Abstract

We describe the fabrication, simulation, and measurement of a terahertz (THz) filter composed of nanoporous silicon multilayers. Using electrochemical etching, we fabricated a structure composed of alternating high- and low-index layers that achieves 93% power reflectivity at the target wavelength of 1.17 THz, with a stopband of 0.26 THz. The measured reflection and transmission spectra of the multilayer filter show excellent agreement with calculations based on the refractive indices determined separately from single-layer measurements. This technique could provide a convenient, flexible, and economical way to produce THz filters, which are essential in a variety of future applications.

© 2009 Optical Society of America

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  1. R. Schiwon, G. Schwaab, E. Brundermann, and M. Havenith, Appl. Phys. Lett. 83, 4119 (2003).
    [CrossRef]
  2. N. Krumbholz, K. Gerlach, F. Rutz, and M. Koch, Appl. Phys. Lett. 88, 202905 (2006).
    [CrossRef]
  3. H. Němec, P. Kužel, F. Garet, and L. Duvillaret, Appl. Opt. 43, 1965 (2004).
    [CrossRef] [PubMed]
  4. T. W. Du Bosq, A. V. Muravjov, R. E. Peale, and C. J. Fredricksen, Appl. Opt. 44, 7191 (2005).
    [CrossRef] [PubMed]
  5. W. Withayachumnankul, B. M. Fischer, and D. Abbott, Opt. Commun. 281, 2374 (2008).
    [CrossRef]
  6. H. Němec, P. Kužel, L. Duvillaret, A. Pashkin, M. Dressel, and M. T. Sebastian, Opt. Lett. 30, 549 (2005).
    [CrossRef] [PubMed]
  7. N. Matsumoto, T. Nakagawa, K. Kageyama, N. Wada, and Y. Sakabe, Jpn. J. Appl. Phys. Part 1 45, 7499 (2006).
    [CrossRef]
  8. F. Rutz, M. Koch, L. Micele, and G. de Portu, Appl. Opt. 45, 8070 (2006).
    [CrossRef] [PubMed]
  9. J. Shao and J. A. Dobrowolski, Appl. Opt. 32, 2361 (1993).
    [CrossRef] [PubMed]
  10. D. Turchinovich, A. Kammoun, P. Knobloch, T. Dobbertin, and M. Koch, Appl. Phys. A 74, 291 (2002).
    [CrossRef]
  11. S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, Polym. Test. 26, 614 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. S. Ramani, A. Cheville, E. Garcia, and V. Agarwal, Phys. Status Solidi C 4, 2111 (2007).
    [CrossRef]
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    [CrossRef]
  19. M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, J. Phys. D 27, 1333 (1994).
    [CrossRef]
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    [CrossRef]

2009 (2)

S.-Z. A. Lo, A. M. Rossi, and T. E. Murphy, Phys. Status Solidi A 206, 1273 (2009).
[CrossRef]

R. Wilk, N. Vieweg, O. Kopschinski, and M. Koch, Opt. Express 17, 7377 (2009).
[CrossRef] [PubMed]

2008 (3)

I. A. Ibraheem, N. Krumbholz, D. Mittleman, and M. Koch, IEEE Microw. Wirel. Compon. Lett. 18, 67 (2008).
[CrossRef]

W. Withayachumnankul, B. M. Fischer, and D. Abbott, Opt. Commun. 281, 2374 (2008).
[CrossRef]

J. Lott, C. Xia, L. Kosnosky, C. Weder, and J. Shan, Adv. Mater. 20, 3649 (2008).
[CrossRef]

2007 (2)

S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, Polym. Test. 26, 614 (2007).
[CrossRef]

S. Ramani, A. Cheville, E. Garcia, and V. Agarwal, Phys. Status Solidi C 4, 2111 (2007).
[CrossRef]

2006 (3)

N. Matsumoto, T. Nakagawa, K. Kageyama, N. Wada, and Y. Sakabe, Jpn. J. Appl. Phys. Part 1 45, 7499 (2006).
[CrossRef]

N. Krumbholz, K. Gerlach, F. Rutz, and M. Koch, Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

F. Rutz, M. Koch, L. Micele, and G. de Portu, Appl. Opt. 45, 8070 (2006).
[CrossRef] [PubMed]

2005 (3)

2004 (2)

2003 (1)

R. Schiwon, G. Schwaab, E. Brundermann, and M. Havenith, Appl. Phys. Lett. 83, 4119 (2003).
[CrossRef]

2002 (1)

D. Turchinovich, A. Kammoun, P. Knobloch, T. Dobbertin, and M. Koch, Appl. Phys. A 74, 291 (2002).
[CrossRef]

2001 (1)

J. N. Heyman, P. Neocleous, D. Hebert, P. A. Crowell, T. Müller, and K. Unterrainer, Phys. Rev. B 64, 085202 (2001).
[CrossRef]

1998 (1)

S. Labbé-Lavigne, S. Barret, F. Garet, L. Duvillaret, and J.-L. Coutaz, J. Appl. Phys. 83, 6007 (1998).
[CrossRef]

1996 (2)

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

L. Duvillaret, F. Garet, and J.-L. Coutaz, IEEE J. Sel. Top. Quantum Electron. 2, 739 (1996).
[CrossRef]

1994 (1)

M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, J. Phys. D 27, 1333 (1994).
[CrossRef]

1993 (1)

1981 (1)

Abbott, D.

W. Withayachumnankul, B. M. Fischer, and D. Abbott, Opt. Commun. 281, 2374 (2008).
[CrossRef]

Agarwal, V.

S. Ramani, A. Cheville, E. Garcia, and V. Agarwal, Phys. Status Solidi C 4, 2111 (2007).
[CrossRef]

Barret, S.

S. Labbé-Lavigne, S. Barret, F. Garet, L. Duvillaret, and J.-L. Coutaz, J. Appl. Phys. 83, 6007 (1998).
[CrossRef]

Berger, M. G.

M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, J. Phys. D 27, 1333 (1994).
[CrossRef]

Brundermann, E.

R. Schiwon, G. Schwaab, E. Brundermann, and M. Havenith, Appl. Phys. Lett. 83, 4119 (2003).
[CrossRef]

Cheville, A.

S. Ramani, A. Cheville, E. Garcia, and V. Agarwal, Phys. Status Solidi C 4, 2111 (2007).
[CrossRef]

Coutaz, J. -L.

S. Labbé-Lavigne, S. Barret, F. Garet, L. Duvillaret, and J.-L. Coutaz, J. Appl. Phys. 83, 6007 (1998).
[CrossRef]

L. Duvillaret, F. Garet, and J.-L. Coutaz, IEEE J. Sel. Top. Quantum Electron. 2, 739 (1996).
[CrossRef]

Crowell, P. A.

J. N. Heyman, P. Neocleous, D. Hebert, P. A. Crowell, T. Müller, and K. Unterrainer, Phys. Rev. B 64, 085202 (2001).
[CrossRef]

Dai, J.

de Portu, G.

Dieker, C.

M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, J. Phys. D 27, 1333 (1994).
[CrossRef]

Dobbertin, T.

D. Turchinovich, A. Kammoun, P. Knobloch, T. Dobbertin, and M. Koch, Appl. Phys. A 74, 291 (2002).
[CrossRef]

Dobrowolski, J. A.

Dressel, M.

Du Bosq, T. W.

Duvillaret, L.

H. Němec, P. Kužel, L. Duvillaret, A. Pashkin, M. Dressel, and M. T. Sebastian, Opt. Lett. 30, 549 (2005).
[CrossRef] [PubMed]

H. Němec, P. Kužel, F. Garet, and L. Duvillaret, Appl. Opt. 43, 1965 (2004).
[CrossRef] [PubMed]

S. Labbé-Lavigne, S. Barret, F. Garet, L. Duvillaret, and J.-L. Coutaz, J. Appl. Phys. 83, 6007 (1998).
[CrossRef]

L. Duvillaret, F. Garet, and J.-L. Coutaz, IEEE J. Sel. Top. Quantum Electron. 2, 739 (1996).
[CrossRef]

Fischer, B. M.

W. Withayachumnankul, B. M. Fischer, and D. Abbott, Opt. Commun. 281, 2374 (2008).
[CrossRef]

Fredricksen, C. J.

Garcia, E.

S. Ramani, A. Cheville, E. Garcia, and V. Agarwal, Phys. Status Solidi C 4, 2111 (2007).
[CrossRef]

Garet, F.

H. Němec, P. Kužel, F. Garet, and L. Duvillaret, Appl. Opt. 43, 1965 (2004).
[CrossRef] [PubMed]

S. Labbé-Lavigne, S. Barret, F. Garet, L. Duvillaret, and J.-L. Coutaz, J. Appl. Phys. 83, 6007 (1998).
[CrossRef]

L. Duvillaret, F. Garet, and J.-L. Coutaz, IEEE J. Sel. Top. Quantum Electron. 2, 739 (1996).
[CrossRef]

Gerlach, K.

N. Krumbholz, K. Gerlach, F. Rutz, and M. Koch, Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

Grischkowsky, D.

Grosse, P.

M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, J. Phys. D 27, 1333 (1994).
[CrossRef]

Havenith, M.

R. Schiwon, G. Schwaab, E. Brundermann, and M. Havenith, Appl. Phys. Lett. 83, 4119 (2003).
[CrossRef]

Hebert, D.

J. N. Heyman, P. Neocleous, D. Hebert, P. A. Crowell, T. Müller, and K. Unterrainer, Phys. Rev. B 64, 085202 (2001).
[CrossRef]

Heinz, T. F.

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

Heyman, J. N.

J. N. Heyman, P. Neocleous, D. Hebert, P. A. Crowell, T. Müller, and K. Unterrainer, Phys. Rev. B 64, 085202 (2001).
[CrossRef]

Hosako, I.

Hunneman, R.

Ibraheem, I. A.

I. A. Ibraheem, N. Krumbholz, D. Mittleman, and M. Koch, IEEE Microw. Wirel. Compon. Lett. 18, 67 (2008).
[CrossRef]

Jansen, C.

S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, Polym. Test. 26, 614 (2007).
[CrossRef]

Kageyama, K.

N. Matsumoto, T. Nakagawa, K. Kageyama, N. Wada, and Y. Sakabe, Jpn. J. Appl. Phys. Part 1 45, 7499 (2006).
[CrossRef]

Kammoun, A.

D. Turchinovich, A. Kammoun, P. Knobloch, T. Dobbertin, and M. Koch, Appl. Phys. A 74, 291 (2002).
[CrossRef]

Knobloch, P.

D. Turchinovich, A. Kammoun, P. Knobloch, T. Dobbertin, and M. Koch, Appl. Phys. A 74, 291 (2002).
[CrossRef]

Koch, M.

R. Wilk, N. Vieweg, O. Kopschinski, and M. Koch, Opt. Express 17, 7377 (2009).
[CrossRef] [PubMed]

I. A. Ibraheem, N. Krumbholz, D. Mittleman, and M. Koch, IEEE Microw. Wirel. Compon. Lett. 18, 67 (2008).
[CrossRef]

S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, Polym. Test. 26, 614 (2007).
[CrossRef]

N. Krumbholz, K. Gerlach, F. Rutz, and M. Koch, Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

F. Rutz, M. Koch, L. Micele, and G. de Portu, Appl. Opt. 45, 8070 (2006).
[CrossRef] [PubMed]

D. Turchinovich, A. Kammoun, P. Knobloch, T. Dobbertin, and M. Koch, Appl. Phys. A 74, 291 (2002).
[CrossRef]

Kopschinski, O.

Kosnosky, L.

J. Lott, C. Xia, L. Kosnosky, C. Weder, and J. Shan, Adv. Mater. 20, 3649 (2008).
[CrossRef]

Krumbholz, N.

I. A. Ibraheem, N. Krumbholz, D. Mittleman, and M. Koch, IEEE Microw. Wirel. Compon. Lett. 18, 67 (2008).
[CrossRef]

N. Krumbholz, K. Gerlach, F. Rutz, and M. Koch, Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

Kužel, P.

Labbé-Lavigne, S.

S. Labbé-Lavigne, S. Barret, F. Garet, L. Duvillaret, and J.-L. Coutaz, J. Appl. Phys. 83, 6007 (1998).
[CrossRef]

Lo, S. -Z. A.

S.-Z. A. Lo, A. M. Rossi, and T. E. Murphy, Phys. Status Solidi A 206, 1273 (2009).
[CrossRef]

Lott, J.

J. Lott, C. Xia, L. Kosnosky, C. Weder, and J. Shan, Adv. Mater. 20, 3649 (2008).
[CrossRef]

Lüth, H.

M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, J. Phys. D 27, 1333 (1994).
[CrossRef]

Matsumoto, N.

N. Matsumoto, T. Nakagawa, K. Kageyama, N. Wada, and Y. Sakabe, Jpn. J. Appl. Phys. Part 1 45, 7499 (2006).
[CrossRef]

Micele, L.

Mittleman, D.

I. A. Ibraheem, N. Krumbholz, D. Mittleman, and M. Koch, IEEE Microw. Wirel. Compon. Lett. 18, 67 (2008).
[CrossRef]

S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, Polym. Test. 26, 614 (2007).
[CrossRef]

Müller, T.

J. N. Heyman, P. Neocleous, D. Hebert, P. A. Crowell, T. Müller, and K. Unterrainer, Phys. Rev. B 64, 085202 (2001).
[CrossRef]

Münder, H.

M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, J. Phys. D 27, 1333 (1994).
[CrossRef]

Muravjov, A. V.

Murphy, T. E.

S.-Z. A. Lo, A. M. Rossi, and T. E. Murphy, Phys. Status Solidi A 206, 1273 (2009).
[CrossRef]

Nahata, A.

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

Nakagawa, T.

N. Matsumoto, T. Nakagawa, K. Kageyama, N. Wada, and Y. Sakabe, Jpn. J. Appl. Phys. Part 1 45, 7499 (2006).
[CrossRef]

Nemec, H.

Neocleous, P.

J. N. Heyman, P. Neocleous, D. Hebert, P. A. Crowell, T. Müller, and K. Unterrainer, Phys. Rev. B 64, 085202 (2001).
[CrossRef]

Pashkin, A.

Peale, R. E.

Ramani, S.

S. Ramani, A. Cheville, E. Garcia, and V. Agarwal, Phys. Status Solidi C 4, 2111 (2007).
[CrossRef]

Rossi, A. M.

S.-Z. A. Lo, A. M. Rossi, and T. E. Murphy, Phys. Status Solidi A 206, 1273 (2009).
[CrossRef]

Rutz, F.

S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, Polym. Test. 26, 614 (2007).
[CrossRef]

N. Krumbholz, K. Gerlach, F. Rutz, and M. Koch, Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

F. Rutz, M. Koch, L. Micele, and G. de Portu, Appl. Opt. 45, 8070 (2006).
[CrossRef] [PubMed]

Sakabe, Y.

N. Matsumoto, T. Nakagawa, K. Kageyama, N. Wada, and Y. Sakabe, Jpn. J. Appl. Phys. Part 1 45, 7499 (2006).
[CrossRef]

Schiwon, R.

R. Schiwon, G. Schwaab, E. Brundermann, and M. Havenith, Appl. Phys. Lett. 83, 4119 (2003).
[CrossRef]

Schwaab, G.

R. Schiwon, G. Schwaab, E. Brundermann, and M. Havenith, Appl. Phys. Lett. 83, 4119 (2003).
[CrossRef]

Sebastian, M. T.

Seeley, J. S.

Shan, J.

J. Lott, C. Xia, L. Kosnosky, C. Weder, and J. Shan, Adv. Mater. 20, 3649 (2008).
[CrossRef]

Shao, J.

Theiss, W.

M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, J. Phys. D 27, 1333 (1994).
[CrossRef]

Thönissen, M.

M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, J. Phys. D 27, 1333 (1994).
[CrossRef]

Turchinovich, D.

D. Turchinovich, A. Kammoun, P. Knobloch, T. Dobbertin, and M. Koch, Appl. Phys. A 74, 291 (2002).
[CrossRef]

Unterrainer, K.

J. N. Heyman, P. Neocleous, D. Hebert, P. A. Crowell, T. Müller, and K. Unterrainer, Phys. Rev. B 64, 085202 (2001).
[CrossRef]

Vescan, L.

M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, J. Phys. D 27, 1333 (1994).
[CrossRef]

Vieweg, N.

Wada, N.

N. Matsumoto, T. Nakagawa, K. Kageyama, N. Wada, and Y. Sakabe, Jpn. J. Appl. Phys. Part 1 45, 7499 (2006).
[CrossRef]

Weder, C.

J. Lott, C. Xia, L. Kosnosky, C. Weder, and J. Shan, Adv. Mater. 20, 3649 (2008).
[CrossRef]

Weling, A. S.

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

Wernke, M.

M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, J. Phys. D 27, 1333 (1994).
[CrossRef]

Whatley, A.

Wietzke, S.

S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, Polym. Test. 26, 614 (2007).
[CrossRef]

Wilk, R.

Withayachumnankul, W.

W. Withayachumnankul, B. M. Fischer, and D. Abbott, Opt. Commun. 281, 2374 (2008).
[CrossRef]

Xia, C.

J. Lott, C. Xia, L. Kosnosky, C. Weder, and J. Shan, Adv. Mater. 20, 3649 (2008).
[CrossRef]

Zhang, J.

Zhang, W.

Adv. Mater. (1)

J. Lott, C. Xia, L. Kosnosky, C. Weder, and J. Shan, Adv. Mater. 20, 3649 (2008).
[CrossRef]

Appl. Opt. (6)

Appl. Phys. A (1)

D. Turchinovich, A. Kammoun, P. Knobloch, T. Dobbertin, and M. Koch, Appl. Phys. A 74, 291 (2002).
[CrossRef]

Appl. Phys. Lett. (3)

R. Schiwon, G. Schwaab, E. Brundermann, and M. Havenith, Appl. Phys. Lett. 83, 4119 (2003).
[CrossRef]

N. Krumbholz, K. Gerlach, F. Rutz, and M. Koch, Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

L. Duvillaret, F. Garet, and J.-L. Coutaz, IEEE J. Sel. Top. Quantum Electron. 2, 739 (1996).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett. (1)

I. A. Ibraheem, N. Krumbholz, D. Mittleman, and M. Koch, IEEE Microw. Wirel. Compon. Lett. 18, 67 (2008).
[CrossRef]

J. Appl. Phys. (1)

S. Labbé-Lavigne, S. Barret, F. Garet, L. Duvillaret, and J.-L. Coutaz, J. Appl. Phys. 83, 6007 (1998).
[CrossRef]

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

J. Phys. D (1)

M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, J. Phys. D 27, 1333 (1994).
[CrossRef]

Jpn. J. Appl. Phys. Part 1 (1)

N. Matsumoto, T. Nakagawa, K. Kageyama, N. Wada, and Y. Sakabe, Jpn. J. Appl. Phys. Part 1 45, 7499 (2006).
[CrossRef]

Opt. Commun. (1)

W. Withayachumnankul, B. M. Fischer, and D. Abbott, Opt. Commun. 281, 2374 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

J. N. Heyman, P. Neocleous, D. Hebert, P. A. Crowell, T. Müller, and K. Unterrainer, Phys. Rev. B 64, 085202 (2001).
[CrossRef]

Phys. Status Solidi A (1)

S.-Z. A. Lo, A. M. Rossi, and T. E. Murphy, Phys. Status Solidi A 206, 1273 (2009).
[CrossRef]

Phys. Status Solidi C (1)

S. Ramani, A. Cheville, E. Garcia, and V. Agarwal, Phys. Status Solidi C 4, 2111 (2007).
[CrossRef]

Polym. Test. (1)

S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, Polym. Test. 26, 614 (2007).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Measured and theoretical THz transmission spectrum for free-standing single-layer porous silicon samples fabricated with (a) low and (b) high porosity. The theoretical curves were obtained by fitting Eq. (2) to the experimental observations, using the index model given in Eq. (1). The refractive indices and attenuation coefficients determined from the theoretical fits are shown directly below the corresponding transmission spectra.

Fig. 2
Fig. 2

Cross-sectional scanning electron micrograph of a 13-layer porous silicon Bragg grating filter, composed of alternating high and low refractive index layers. Inset, top-down scanning electron micrograph showing nanoscale structure of porous material.

Fig. 3
Fig. 3

THz transmission and reflection spectra of a porous silicon Bragg filter. The solid curves indicate a theoretical calculation based on the measured film thicknesses and separately measured layer properties.

Equations (2)

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

ϵ r ( ω ) = A + i B ω ,
T ( ω ) = 4 n ̃ ( n ̃ + 1 ) 2 e i ( n ̃ 1 ) ω d / c 1 ( n ̃ 1 n ̃ + 1 ) 2 e i 2 n ̃ ω d / c ,

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