Abstract

A multiple narrow bandpass filter with both high Q factor and complete transmission using quasi-periodic Thue–Morse dielectric multilayers is proposed. The Q factor of the system increases exponentially with the generation order. Even though the Q factor of resonances increases as the generation order of the multilayers increases, these resonances are still complete resonances. The number of resonance peaks for the bandpass filter of the system also increases as the generation order increases. These resonance peaks have a multifractal distribution throughout the frequency range, which is different from that in traditional periodical multilayers.

© 2013 Optical Society of America

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L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, Nat. Photonics 4, 165 (2010).
[CrossRef]

Beltram, F.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, Nat. Photonics 4, 165 (2010).
[CrossRef]

Blaya, S.

Carretero, L.

Chang, C. H.

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef]

Chen, J.

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, Phys. Rev. B 75, 205109 (2007).
[CrossRef]

Cheng, Y. H.

Dal Negro, L.

L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, Appl. Phys. Lett. 86, 261905 (2005).
[CrossRef]

De La Rue, R. M.

De Stefano, L.

Faist, J.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, Nat. Photonics 4, 165 (2010).
[CrossRef]

Fan, S.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998).
[CrossRef]

Feng, D.

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, Phys. Rev. B 69, 165109 (2004).
[CrossRef]

Feng, S.

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, Phys. Rev. B 75, 205109 (2007).
[CrossRef]

Fimia, A.

Fink, Y.

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef]

Gong, Q.

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, Phys. Rev. B 75, 205109 (2007).
[CrossRef]

Hsueh, W. J.

Hu, A.

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, Europhys. Lett. 63, 853 (2003).
[CrossRef]

Huang, X. Q.

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, Europhys. Lett. 63, 853 (2003).
[CrossRef]

Iguchi, K.

M. Kohmoto, B. Sutherland, and K. Iguchi, Phys. Rev. Lett. 58, 2436 (1987).
[CrossRef]

Jiang, S. S.

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, Europhys. Lett. 63, 853 (2003).
[CrossRef]

Jiang, X.

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, Phys. Rev. B 75, 205109 (2007).
[CrossRef]

Joannopoulos, J. D.

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef]

Johnson, N. P.

Kim, K.-Y.

K.-Y. Kim and B. Lee, IEEE Photon. Technol. Lett. 20, 1057 (2008).
[CrossRef]

Kimerling, L. C.

L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, Appl. Phys. Lett. 86, 261905 (2005).
[CrossRef]

Kohmoto, M.

M. Kohmoto, B. Sutherland, and K. Iguchi, Phys. Rev. Lett. 58, 2436 (1987).
[CrossRef]

Lee, B.

K.-Y. Kim and B. Lee, IEEE Photon. Technol. Lett. 20, 1057 (2008).
[CrossRef]

Lei, H.

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, Phys. Rev. B 75, 205109 (2007).
[CrossRef]

Lin, Z. J.

Liu, N.-H.

N.-H. Liu, Phys. Rev. B 55, 3543 (1997).
[CrossRef]

Liu, Y. M.

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, Europhys. Lett. 63, 853 (2003).
[CrossRef]

Lu, Z.

Macia, E.

E. Macia, Appl. Phys. Lett. 73, 3330 (1998).
[CrossRef]

Mahler, L.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, Nat. Photonics 4, 165 (2010).
[CrossRef]

Marino, A.

Md Zain, R.

Michel, J.

L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, Appl. Phys. Lett. 86, 261905 (2005).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef]

Moretti, L.

Muriel, M. A.

Nguyen, V.

L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, Appl. Phys. Lett. 86, 261905 (2005).
[CrossRef]

Noda, S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef]

Nouet, G.

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, Phys. Rev. B 75, 205109 (2007).
[CrossRef]

Ouyang, L. Z.

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, Phys. Rev. B 69, 165109 (2004).
[CrossRef]

Peng, R. W.

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, Europhys. Lett. 63, 853 (2003).
[CrossRef]

Perez-Molina, M.

Preciado, M. A.

Qiu, F.

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, Europhys. Lett. 63, 853 (2003).
[CrossRef]

Rea, I.

Rendina, I.

Ritchie, D. A.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, Nat. Photonics 4, 165 (2010).
[CrossRef]

Rotiroti, L.

Song, B.-S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef]

Sorel, M.

Sutherland, B.

M. Kohmoto, B. Sutherland, and K. Iguchi, Phys. Rev. Lett. 58, 2436 (1987).
[CrossRef]

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef]

Tredicucci, A.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, Nat. Photonics 4, 165 (2010).
[CrossRef]

Walther, C.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, Nat. Photonics 4, 165 (2010).
[CrossRef]

Wang, M.

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, Phys. Rev. B 69, 165109 (2004).
[CrossRef]

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, Europhys. Lett. 63, 853 (2003).
[CrossRef]

Wiersma, D. S.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, Nat. Photonics 4, 165 (2010).
[CrossRef]

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998).
[CrossRef]

Wun, S. J.

Yi, J. H.

L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, Appl. Phys. Lett. 86, 261905 (2005).
[CrossRef]

Yi, Y.

L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, Appl. Phys. Lett. 86, 261905 (2005).
[CrossRef]

Zou, J.

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, Phys. Rev. B 69, 165109 (2004).
[CrossRef]

Appl. Phys. Lett. (2)

L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, Appl. Phys. Lett. 86, 261905 (2005).
[CrossRef]

E. Macia, Appl. Phys. Lett. 73, 3330 (1998).
[CrossRef]

Europhys. Lett. (1)

F. Qiu, R. W. Peng, X. Q. Huang, Y. M. Liu, M. Wang, A. Hu, and S. S. Jiang, Europhys. Lett. 63, 853 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K.-Y. Kim and B. Lee, IEEE Photon. Technol. Lett. 20, 1057 (2008).
[CrossRef]

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

Nat. Photonics (1)

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, Nat. Photonics 4, 165 (2010).
[CrossRef]

Nature (1)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef]

Opt. Express (4)

Opt. Lett. (4)

Phys. Rev. B (3)

R. W. Peng, Y. M. Liu, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, D. Feng, L. Z. Ouyang, and J. Zou, Phys. Rev. B 69, 165109 (2004).
[CrossRef]

N.-H. Liu, Phys. Rev. B 55, 3543 (1997).
[CrossRef]

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, Phys. Rev. B 75, 205109 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

M. Kohmoto, B. Sutherland, and K. Iguchi, Phys. Rev. Lett. 58, 2436 (1987).
[CrossRef]

Science (1)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Transmission spectra for TMMLs for generation orders of (a) v=5 and (b) v=7, versus the normalized frequency for normal incidence. The left portion of (b) is depicted in (c). (d) Transmission spectra of the BPML, which has the same layer number as the seventh TMMLs of (b). The parameters of the system are nA=1.0, nB=3.0, nC=nS=n0, N=1, D=1.0μm, and F=0.8. The gray areas in (a)–(c) correspond to the region with band gaps. Note that all of the complete transmission resonances lie beyond the band gaps.

Fig. 2.
Fig. 2.

Q factor for complete transmission resonances and the corresponding normalized frequency centers. The (blue) circles, (black) crosses, and (red) squares denote the bandpasses from the fifth, sixth, and seventh generation orders of the TMMLs, respectively. The parameters and the frequency range for the system are all the same as those for Fig. 1. It is noteworthy that these Q factors increase exponentially with the generation order of the TMMLs.

Fig. 3.
Fig. 3.

(a) Transmission spectra and (b) eigenfunction, cos(KL), of the sixth generation order TMMLs versus the normalized frequency for normal incidence. The insets in the lower left corner are the transmission spectra and cosine function of point A. The insets in the lower right corner are the transmission spectra and the cosine function of point B. The parameters and the frequency range of the system are the same as those for Fig. 1. The (green) circles in (a) mark the complete transmission resonances due to RUBs. The (green) rectangular marks in (b) denote RUBs where cos(KL)=1. The dashed (blue) lines correspond to the frequency of the repeated band edges, and the gray areas correspond to the region of the band gaps.

Fig. 4.
Fig. 4.

|E|2 distribution at complete transmission resonances in TMMLs for (a) v=5 and Ω=0.32987 and (b) v=6 and Ω=0.27879. The (blue) dotted lines are the boundaries of different layers. The characters, A (in yellow areas), symbolize material A. The dots (in green areas) mark material B. The characters, C (in white areas), denote the bonding media with nC=nS=n0. All of the parameters of the system are the same as those in Fig. 1.

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