Abstract

We demonstrate the possibility to create materials with chosen refractive indices and a strong birefringence in the terahertz range by etching of patterns with appropriate filling factors in a dielectric substrate. We show that by using deep inductive plasma etching of silicon wafers, it is possible to achieve a birefringence as high as 1.2 in an 80μm thick layer. The resulting stacks were used as building blocks for a photonic crystal displaying sharp defect mode peaks in transmittance.

© 2008 Optical Society of America

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  1. H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, Nat. Photonics 2, 295 (2008).
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  3. J. Li, J. He, and Z. Hong, Appl. Opt. 46, 5034 (2007).
    [CrossRef] [PubMed]
  4. P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, Appl. Phys. Lett. 91, 232911 (2007).
    [CrossRef]
  5. L. Fekete, F. Kadlec, P. Kužel, and H. Němec, Opt. Lett. 32, 680 (2007).
    [CrossRef] [PubMed]
  6. L. Fekete, F. Kadlec, P. Kužel, and H. Němec, Opt. Express 15, 8898 (2007).
    [CrossRef] [PubMed]
  7. P. Kužel and F. Kadlec, C. R. Acad. Sci.--Physique 9, 197 (2008).
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    [CrossRef]
  9. M. Reid and R. Fedosejevs, Appl. Opt. 45, 2766 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  11. S. Biber, D. Schneiderbanger, and L.-P. Schmidt, Frequenz 59, 141 (2005).
    [CrossRef]
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2008 (4)

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, Nat. Photonics 2, 295 (2008).
[CrossRef]

Y. Sun, X. Xia, H. Feng, H. Yang, C. Gu, and L. Wang, Appl. Phys. Lett. 92, 221101 (2008).
[CrossRef]

O. L. Muskens, S. L. Diedenhofen, M. H. M. van Weert, M. T. Borgström, E. P. A. M. Bakkers, and J. G. Rivas, Adv. Funct. Mater. 18, 1039 (2008).
[CrossRef]

P. Kužel and F. Kadlec, C. R. Acad. Sci.--Physique 9, 197 (2008).

2007 (6)

2006 (1)

2005 (3)

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

S. Biber, D. Schneiderbanger, and L.-P. Schmidt, Frequenz 59, 141 (2005).
[CrossRef]

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Averitt, R. D.

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, Nat. Photonics 2, 295 (2008).
[CrossRef]

Azad, A. K.

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, Nat. Photonics 2, 295 (2008).
[CrossRef]

Bakkers, E. P. A. M.

O. L. Muskens, S. L. Diedenhofen, M. H. M. van Weert, M. T. Borgström, E. P. A. M. Bakkers, and J. G. Rivas, Adv. Funct. Mater. 18, 1039 (2008).
[CrossRef]

Biber, S.

S. Biber, D. Schneiderbanger, and L.-P. Schmidt, Frequenz 59, 141 (2005).
[CrossRef]

Borgström, M. T.

O. L. Muskens, S. L. Diedenhofen, M. H. M. van Weert, M. T. Borgström, E. P. A. M. Bakkers, and J. G. Rivas, Adv. Funct. Mater. 18, 1039 (2008).
[CrossRef]

Brückner, C.

Chen, H.-T.

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, Nat. Photonics 2, 295 (2008).
[CrossRef]

Dekorsy, T.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Diedenhofen, S. L.

O. L. Muskens, S. L. Diedenhofen, M. H. M. van Weert, M. T. Borgström, E. P. A. M. Bakkers, and J. G. Rivas, Adv. Funct. Mater. 18, 1039 (2008).
[CrossRef]

Dressel, M.

Dreyhaupt, A.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Duvillaret, L.

Fedosejevs, R.

Fekete, L.

Feng, H.

Y. Sun, X. Xia, H. Feng, H. Yang, C. Gu, and L. Wang, Appl. Phys. Lett. 92, 221101 (2008).
[CrossRef]

Gu, C.

Y. Sun, X. Xia, H. Feng, H. Yang, C. Gu, and L. Wang, Appl. Phys. Lett. 92, 221101 (2008).
[CrossRef]

He, J.

Helm, M.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Hong, Z.

Hou, B.-H.

Y.-M. Sun, Z.-L. Mao, B.-H. Hou, G.-Q. Liu, and L. Wang, Chin. Phys. Lett. 24, 414 (2007).
[CrossRef]

Kadlec, F.

P. Kužel and F. Kadlec, C. R. Acad. Sci.--Physique 9, 197 (2008).

L. Fekete, F. Kadlec, P. Kužel, and H. Němec, Opt. Express 15, 8898 (2007).
[CrossRef] [PubMed]

L. Fekete, F. Kadlec, P. Kužel, and H. Němec, Opt. Lett. 32, 680 (2007).
[CrossRef] [PubMed]

P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, Appl. Phys. Lett. 91, 232911 (2007).
[CrossRef]

Kužel, P.

Li, J.

Liu, G.-Q.

Y.-M. Sun, Z.-L. Mao, B.-H. Hou, G.-Q. Liu, and L. Wang, Chin. Phys. Lett. 24, 414 (2007).
[CrossRef]

Mao, Z.-L.

Y.-M. Sun, Z.-L. Mao, B.-H. Hou, G.-Q. Liu, and L. Wang, Chin. Phys. Lett. 24, 414 (2007).
[CrossRef]

Muskens, O. L.

O. L. Muskens, S. L. Diedenhofen, M. H. M. van Weert, M. T. Borgström, E. P. A. M. Bakkers, and J. G. Rivas, Adv. Funct. Mater. 18, 1039 (2008).
[CrossRef]

Nemec, H.

Notni, G.

O'Hara, J. F.

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, Nat. Photonics 2, 295 (2008).
[CrossRef]

Padilla, W. J.

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, Nat. Photonics 2, 295 (2008).
[CrossRef]

Panaitov, G.

P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, Appl. Phys. Lett. 91, 232911 (2007).
[CrossRef]

Pashkin, A.

Petzelt, J.

P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, Appl. Phys. Lett. 91, 232911 (2007).
[CrossRef]

Pradarutti, B.

Reid, M.

Reihemann, S.

Rivas, J. G.

O. L. Muskens, S. L. Diedenhofen, M. H. M. van Weert, M. T. Borgström, E. P. A. M. Bakkers, and J. G. Rivas, Adv. Funct. Mater. 18, 1039 (2008).
[CrossRef]

Schmidt, L.-P.

S. Biber, D. Schneiderbanger, and L.-P. Schmidt, Frequenz 59, 141 (2005).
[CrossRef]

Schneiderbanger, D.

S. Biber, D. Schneiderbanger, and L.-P. Schmidt, Frequenz 59, 141 (2005).
[CrossRef]

Schubert, J.

P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, Appl. Phys. Lett. 91, 232911 (2007).
[CrossRef]

Sebastian, M.

Shrekenhamer, D. B.

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, Nat. Photonics 2, 295 (2008).
[CrossRef]

Steinkopf, R.

Stenzel, O.

Sun, Y.

Y. Sun, X. Xia, H. Feng, H. Yang, C. Gu, and L. Wang, Appl. Phys. Lett. 92, 221101 (2008).
[CrossRef]

Sun, Y.-M.

Y.-M. Sun, Z.-L. Mao, B.-H. Hou, G.-Q. Liu, and L. Wang, Chin. Phys. Lett. 24, 414 (2007).
[CrossRef]

Taylor, A. J.

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, Nat. Photonics 2, 295 (2008).
[CrossRef]

Tünnermann, A.

van Weert, M. H. M.

O. L. Muskens, S. L. Diedenhofen, M. H. M. van Weert, M. T. Borgström, E. P. A. M. Bakkers, and J. G. Rivas, Adv. Funct. Mater. 18, 1039 (2008).
[CrossRef]

Wang, L.

Y. Sun, X. Xia, H. Feng, H. Yang, C. Gu, and L. Wang, Appl. Phys. Lett. 92, 221101 (2008).
[CrossRef]

Y.-M. Sun, Z.-L. Mao, B.-H. Hou, G.-Q. Liu, and L. Wang, Chin. Phys. Lett. 24, 414 (2007).
[CrossRef]

Winnerl, S.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Xia, X.

Y. Sun, X. Xia, H. Feng, H. Yang, C. Gu, and L. Wang, Appl. Phys. Lett. 92, 221101 (2008).
[CrossRef]

Yang, H.

Y. Sun, X. Xia, H. Feng, H. Yang, C. Gu, and L. Wang, Appl. Phys. Lett. 92, 221101 (2008).
[CrossRef]

Adv. Funct. Mater. (1)

O. L. Muskens, S. L. Diedenhofen, M. H. M. van Weert, M. T. Borgström, E. P. A. M. Bakkers, and J. G. Rivas, Adv. Funct. Mater. 18, 1039 (2008).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

Y. Sun, X. Xia, H. Feng, H. Yang, C. Gu, and L. Wang, Appl. Phys. Lett. 92, 221101 (2008).
[CrossRef]

P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, Appl. Phys. Lett. 91, 232911 (2007).
[CrossRef]

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

C. R. Acad. Sci.--Physique (1)

P. Kužel and F. Kadlec, C. R. Acad. Sci.--Physique 9, 197 (2008).

Chin. Phys. Lett. (1)

Y.-M. Sun, Z.-L. Mao, B.-H. Hou, G.-Q. Liu, and L. Wang, Chin. Phys. Lett. 24, 414 (2007).
[CrossRef]

Frequenz (1)

S. Biber, D. Schneiderbanger, and L.-P. Schmidt, Frequenz 59, 141 (2005).
[CrossRef]

Nat. Photonics (1)

H.-T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, Nat. Photonics 2, 295 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

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Figures (3)

Fig. 1
Fig. 1

(a) Scheme of a unit cell of an etched material with permittivity ε placed in air; (b) equivalent circuit applicable for evaluating its effective response. The dimensions are in relative units. (c) Scanning electron microscope picture of the structure with an array of pillars.

Fig. 2
Fig. 2

Refractive indices for different patterns of etched layers (solid and dashed curves, walls; dotted curve, pillars). n, real part; κ, index of absorption.

Fig. 3
Fig. 3

Top, amplitude transmittance of the PC. The simulation is based on refractive indices n 1 = 1.33 and n Si = 3.415 . Bottom, band structure of an infinite defect-free PC (…SWSWSW…) and twin defect levels (dashed curves); inset, scheme of the PC.

Equations (4)

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

C = ( 1 C 1 + 1 C 2 ) 1 + C 3 ,
ε 1 = 1 + x 1 x 2 ε ε 1 x 2 = n 1 2 ,
ε 2 = 1 + x 1 x 2 ε ε 1 x 1 = n 2 2 .
E ( t , θ ) = E ( t ) cos 2 θ + E ( t ) sin 2 θ ,

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