Abstract

Dielectric aperiodic Thue-Morse structures up to 128 layers have been fabricated by using porous silicon technology. The photonic band gap properties of Thue-Morse multilayers have been theoretically investigated by means of the transfer matrix method and the integrated density of states. The theoretical approach has been compared and discussed with the reflectivity measurements at variable angles for both the transverse electric and transverse magnetic polarizations of light. The photonic band gap regions, wide 70 nm and 90 nm, included between 0 and 30°, have been observed for the sixth and seventh orders, respectively.

© 2006 Optical Society of America

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  1. E. Yablonovitch, "Inhibited spontaneous emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef] [PubMed]
  3. S. M. Weiss, M. Haurylau, P. M. Fauchet, "Tunable photonic bandgap structures for optical interconnects," Opt. Mater. 27, 740 (2005).
    [CrossRef]
  4. C. M. Soukoulis and E. N. Economou, "Localization in one-dimensional lattices in the presence of incommensurate potentials," Phys. Rev. Lett. 48, 1043 (1982).
    [CrossRef]
  5. A. Bruyant, G. Lérondel, P. J. Reece, and M. Gal, "All-silicon omnidirectional mirrors based on onedimensional photonic crystal," Appl. Phys. Lett. 82, 3227 (2003).
    [CrossRef]
  6. V. Agarwal and J. A. del Rio, "Tailoring the photonic band gap of a porous silicon dielectric mirror," Appl. Phys. Lett. 82, 1512 (2003).
    [CrossRef]
  7. N. Liu, "Propagation of light waves in Thue-Morse dielectric multilayers," Phys. Rev. B 55, 3543 (1997).
    [CrossRef]
  8. J. M. Luck, "Cantor spectra and scaling of gap widths in deterministic aperiodic systems," Phys. Rev. B 39, 5834 (1989).
    [CrossRef]
  9. M. Dulea, M. Severin and R. Riklund, "Transmission of light through deterministic aperiodic non-Fibonaccian multilayers," Phys. Rev. B 42,3680 (1990).
    [CrossRef]
  10. L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186 (2004).
    [CrossRef]
  11. F. Qui, R. W. Peng, X. Q. Huang, X. F. Hu, Mu Wang, A. Hu, S. S. Jiang and D. Feng, "Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers," Europhys. Lett. 68, 658-663 (2004).
    [CrossRef]
  12. L. Canham, Properties of Porous Silicon, (London IEE-INSPEC, 1997).
  13. L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, M. Righini, L. Colocci, and D. Wiersma, "Light transport through the band-edge states of Fibonacci Quasicrystals," Phys. Rev. Lett. 90, 55501 (2003).
    [CrossRef]
  14. V. Agarwal, J. A. Soto-Urueta, D. Becera, M. E. Mora-Ramos, "Light propagation in polytype Thue-Morse structures made of porous silicon," Photonics Nanostruct. Fundam. 3, 155 (2005).
    [CrossRef]
  15. M. Born, E. Wolf, Principles of Optics, (Cambridge University Press, New York, 2001).
  16. J. M. Bendickson, J. P. Dowling, M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107 (1996).
    [CrossRef]
  17. X. Jiang, Y. Zhang, S. Feng, K. C. Huang, Y. Yi, and J. D. Joannopoulos, "Photonic band gaps and localization in the Thue-Morse structures," Appl. Phys. Lett. 86, 201110 (2005).
    [CrossRef]

2005

S. M. Weiss, M. Haurylau, P. M. Fauchet, "Tunable photonic bandgap structures for optical interconnects," Opt. Mater. 27, 740 (2005).
[CrossRef]

V. Agarwal, J. A. Soto-Urueta, D. Becera, M. E. Mora-Ramos, "Light propagation in polytype Thue-Morse structures made of porous silicon," Photonics Nanostruct. Fundam. 3, 155 (2005).
[CrossRef]

X. Jiang, Y. Zhang, S. Feng, K. C. Huang, Y. Yi, and J. D. Joannopoulos, "Photonic band gaps and localization in the Thue-Morse structures," Appl. Phys. Lett. 86, 201110 (2005).
[CrossRef]

2004

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186 (2004).
[CrossRef]

F. Qui, R. W. Peng, X. Q. Huang, X. F. Hu, Mu Wang, A. Hu, S. S. Jiang and D. Feng, "Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers," Europhys. Lett. 68, 658-663 (2004).
[CrossRef]

2003

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, M. Righini, L. Colocci, and D. Wiersma, "Light transport through the band-edge states of Fibonacci Quasicrystals," Phys. Rev. Lett. 90, 55501 (2003).
[CrossRef]

A. Bruyant, G. Lérondel, P. J. Reece, and M. Gal, "All-silicon omnidirectional mirrors based on onedimensional photonic crystal," Appl. Phys. Lett. 82, 3227 (2003).
[CrossRef]

V. Agarwal and J. A. del Rio, "Tailoring the photonic band gap of a porous silicon dielectric mirror," Appl. Phys. Lett. 82, 1512 (2003).
[CrossRef]

1997

N. Liu, "Propagation of light waves in Thue-Morse dielectric multilayers," Phys. Rev. B 55, 3543 (1997).
[CrossRef]

1996

J. M. Bendickson, J. P. Dowling, M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107 (1996).
[CrossRef]

1990

M. Dulea, M. Severin and R. Riklund, "Transmission of light through deterministic aperiodic non-Fibonaccian multilayers," Phys. Rev. B 42,3680 (1990).
[CrossRef]

1989

J. M. Luck, "Cantor spectra and scaling of gap widths in deterministic aperiodic systems," Phys. Rev. B 39, 5834 (1989).
[CrossRef]

1987

E. Yablonovitch, "Inhibited spontaneous emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

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

1982

C. M. Soukoulis and E. N. Economou, "Localization in one-dimensional lattices in the presence of incommensurate potentials," Phys. Rev. Lett. 48, 1043 (1982).
[CrossRef]

Agarwal, V.

V. Agarwal, J. A. Soto-Urueta, D. Becera, M. E. Mora-Ramos, "Light propagation in polytype Thue-Morse structures made of porous silicon," Photonics Nanostruct. Fundam. 3, 155 (2005).
[CrossRef]

V. Agarwal and J. A. del Rio, "Tailoring the photonic band gap of a porous silicon dielectric mirror," Appl. Phys. Lett. 82, 1512 (2003).
[CrossRef]

Becera, D.

V. Agarwal, J. A. Soto-Urueta, D. Becera, M. E. Mora-Ramos, "Light propagation in polytype Thue-Morse structures made of porous silicon," Photonics Nanostruct. Fundam. 3, 155 (2005).
[CrossRef]

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107 (1996).
[CrossRef]

Bruyant, A.

A. Bruyant, G. Lérondel, P. J. Reece, and M. Gal, "All-silicon omnidirectional mirrors based on onedimensional photonic crystal," Appl. Phys. Lett. 82, 3227 (2003).
[CrossRef]

Colocci, L.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, M. Righini, L. Colocci, and D. Wiersma, "Light transport through the band-edge states of Fibonacci Quasicrystals," Phys. Rev. Lett. 90, 55501 (2003).
[CrossRef]

Dal Negro, L.

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186 (2004).
[CrossRef]

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, M. Righini, L. Colocci, and D. Wiersma, "Light transport through the band-edge states of Fibonacci Quasicrystals," Phys. Rev. Lett. 90, 55501 (2003).
[CrossRef]

del Rio, J. A.

V. Agarwal and J. A. del Rio, "Tailoring the photonic band gap of a porous silicon dielectric mirror," Appl. Phys. Lett. 82, 1512 (2003).
[CrossRef]

Dowling, J. P.

J. M. Bendickson, J. P. Dowling, M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107 (1996).
[CrossRef]

Duan, X.

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186 (2004).
[CrossRef]

Dulea, M.

M. Dulea, M. Severin and R. Riklund, "Transmission of light through deterministic aperiodic non-Fibonaccian multilayers," Phys. Rev. B 42,3680 (1990).
[CrossRef]

Economou, E. N.

C. M. Soukoulis and E. N. Economou, "Localization in one-dimensional lattices in the presence of incommensurate potentials," Phys. Rev. Lett. 48, 1043 (1982).
[CrossRef]

Fauchet, P. M.

S. M. Weiss, M. Haurylau, P. M. Fauchet, "Tunable photonic bandgap structures for optical interconnects," Opt. Mater. 27, 740 (2005).
[CrossRef]

Feng, S.

X. Jiang, Y. Zhang, S. Feng, K. C. Huang, Y. Yi, and J. D. Joannopoulos, "Photonic band gaps and localization in the Thue-Morse structures," Appl. Phys. Lett. 86, 201110 (2005).
[CrossRef]

Gaburro, Z.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, M. Righini, L. Colocci, and D. Wiersma, "Light transport through the band-edge states of Fibonacci Quasicrystals," Phys. Rev. Lett. 90, 55501 (2003).
[CrossRef]

Gal, M.

A. Bruyant, G. Lérondel, P. J. Reece, and M. Gal, "All-silicon omnidirectional mirrors based on onedimensional photonic crystal," Appl. Phys. Lett. 82, 3227 (2003).
[CrossRef]

Haavisto, J.

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186 (2004).
[CrossRef]

Haurylau, M.

S. M. Weiss, M. Haurylau, P. M. Fauchet, "Tunable photonic bandgap structures for optical interconnects," Opt. Mater. 27, 740 (2005).
[CrossRef]

Hu, X. F.

F. Qui, R. W. Peng, X. Q. Huang, X. F. Hu, Mu Wang, A. Hu, S. S. Jiang and D. Feng, "Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers," Europhys. Lett. 68, 658-663 (2004).
[CrossRef]

Huang, K. C.

X. Jiang, Y. Zhang, S. Feng, K. C. Huang, Y. Yi, and J. D. Joannopoulos, "Photonic band gaps and localization in the Thue-Morse structures," Appl. Phys. Lett. 86, 201110 (2005).
[CrossRef]

Huang, X. Q.

F. Qui, R. W. Peng, X. Q. Huang, X. F. Hu, Mu Wang, A. Hu, S. S. Jiang and D. Feng, "Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers," Europhys. Lett. 68, 658-663 (2004).
[CrossRef]

Jiang, X.

X. Jiang, Y. Zhang, S. Feng, K. C. Huang, Y. Yi, and J. D. Joannopoulos, "Photonic band gaps and localization in the Thue-Morse structures," Appl. Phys. Lett. 86, 201110 (2005).
[CrossRef]

Joannopoulos, J. D.

X. Jiang, Y. Zhang, S. Feng, K. C. Huang, Y. Yi, and J. D. Joannopoulos, "Photonic band gaps and localization in the Thue-Morse structures," Appl. Phys. Lett. 86, 201110 (2005).
[CrossRef]

John, S.

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

Johnson, P.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, M. Righini, L. Colocci, and D. Wiersma, "Light transport through the band-edge states of Fibonacci Quasicrystals," Phys. Rev. Lett. 90, 55501 (2003).
[CrossRef]

Kimerling, L. C.

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186 (2004).
[CrossRef]

Lagendijk, A.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, M. Righini, L. Colocci, and D. Wiersma, "Light transport through the band-edge states of Fibonacci Quasicrystals," Phys. Rev. Lett. 90, 55501 (2003).
[CrossRef]

LeBlanc, J.

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186 (2004).
[CrossRef]

Lérondel, G.

A. Bruyant, G. Lérondel, P. J. Reece, and M. Gal, "All-silicon omnidirectional mirrors based on onedimensional photonic crystal," Appl. Phys. Lett. 82, 3227 (2003).
[CrossRef]

Liu, N.

N. Liu, "Propagation of light waves in Thue-Morse dielectric multilayers," Phys. Rev. B 55, 3543 (1997).
[CrossRef]

Luck, J. M.

J. M. Luck, "Cantor spectra and scaling of gap widths in deterministic aperiodic systems," Phys. Rev. B 39, 5834 (1989).
[CrossRef]

Michel, J.

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186 (2004).
[CrossRef]

Mora-Ramos, M. E.

V. Agarwal, J. A. Soto-Urueta, D. Becera, M. E. Mora-Ramos, "Light propagation in polytype Thue-Morse structures made of porous silicon," Photonics Nanostruct. Fundam. 3, 155 (2005).
[CrossRef]

Mu Wang, X. F.

F. Qui, R. W. Peng, X. Q. Huang, X. F. Hu, Mu Wang, A. Hu, S. S. Jiang and D. Feng, "Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers," Europhys. Lett. 68, 658-663 (2004).
[CrossRef]

Oton, C. J.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, M. Righini, L. Colocci, and D. Wiersma, "Light transport through the band-edge states of Fibonacci Quasicrystals," Phys. Rev. Lett. 90, 55501 (2003).
[CrossRef]

Pavesi, L.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, M. Righini, L. Colocci, and D. Wiersma, "Light transport through the band-edge states of Fibonacci Quasicrystals," Phys. Rev. Lett. 90, 55501 (2003).
[CrossRef]

Peng, R. W.

F. Qui, R. W. Peng, X. Q. Huang, X. F. Hu, Mu Wang, A. Hu, S. S. Jiang and D. Feng, "Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers," Europhys. Lett. 68, 658-663 (2004).
[CrossRef]

Qui, F.

F. Qui, R. W. Peng, X. Q. Huang, X. F. Hu, Mu Wang, A. Hu, S. S. Jiang and D. Feng, "Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers," Europhys. Lett. 68, 658-663 (2004).
[CrossRef]

Reece, P. J.

A. Bruyant, G. Lérondel, P. J. Reece, and M. Gal, "All-silicon omnidirectional mirrors based on onedimensional photonic crystal," Appl. Phys. Lett. 82, 3227 (2003).
[CrossRef]

Righini, M.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, M. Righini, L. Colocci, and D. Wiersma, "Light transport through the band-edge states of Fibonacci Quasicrystals," Phys. Rev. Lett. 90, 55501 (2003).
[CrossRef]

Riklund, R.

M. Dulea, M. Severin and R. Riklund, "Transmission of light through deterministic aperiodic non-Fibonaccian multilayers," Phys. Rev. B 42,3680 (1990).
[CrossRef]

Scalora, M.

J. M. Bendickson, J. P. Dowling, M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107 (1996).
[CrossRef]

Severin, M.

M. Dulea, M. Severin and R. Riklund, "Transmission of light through deterministic aperiodic non-Fibonaccian multilayers," Phys. Rev. B 42,3680 (1990).
[CrossRef]

Soto-Urueta, J. A.

V. Agarwal, J. A. Soto-Urueta, D. Becera, M. E. Mora-Ramos, "Light propagation in polytype Thue-Morse structures made of porous silicon," Photonics Nanostruct. Fundam. 3, 155 (2005).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis and E. N. Economou, "Localization in one-dimensional lattices in the presence of incommensurate potentials," Phys. Rev. Lett. 48, 1043 (1982).
[CrossRef]

Stolfi, M.

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186 (2004).
[CrossRef]

Weiss, S. M.

S. M. Weiss, M. Haurylau, P. M. Fauchet, "Tunable photonic bandgap structures for optical interconnects," Opt. Mater. 27, 740 (2005).
[CrossRef]

Wiersma, D.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, M. Righini, L. Colocci, and D. Wiersma, "Light transport through the band-edge states of Fibonacci Quasicrystals," Phys. Rev. Lett. 90, 55501 (2003).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, "Inhibited spontaneous emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Yi, Y.

X. Jiang, Y. Zhang, S. Feng, K. C. Huang, Y. Yi, and J. D. Joannopoulos, "Photonic band gaps and localization in the Thue-Morse structures," Appl. Phys. Lett. 86, 201110 (2005).
[CrossRef]

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186 (2004).
[CrossRef]

Zhang, Y.

X. Jiang, Y. Zhang, S. Feng, K. C. Huang, Y. Yi, and J. D. Joannopoulos, "Photonic band gaps and localization in the Thue-Morse structures," Appl. Phys. Lett. 86, 201110 (2005).
[CrossRef]

Appl. Phys. Lett.

A. Bruyant, G. Lérondel, P. J. Reece, and M. Gal, "All-silicon omnidirectional mirrors based on onedimensional photonic crystal," Appl. Phys. Lett. 82, 3227 (2003).
[CrossRef]

V. Agarwal and J. A. del Rio, "Tailoring the photonic band gap of a porous silicon dielectric mirror," Appl. Phys. Lett. 82, 1512 (2003).
[CrossRef]

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186 (2004).
[CrossRef]

X. Jiang, Y. Zhang, S. Feng, K. C. Huang, Y. Yi, and J. D. Joannopoulos, "Photonic band gaps and localization in the Thue-Morse structures," Appl. Phys. Lett. 86, 201110 (2005).
[CrossRef]

Europhys. Lett.

F. Qui, R. W. Peng, X. Q. Huang, X. F. Hu, Mu Wang, A. Hu, S. S. Jiang and D. Feng, "Omnidirectional reflection of electromagnetic waves on Thue-Morse dielectric multilayers," Europhys. Lett. 68, 658-663 (2004).
[CrossRef]

Opt. Mater.

S. M. Weiss, M. Haurylau, P. M. Fauchet, "Tunable photonic bandgap structures for optical interconnects," Opt. Mater. 27, 740 (2005).
[CrossRef]

Photonics Nanostruct. Fundam.

V. Agarwal, J. A. Soto-Urueta, D. Becera, M. E. Mora-Ramos, "Light propagation in polytype Thue-Morse structures made of porous silicon," Photonics Nanostruct. Fundam. 3, 155 (2005).
[CrossRef]

Phys. Rev. B

N. Liu, "Propagation of light waves in Thue-Morse dielectric multilayers," Phys. Rev. B 55, 3543 (1997).
[CrossRef]

J. M. Luck, "Cantor spectra and scaling of gap widths in deterministic aperiodic systems," Phys. Rev. B 39, 5834 (1989).
[CrossRef]

M. Dulea, M. Severin and R. Riklund, "Transmission of light through deterministic aperiodic non-Fibonaccian multilayers," Phys. Rev. B 42,3680 (1990).
[CrossRef]

Phys. Rev. E

J. M. Bendickson, J. P. Dowling, M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107 (1996).
[CrossRef]

Phys. Rev. Lett.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, M. Righini, L. Colocci, and D. Wiersma, "Light transport through the band-edge states of Fibonacci Quasicrystals," Phys. Rev. Lett. 90, 55501 (2003).
[CrossRef]

C. M. Soukoulis and E. N. Economou, "Localization in one-dimensional lattices in the presence of incommensurate potentials," Phys. Rev. Lett. 48, 1043 (1982).
[CrossRef]

E. Yablonovitch, "Inhibited spontaneous emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

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

Other

M. Born, E. Wolf, Principles of Optics, (Cambridge University Press, New York, 2001).

L. Canham, Properties of Porous Silicon, (London IEE-INSPEC, 1997).

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Figures (7)

Fig. 1.
Fig. 1.

Fourier power spectrum of the associated T-M strings with 32 (a) 128 (b) and 4096 (c) characters, respectively.

Fig. 2.
Fig. 2.

Plots of Integrated Density Of States (a) and transmittance (b) against the phase (bottom axis) and wavelength (top axis) for S7 with resonant wavelength λ0=700 nm. The indicated values of phase correspond to the band gaps discussed in the text.

Fig. 3.
Fig. 3.

Schematic of the PSi T-M sequences realized.

Fig.4.
Fig.4.

Experimental (solid curves) and calculate (dashed curves) reflectivity for S3 T-M structure (a), S4 T-M structure (b) and S5 T-M structure (c). The measurements have been taken at normal incidence.

Fig. 5.
Fig. 5.

Experimental (solid curves) and calculate (dash curves) reflectivity for S6 T-M structure (a) and S7 T-M structure (b). The measurements have been taken at normal incidence.

Fig. 6.
Fig. 6.

Experimental reflectivity spectra of S6 T-M structure for TE mode (solid curves) and TM mode (dashed curves) for different incident angles.

Fig. 7.
Fig. 7.

Experimental reflectivity spectra of S7 for TE mode (solid curve) and TM mode (dashed curve) for different incident angles.

Equations (10)

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{ S N ( 2 j ) = S N ( j ) S N ( 2 j + 1 ) = 1 S N ( j ) with j = 0 , 1
χ ( 0 ) = M ( z ) · χ ( z )
χ ( z ) = ( U ( z ) V ( z ) ) with { { U ( z ) = E x V ( z ) = H y for TM mode { U ( z ) = H x V ( z ) = E y for TE mode
M T E ( z ) = ( cos ( ϕ ( z ) ) i n cos ( θ ) sin ( ϕ ( z ) ) i n cos ( θ ) sin ( ϕ ( z ) ) cos ( ϕ ( z ) ) )
M T M ( z ) = ( cos ( ϕ ( z ) ) i n cos ( θ ) sin ( ϕ ( z ) ) i n cos ( θ ) sin ( ϕ ( z ) ) cos ( ϕ ( z ) ) ) with φ ( z ) = k 0 n ( z ) z cos ( θ )
χ ( z 0 ) = Γ N · χ ( z N )
Γ N = Γ N 1 · Γ ˜ N 1 with Γ 1 = M A ( d A ) · M B ( d B )
t N = 2 ( Γ N , 11 + Γ N , 12 ) + ( Γ N , 21 + Γ N , 22 ) = x N + i y N
ρ N ( ω ) = 1 d N y N x N x N y N x N 2 + y N 2
IDOS ( ω ) = 0 ω ρ N ( ω ) d ω 0 2 ω 0 ρ N ( ω ) d ω

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