.

D. C. Diaz, C. L. Schow, J. Qi, J. C. Campbell, J. C. Bean, L. J. Peticolas, “Si/SiO2 resonant cavity detector,” Appl. Phys. Lett. 69, 2798–2800 (1996).
[CrossRef]

Dobrowolski, J. A.

Fink, Y.

Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Fisson, S.

D. Souche, A. Brunet-Bruneau, S. Fisson, V. Nguyen Van, G. Vuye, F. Abelès, J. Rivory, “Visible and infrared ellipsometry study of ion assisted SiO2 films,” Thin Solid Films 313–314, 676–681 (1998).

Forouhi, A. R.

A. R. Forouhi, I. Bloomer, “Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,” Phys. Rev. B 34, 7018–7026 (1986).
[CrossRef]

Fortmann, C. M.

W. Fukato, K. Yoshino, C. M. Fortmann, I. Shimizu, “Wide band gap amorphous silicon thin films prepared by chemical annealing,” J. Appl. Phys. 85, 812–818 (1999).
[CrossRef]

Fukato, W.

W. Fukato, K. Yoshino, C. M. Fortmann, I. Shimizu, “Wide band gap amorphous silicon thin films prepared by chemical annealing,” J. Appl. Phys. 85, 812–818 (1999).
[CrossRef]

Fukatsu, S.

Y. Ishikawa, N. Shibata, S. Fukatsu, “Epitaxy-ready Si/SiO2 Bragg reflectors by multiple separation-by-implantation oxygen,” Appl. Phys. Lett. 69, 3881–3883 (1996).
[CrossRef]

Gaponenko, S. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, S. V. Gaponenko, “All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control,” J. Lightwave Technol. 17, 2018–2024 (1999).
[CrossRef]

Heavens, O. S.

Houdré, R.

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

Ishikawa, Y.

Y. Ishikawa, N. Shibata, S. Fukatsu, “Epitaxy-ready Si/SiO2 Bragg reflectors by multiple separation-by-implantation oxygen,” Appl. Phys. Lett. 69, 3881–3883 (1996).
[CrossRef]

Joannopoulos, J. D.

Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Kawakami, S.

S. Kawakami, “Fabrication of submicrometer 3D periodic structures composed of Si/SiO2,” Electron. Lett. 33, 1260–1261 (1997).
[CrossRef]

Kimerling, L. C.

K. M. Chen, A. W. Sparks, S.-C. Luan, D. R. Lim, K. Wada, L. C. Kimerling, “SiO2/TiO2 omnidirectional reflector and microcavity resonator via the sol-gel method,” Appl. Phys. Lett. 75, 3805–3807 (1999).
[CrossRef]

Krauss, T. F.

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

Labilloy, D.

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

Lavrinenko, A. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, S. V. Gaponenko, “All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control,” J. Lightwave Technol. 17, 2018–2024 (1999).
[CrossRef]

Liddell, H. M.

Lim, D. R.

K. M. Chen, A. W. Sparks, S.-C. Luan, D. R. Lim, K. Wada, L. C. Kimerling, “SiO2/TiO2 omnidirectional reflector and microcavity resonator via the sol-gel method,” Appl. Phys. Lett. 75, 3805–3807 (1999).
[CrossRef]

Luan, S.-C.

K. M. Chen, A. W. Sparks, S.-C. Luan, D. R. Lim, K. Wada, L. C. Kimerling, “SiO2/TiO2 omnidirectional reflector and microcavity resonator via the sol-gel method,” Appl. Phys. Lett. 75, 3805–3807 (1999).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Hilger, Bristol, UK, 1986), pp. 139–142 and 247–249.

Michel, J.

Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Nguyen Van, V.

D. Souche, A. Brunet-Bruneau, S. Fisson, V. Nguyen Van, G. Vuye, F. Abelès, J. Rivory, “Visible and infrared ellipsometry study of ion assisted SiO2 films,” Thin Solid Films 313–314, 676–681 (1998).

Oesterle, U.

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

Peticolas, L. J.

D. C. Diaz, C. L. Schow, J. Qi, J. C. Campbell, J. C. Bean, L. J. Peticolas, “Si/SiO2 resonant cavity detector,” Appl. Phys. Lett. 69, 2798–2800 (1996).
[CrossRef]

Popov, K. V.

Qi, J.

D. C. Diaz, C. L. Schow, J. Qi, J. C. Campbell, J. C. Bean, L. J. Peticolas, “Si/SiO2 resonant cavity detector,” Appl. Phys. Lett. 69, 2798–2800 (1996).
[CrossRef]

Rivory, J.

D. Souche, A. Brunet-Bruneau, S. Fisson, V. Nguyen Van, G. Vuye, F. Abelès, J. Rivory, “Visible and infrared ellipsometry study of ion assisted SiO2 films,” Thin Solid Films 313–314, 676–681 (1998).

Schow, C. L.

D. C. Diaz, C. L. Schow, J. Qi, J. C. Campbell, J. C. Bean, L. J. Peticolas, “Si/SiO2 resonant cavity detector,” Appl. Phys. Lett. 69, 2798–2800 (1996).
[CrossRef]

Shanhui, F.

Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Shibata, N.

Y. Ishikawa, N. Shibata, S. Fukatsu, “Epitaxy-ready Si/SiO2 Bragg reflectors by multiple separation-by-implantation oxygen,” Appl. Phys. Lett. 69, 3881–3883 (1996).
[CrossRef]

Shimizu, I.

W. Fukato, K. Yoshino, C. M. Fortmann, I. Shimizu, “Wide band gap amorphous silicon thin films prepared by chemical annealing,” J. Appl. Phys. 85, 812–818 (1999).
[CrossRef]

Smith, C. J. M.

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

Souche, D.

D. Souche, A. Brunet-Bruneau, S. Fisson, V. Nguyen Van, G. Vuye, F. Abelès, J. Rivory, “Visible and infrared ellipsometry study of ion assisted SiO2 films,” Thin Solid Films 313–314, 676–681 (1998).

Southwell, W. H.

Sparks, A. W.

K. M. Chen, A. W. Sparks, S.-C. Luan, D. R. Lim, K. Wada, L. C. Kimerling, “SiO2/TiO2 omnidirectional reflector and microcavity resonator via the sol-gel method,” Appl. Phys. Lett. 75, 3805–3807 (1999).
[CrossRef]

Sullivan, B. T.

Thomas, E. L.

Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Tikhonravov, A. V.

Vuye, G.

D. Souche, A. Brunet-Bruneau, S. Fisson, V. Nguyen Van, G. Vuye, F. Abelès, J. Rivory, “Visible and infrared ellipsometry study of ion assisted SiO2 films,” Thin Solid Films 313–314, 676–681 (1998).

Wada, K.

K. M. Chen, A. W. Sparks, S.-C. Luan, D. R. Lim, K. Wada, L. C. Kimerling, “SiO2/TiO2 omnidirectional reflector and microcavity resonator via the sol-gel method,” Appl. Phys. Lett. 75, 3805–3807 (1999).
[CrossRef]

Weisbuch, C.

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

Winn, J. N.

Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Yablonovitch, E.

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

Yarotsky, D. A.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, S. V. Gaponenko, “All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control,” J. Lightwave Technol. 17, 2018–2024 (1999).
[CrossRef]

Yoshino, K.

W. Fukato, K. Yoshino, C. M. Fortmann, I. Shimizu, “Wide band gap amorphous silicon thin films prepared by chemical annealing,” J. Appl. Phys. 85, 812–818 (1999).
[CrossRef]

Ann. Phys. (Paris) (1)

F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés,” Ann. Phys. (Paris) 5, 596–640 and 706–784 (1950).

Appl. Opt. (3)

Appl. Phys. A (1)

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
[CrossRef]

Appl. Phys. Lett. (3)

K. M. Chen, A. W. Sparks, S.-C. Luan, D. R. Lim, K. Wada, L. C. Kimerling, “SiO2/TiO2 omnidirectional reflector and microcavity resonator via the sol-gel method,” Appl. Phys. Lett. 75, 3805–3807 (1999).
[CrossRef]

Y. Ishikawa, N. Shibata, S. Fukatsu, “Epitaxy-ready Si/SiO2 Bragg reflectors by multiple separation-by-implantation oxygen,” Appl. Phys. Lett. 69, 3881–3883 (1996).
[CrossRef]

D. C. Diaz, C. L. Schow, J. Qi, J. C. Campbell, J. C. Bean, L. J. Peticolas, “Si/SiO2 resonant cavity detector,” Appl. Phys. Lett. 69, 2798–2800 (1996).
[CrossRef]

Electron. Lett. (1)

S. Kawakami, “Fabrication of submicrometer 3D periodic structures composed of Si/SiO2,” Electron. Lett. 33, 1260–1261 (1997).
[CrossRef]

J. Appl. Phys. (1)

W. Fukato, K. Yoshino, C. M. Fortmann, I. Shimizu, “Wide band gap amorphous silicon thin films prepared by chemical annealing,” J. Appl. Phys. 85, 812–818 (1999).
[CrossRef]

J. Lightwave Technol. (1)

Phys. Rev. B (2)

A. R. Forouhi, I. Bloomer, “Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,” Phys. Rev. B 34, 7018–7026 (1986).
[CrossRef]

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

Phys. Rev. Lett. (1)

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

Science (1)

Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Thin Solid Films (1)

D. Souche, A. Brunet-Bruneau, S. Fisson, V. Nguyen Van, G. Vuye, F. Abelès, J. Rivory, “Visible and infrared ellipsometry study of ion assisted SiO2 films,” Thin Solid Films 313–314, 676–681 (1998).

Other (1)

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Hilger, Bristol, UK, 1986), pp. 139–142 and 247–249.

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Figures (8)

Fig. 1
Fig. 1

Comparison between analytically (squares) and numerically (curves) calculated values of the admittance Y at 1200 nm versus incidence angle for (a) Si–LH–air and (b) Si–LHL–air structures with L = SiO2 and H = a-Si. The analytic values were determined assuming that the phase difference from π/2 arising from the nonnormal incidence angle was small [Eqs. (1) and (2)].

Fig. 2
Fig. 2

Calculated reflectivity in p polarization at 1200 nm versus incidence angle for (1) Si–(LH)L–air (open squares and dotted curve), (2) Si–(LH)2–air (filled squares and line solid curve), and (3) Si–(LH)2 L–air (diamonds and dashed curve) with L = SiO2 and H = a-Si. Curves, results of numerical simulations; symbols, results from analytical calculations. Surprisingly, the design with a whole number of layers (2) yields the lowest reflectivity.

Fig. 3
Fig. 3

Ex situ refractive index and extinction coefficient of evaporated a-Si as determined by ellipsometry in the 300–1700-nm range.

Fig. 4
Fig. 4

Indices of evaporated SiO2 as determined by fitting ellipsometry in the 300–1700-nm range with a Sellmeier model before (solid curve) and after venting or annealing (dotted curve). The extinction coefficient is equal to zero and is not presented.

Fig. 5
Fig. 5

Ellipsometric measurements (symbols) at 75° in the 300–1700-nm range of the seven-layer structure evaporated on Si substrate. The fit to the measured values of tan(Ψ) and cos(Δ) (dotted curve) was performed by means of varying only the thickness of each layer. It should be noted that the unity value of tan(Ψ) near 1200 nm also confirm that at 75° p and s reflections are of the same order of magnitude.

Fig. 6
Fig. 6

Reflectivity measurements in p polarization (filled diamonds) versus the wavelength near 1200 nm of the structure evaporated on Si substrate. The incidence angle varies between 0° and 70° according to the arrow. Simulations using the thicknesses determined by ellipsometry is also presented (curves). Reflectivity measurements at 1200 nm in p (filled diamonds) and s polarization (open diamonds) versus the incidence angle are shown in the inset.

Fig. 7
Fig. 7

p-polarization reflectivity measurements (diamonds) and simulations (curves) versus wavelength between 800 and 1700 nm for the SiO2–(HL)3–air structure after annealing. The incidence angle varies between 0° and 70° according to the arrow.

Fig. 8
Fig. 8

Simulated transmission at normal incidence before annealing (solid curve) and measured (diamonds) and simulated (dotted curve) transmission values after annealing versus wavelength. A strong increase of transmission is observed after annealing in the visible range, whereas transmission remains low in the near-infrared range. A shift in the position of the minimum value of transmission near 1000 nm is observed. The shift is due to both Si index reduction and thickness variation of the layers upon annealing.

Tables (3)

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Table 1 Calculated Thicknesses of the Final Layer to Improve Reflectivity on Si Substratea

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Table 2 Optimization Results with All Possible Incidence Angles Accounted fora

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Table 3 Thickness Targeted and Deduced from ex situ Ellipsometry Measurements before and after Annealing for Omnidirectional Reflectors on Si and on SiO2 Substrates

Equations (3)

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ReY=ηsubηHηL2PηH2-ηL22ηLηH2P+ηHηLHηH+LηLLηH+HηLηH2-ηL22ηLηH2P+ηsub2HηH+LηL2ηHηL2P, ImY=ηH2-ηL22HηH+LηLηHηL2P-ηHηLHηL+LηHηH2-ηL22ηLηH2P+ηsub2HηH+LηL2ηHηL2P,
ReY=ηsubηLηH2P×ηH2-ηL22+ηH2HηL+LηH2ηHηL2PηH2-ηL22ηsub2ηL2+ηH2LηH+HηL2, ImY=ηHLηH+HηLηH2-ηL2ηLηH2P×ηL-ηsub2ηLηHηL2PηH2-ηL22ηsub2ηL2+ηH2LηH+HηL2.
Dλ0=14πatan-2ηβη2-α2-β2+m4 with m=0, 1, 2,.

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