Abstract

We present experimental results of the transmission magnitude and phase change of terahertz pulses through thin metallic films patterned with subwavelength hole arrays on silicon wafers. Terahertz time-domain spectroscopy measurements reveal a sharp phase peak centered on the surface plasmon resonance. Correspondingly, and consistent with the Kramers–Kronig relations, the measured transmission magnitude has the shape of the derivative of this peak. In addition, we determine that the aperture shape has a notable effect on the transmission properties of two-dimensional hole arrays.

© 2004 Optical Society of America

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2003 (5)

F. Baumann, W. A. Bailey, A. Naweed, W. D. Goodhue, and A. J. Gatesman, Opt. Lett. 28, 938 (2003).
[CrossRef] [PubMed]

N. Jukam and M. S. Sherwin, Appl. Phys. Lett. 83, 21 (2003).
[CrossRef]

F. Miyamary, T. Kondo, T. Nagashima, and M. Hangyo, Appl. Phys. Lett. 82, 2568 (2003).
[CrossRef]

D. Wu, N. Fang, C. Sun, and X. Zhang, Appl. Phys. Lett. 83, 201 (2003).
[CrossRef]

W. Zhang, A. Azad, and D. Grischkowsky, Appl. Phys. Lett. 82, 2841 (2003).
[CrossRef]

2002 (2)

W. Liu and D. Tsai, Phys. Rev. B 65, 155423 (2002).
[CrossRef]

F. J. García-Vidall and L. Martín-Moreno, Phys. Rev. B 66, 155412 (2002).
[CrossRef]

2001 (2)

L. Martín-Moreno, F. J. García-Vidall, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

A. Dogariu, T. Thio, L. J. Wang, T. W. Ebbesen, and H. J. Lezec, Opt. Lett. 26, 450 (2001).
[CrossRef]

1999 (2)

C. Winnewisser, F. Lewen, J. Weinzierl, and H. Helm, Appl. Opt. 38, 3961 (1999).
[CrossRef]

C. Jin, B. Cheng, Z. Li, D. Zhang, L. Li, and Z. Zhang, Opt. Commun. 166, 9 (1999).
[CrossRef]

1998 (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. Q. Wolff, Nature 391, 667 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
[CrossRef]

1991 (1)

F. Yang, J. R. Sambles, and G. W. Bradberry, Phys. Rev. B 44, 5855 (1991).
[CrossRef]

1990 (1)

1983 (1)

1973 (1)

C.-C. Chen, IEEE Trans. Microwave Theory Tech. 21, 1 (1973).
[CrossRef]

Alexander, R. W.

Azad, A.

W. Zhang, A. Azad, and D. Grischkowsky, Appl. Phys. Lett. 82, 2841 (2003).
[CrossRef]

Bailey, W. A.

Baumann, F.

Bell, R. J.

Bell, R. R.

Bell, S. E.

Bradberry, G. W.

F. Yang, J. R. Sambles, and G. W. Bradberry, Phys. Rev. B 44, 5855 (1991).
[CrossRef]

Chen, C.-C.

C.-C. Chen, IEEE Trans. Microwave Theory Tech. 21, 1 (1973).
[CrossRef]

Cheng, B.

C. Jin, B. Cheng, Z. Li, D. Zhang, L. Li, and Z. Zhang, Opt. Commun. 166, 9 (1999).
[CrossRef]

Dogariu, A.

Ebbesen, T. W.

A. Dogariu, T. Thio, L. J. Wang, T. W. Ebbesen, and H. J. Lezec, Opt. Lett. 26, 450 (2001).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidall, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. Q. Wolff, Nature 391, 667 (1998).
[CrossRef]

Ehrenberg, W.

W. Ehrenberg, Electric Conduction in Semiconductors and Metals (Clarendon, Oxford, 1958).

Fang, N.

D. Wu, N. Fang, C. Sun, and X. Zhang, Appl. Phys. Lett. 83, 201 (2003).
[CrossRef]

Fattinger, Ch.

García-Vidall, F. J.

F. J. García-Vidall and L. Martín-Moreno, Phys. Rev. B 66, 155412 (2002).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidall, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

Gatesman, A. J.

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. Q. Wolff, Nature 391, 667 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
[CrossRef]

Goodhue, W. D.

Grischkowsky, D.

Grupp, D. E.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
[CrossRef]

Hangyo, M.

F. Miyamary, T. Kondo, T. Nagashima, and M. Hangyo, Appl. Phys. Lett. 82, 2568 (2003).
[CrossRef]

Helm, H.

Jin, C.

C. Jin, B. Cheng, Z. Li, D. Zhang, L. Li, and Z. Zhang, Opt. Commun. 166, 9 (1999).
[CrossRef]

Jukam, N.

N. Jukam and M. S. Sherwin, Appl. Phys. Lett. 83, 21 (2003).
[CrossRef]

Keiding, S.

Kondo, T.

F. Miyamary, T. Kondo, T. Nagashima, and M. Hangyo, Appl. Phys. Lett. 82, 2568 (2003).
[CrossRef]

Lewen, F.

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidall, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

A. Dogariu, T. Thio, L. J. Wang, T. W. Ebbesen, and H. J. Lezec, Opt. Lett. 26, 450 (2001).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. Q. Wolff, Nature 391, 667 (1998).
[CrossRef]

Li, L.

C. Jin, B. Cheng, Z. Li, D. Zhang, L. Li, and Z. Zhang, Opt. Commun. 166, 9 (1999).
[CrossRef]

Li, Z.

C. Jin, B. Cheng, Z. Li, D. Zhang, L. Li, and Z. Zhang, Opt. Commun. 166, 9 (1999).
[CrossRef]

Liu, W.

W. Liu and D. Tsai, Phys. Rev. B 65, 155423 (2002).
[CrossRef]

Long, L. L.

Martín-Moreno, L.

F. J. García-Vidall and L. Martín-Moreno, Phys. Rev. B 66, 155412 (2002).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidall, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

Miyamary, F.

F. Miyamary, T. Kondo, T. Nagashima, and M. Hangyo, Appl. Phys. Lett. 82, 2568 (2003).
[CrossRef]

Nagashima, T.

F. Miyamary, T. Kondo, T. Nagashima, and M. Hangyo, Appl. Phys. Lett. 82, 2568 (2003).
[CrossRef]

Naweed, A.

Ordal, M. A.

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidall, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

Pendry, J. B.

L. Martín-Moreno, F. J. García-Vidall, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

Saleh, E. A.

E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Sambles, J. R.

F. Yang, J. R. Sambles, and G. W. Bradberry, Phys. Rev. B 44, 5855 (1991).
[CrossRef]

Sherwin, M. S.

N. Jukam and M. S. Sherwin, Appl. Phys. Lett. 83, 21 (2003).
[CrossRef]

Sun, C.

D. Wu, N. Fang, C. Sun, and X. Zhang, Appl. Phys. Lett. 83, 201 (2003).
[CrossRef]

Teich, M. C.

E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Thio, T.

A. Dogariu, T. Thio, L. J. Wang, T. W. Ebbesen, and H. J. Lezec, Opt. Lett. 26, 450 (2001).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidall, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. Q. Wolff, Nature 391, 667 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
[CrossRef]

Tsai, D.

W. Liu and D. Tsai, Phys. Rev. B 65, 155423 (2002).
[CrossRef]

van Exter, M.

Wang, L. J.

Ward, C. A.

Weinzierl, J.

Winnewisser, C.

Wolff, P. Q.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. Q. Wolff, Nature 391, 667 (1998).
[CrossRef]

Wu, D.

D. Wu, N. Fang, C. Sun, and X. Zhang, Appl. Phys. Lett. 83, 201 (2003).
[CrossRef]

Yang, F.

F. Yang, J. R. Sambles, and G. W. Bradberry, Phys. Rev. B 44, 5855 (1991).
[CrossRef]

Zhang, D.

C. Jin, B. Cheng, Z. Li, D. Zhang, L. Li, and Z. Zhang, Opt. Commun. 166, 9 (1999).
[CrossRef]

Zhang, W.

W. Zhang, A. Azad, and D. Grischkowsky, Appl. Phys. Lett. 82, 2841 (2003).
[CrossRef]

Zhang, X.

D. Wu, N. Fang, C. Sun, and X. Zhang, Appl. Phys. Lett. 83, 201 (2003).
[CrossRef]

Zhang, Z.

C. Jin, B. Cheng, Z. Li, D. Zhang, L. Li, and Z. Zhang, Opt. Commun. 166, 9 (1999).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (4)

W. Zhang, A. Azad, and D. Grischkowsky, Appl. Phys. Lett. 82, 2841 (2003).
[CrossRef]

N. Jukam and M. S. Sherwin, Appl. Phys. Lett. 83, 21 (2003).
[CrossRef]

F. Miyamary, T. Kondo, T. Nagashima, and M. Hangyo, Appl. Phys. Lett. 82, 2568 (2003).
[CrossRef]

D. Wu, N. Fang, C. Sun, and X. Zhang, Appl. Phys. Lett. 83, 201 (2003).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

C.-C. Chen, IEEE Trans. Microwave Theory Tech. 21, 1 (1973).
[CrossRef]

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

Nature (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. Q. Wolff, Nature 391, 667 (1998).
[CrossRef]

Opt. Commun. (1)

C. Jin, B. Cheng, Z. Li, D. Zhang, L. Li, and Z. Zhang, Opt. Commun. 166, 9 (1999).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (4)

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
[CrossRef]

W. Liu and D. Tsai, Phys. Rev. B 65, 155423 (2002).
[CrossRef]

F. J. García-Vidall and L. Martín-Moreno, Phys. Rev. B 66, 155412 (2002).
[CrossRef]

F. Yang, J. R. Sambles, and G. W. Bradberry, Phys. Rev. B 44, 5855 (1991).
[CrossRef]

Phys. Rev. Lett. (1)

L. Martín-Moreno, F. J. García-Vidall, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

Other (2)

W. Ehrenberg, Electric Conduction in Semiconductors and Metals (Clarendon, Oxford, 1958).

E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

(a) Measured transmitted terahertz pulses and (b) the corresponding spectra through reference and samples (multiplied by two). The curves in (a) and (b) are displaced vertically for clarity.

Fig. 2
Fig. 2

(a) Spectra of the measured transmission magnitude of the signal pulse compared with the reference pulse and (b) the corresponding comparative phase change in radians for 80 µm×100 µm rectangular hole arrays (sample A, without zero pad, filled squares; three times zero pad, open squares) and 100-µm-diameter circular hole arrays (sample B without zero pad, filled circles; three times zero pad, open circles). In (a) the spectrum of sample B is moved up by 0.1, and in (b) the phase change of sample B is moved down by 0.1 for clarity. The dashed lines indicate the SP frequencies.

Equations (6)

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ksp=k01r2+12+i221/2e2+e4+12i221/221/2,
kspk01.
λresonance=Lm2+n21.
Sx=S0 exp-kix,
ki=k01r2+12+i221/2×1i22e2+e4+12i221/21/2.
ki=k013/22i2.

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