Abstract

We propose and demonstrate polarization rotation of a terahertz (THz) electromagnetic wave by using two-dimensional gratings consisting of two displaced layers of gold film with complimentary chiral patterns with four-fold symmetry. We develop a time domain THz polarimetry method with three wire grid polarizers and distinguish optical activity from optical anisotropy. We obtain the isotropic polarization rotation of a terahertz wave free from the birefringence of the structures. Results indicate the possibility of controlling THz polarization with artificial chiral structures fabricated with thin metal films.

© 2007 Optical Society of America

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  1. D. M. Mittleman, J. Cunningham, M. C. Nuss, and M. Geva, "Noncontact semiconductor wafer characterization with the terahertz Hall effect," Appl. Phys. Lett. 71, 16-18 (1997).
    [CrossRef]
  2. M. Walther, B. Fischer, M. Schall, H. Helm, and P. Uhd Jepsen, "Far-infrared vibrational spectra of all-trans, 9-cis and 13-cis retinal measured by THz time-domain spectroscopy," Chem. Phys. Lett. 332, 389-395 (2000).
    [CrossRef]
  3. N. Nagai, R. Kumazawa, and R. Fukuyama, "Direct evidence of inter-molecular vibrations by THz spectroscopy," Chem. Phys. Lett. 413, 495-500 (2005).
    [CrossRef]
  4. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, "Terahertz semiconductor-heterostructure laser," Nature 417, 156-159 (2003).
    [CrossRef]
  5. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum Cascade Laser," Science 264, 553-556 (1994).
    [CrossRef] [PubMed]
  6. T. Hofmann, U. Schade, C. M. Herzinger, P. Esquinazi, and M. Schubert, "Terahertz magneto-optic generalized ellipsometry using synchrotron and blackbody radiation," Rev. Sci. Instrum. 77, 063902 (2006).
    [CrossRef]
  7. B. Parks, S. Spielman, and J. Orenstein, "High-frequency Hall effect in the normal state of YBa2Cu3O7," Phys. Rev. B 56, 115-117 (1997).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  10. R. Shimano, Y. Ino, Yu. P. Svirko, and M. Kuwata-Gonokami, "Terahertz frequency Hall measurement by magneto-optical Kerr spectroscopy in InAs," Appl. Phys. Lett. 81, 199-201 (2002).
    [CrossRef]
  11. Y. Ino, R. Shimano, Yu. P. Svirko and M. Kuwata-Gonokami, "Terahertz time domain magneto-optical ellipsometry in reflection geometry," Phys. Rev. B 70, 155101 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. H.-T. Chen, J. F. O'Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, "Complementary planar terahertz metamaterials," Opt. Express. 15, 1084-1095 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  21. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science 305, 847-848 (2004).
    [CrossRef] [PubMed]
  22. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 10, 4785-4809 (1998).
    [CrossRef]
  23. K. Konishi, T. Sugimoto, B. Bai, Y. Svirko, and M. Kuwata-Gonokami, "Effect of surface plasmon resonance on the optical activity of chiral metal nanogratings," Opt. Express. 15, 9575-9583 (2007).
    [CrossRef] [PubMed]
  24. A. Rice, Y. Jin, X. F. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, "Terahertz optical rectification from <110> zinc-blende crystals," Appl. Phys. Lett. 64, 1324-1326 (1993).
    [CrossRef]
  25. Q. Wu, and X.-C. Zhang, "Ultrafast electro-optic field sensors," Appl. Phys. Lett. 68, 1604-1606 (1996).
    [CrossRef]
  26. F. Miyamaru, T. Kondo, T. Nagashima, and M. Hangyo, "Large polarization change in two-dimensional metallic photonic crystals in subterahertz region," Appl. Phys. Lett. 82, 2568-2570 (2003).
    [CrossRef]
  27. E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, and Y. Chen, "Giant optical gyrotropy due to electromagnetic coupling," Appl. Phys. Lett. 90, 223113 (2007).
    [CrossRef]
  28. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, 1975) 2nd Edition.

2007 (4)

M. Decker, M. W. Klein, M. Wegener, and S. Linden, "Circular dichroism of planar chiral magnetic metamaterials," Opt. Lett. 32, 856-858 (2007).
[CrossRef] [PubMed]

H.-T. Chen, J. F. O'Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, "Complementary planar terahertz metamaterials," Opt. Express. 15, 1084-1095 (2007).
[CrossRef] [PubMed]

K. Konishi, T. Sugimoto, B. Bai, Y. Svirko, and M. Kuwata-Gonokami, "Effect of surface plasmon resonance on the optical activity of chiral metal nanogratings," Opt. Express. 15, 9575-9583 (2007).
[CrossRef] [PubMed]

E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, and Y. Chen, "Giant optical gyrotropy due to electromagnetic coupling," Appl. Phys. Lett. 90, 223113 (2007).
[CrossRef]

2006 (4)

A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, "Giant Gyrotropy due to Electromagnetic-Field Coupling in a Bilayered Chiral Structure," Phys. Rev. Lett. 97, 177401 (2006).
[CrossRef] [PubMed]

F. Miyamaru, and M. Hangyo, "Strong optical activity in chiral metamaterials of metal screw hole arrays," Appl. Phys. Lett. 89, 211105 (2006).
[CrossRef]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

T. Hofmann, U. Schade, C. M. Herzinger, P. Esquinazi, and M. Schubert, "Terahertz magneto-optic generalized ellipsometry using synchrotron and blackbody radiation," Rev. Sci. Instrum. 77, 063902 (2006).
[CrossRef]

2005 (4)

K. Yamamoto, K. Tominaga, H. Sasakawa, A. Tamura, H. Murakami, H. Ohtake, and N. Sarukura, "Terahertz Time-Domain Spectroscopy of Amino Acids and Polypeptides," Biophys. J, L22-L24 (2005).
[CrossRef] [PubMed]

N. Nagai, R. Kumazawa, and R. Fukuyama, "Direct evidence of inter-molecular vibrations by THz spectroscopy," Chem. Phys. Lett. 413, 495-500 (2005).
[CrossRef]

N. C. J. van der Valk, W. A. M. van der Marel, and P. C. M. Planken, "Terahertz polarization imaging" Opt. Lett. 30, 2802-2804 (2005).
[CrossRef] [PubMed]

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, "Giant Optical Activity in Quasi-Two-Dimensional Planar Nanostructures," Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

2004 (2)

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

Y. Ino, R. Shimano, Yu. P. Svirko and M. Kuwata-Gonokami, "Terahertz time domain magneto-optical ellipsometry in reflection geometry," Phys. Rev. B 70, 155101 (2004).
[CrossRef]

2003 (3)

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, "Terahertz semiconductor-heterostructure laser," Nature 417, 156-159 (2003).
[CrossRef]

A. Papakostas, A. Potts, D.M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, "Optical Manifestations of Planar Chirality," Phys. Rev. Lett. 90, 107404 (2003).
[CrossRef] [PubMed]

F. Miyamaru, T. Kondo, T. Nagashima, and M. Hangyo, "Large polarization change in two-dimensional metallic photonic crystals in subterahertz region," Appl. Phys. Lett. 82, 2568-2570 (2003).
[CrossRef]

2002 (2)

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H Linfield, and M. Pepper, "Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue," Physics in Medicine and Biology 47, 3853-3863 (2002).
[CrossRef] [PubMed]

R. Shimano, Y. Ino, Yu. P. Svirko, and M. Kuwata-Gonokami, "Terahertz frequency Hall measurement by magneto-optical Kerr spectroscopy in InAs," Appl. Phys. Lett. 81, 199-201 (2002).
[CrossRef]

2000 (1)

M. Walther, B. Fischer, M. Schall, H. Helm, and P. Uhd Jepsen, "Far-infrared vibrational spectra of all-trans, 9-cis and 13-cis retinal measured by THz time-domain spectroscopy," Chem. Phys. Lett. 332, 389-395 (2000).
[CrossRef]

1998 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

1997 (2)

D. M. Mittleman, J. Cunningham, M. C. Nuss, and M. Geva, "Noncontact semiconductor wafer characterization with the terahertz Hall effect," Appl. Phys. Lett. 71, 16-18 (1997).
[CrossRef]

B. Parks, S. Spielman, and J. Orenstein, "High-frequency Hall effect in the normal state of YBa2Cu3O7," Phys. Rev. B 56, 115-117 (1997).
[CrossRef]

1996 (1)

Q. Wu, and X.-C. Zhang, "Ultrafast electro-optic field sensors," Appl. Phys. Lett. 68, 1604-1606 (1996).
[CrossRef]

1994 (1)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum Cascade Laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

1993 (1)

A. Rice, Y. Jin, X. F. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, "Terahertz optical rectification from <110> zinc-blende crystals," Appl. Phys. Lett. 64, 1324-1326 (1993).
[CrossRef]

1978 (1)

P. Yeh, "A new optical model for wire grid polarizers," Opt. Commun. 26, 289-292 (1978).
[CrossRef]

Appl. Phys. Lett. (7)

D. M. Mittleman, J. Cunningham, M. C. Nuss, and M. Geva, "Noncontact semiconductor wafer characterization with the terahertz Hall effect," Appl. Phys. Lett. 71, 16-18 (1997).
[CrossRef]

R. Shimano, Y. Ino, Yu. P. Svirko, and M. Kuwata-Gonokami, "Terahertz frequency Hall measurement by magneto-optical Kerr spectroscopy in InAs," Appl. Phys. Lett. 81, 199-201 (2002).
[CrossRef]

F. Miyamaru, and M. Hangyo, "Strong optical activity in chiral metamaterials of metal screw hole arrays," Appl. Phys. Lett. 89, 211105 (2006).
[CrossRef]

A. Rice, Y. Jin, X. F. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, "Terahertz optical rectification from <110> zinc-blende crystals," Appl. Phys. Lett. 64, 1324-1326 (1993).
[CrossRef]

Q. Wu, and X.-C. Zhang, "Ultrafast electro-optic field sensors," Appl. Phys. Lett. 68, 1604-1606 (1996).
[CrossRef]

F. Miyamaru, T. Kondo, T. Nagashima, and M. Hangyo, "Large polarization change in two-dimensional metallic photonic crystals in subterahertz region," Appl. Phys. Lett. 82, 2568-2570 (2003).
[CrossRef]

E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, and Y. Chen, "Giant optical gyrotropy due to electromagnetic coupling," Appl. Phys. Lett. 90, 223113 (2007).
[CrossRef]

Biophys. J (1)

K. Yamamoto, K. Tominaga, H. Sasakawa, A. Tamura, H. Murakami, H. Ohtake, and N. Sarukura, "Terahertz Time-Domain Spectroscopy of Amino Acids and Polypeptides," Biophys. J, L22-L24 (2005).
[CrossRef] [PubMed]

Chem. Phys. Lett. (2)

M. Walther, B. Fischer, M. Schall, H. Helm, and P. Uhd Jepsen, "Far-infrared vibrational spectra of all-trans, 9-cis and 13-cis retinal measured by THz time-domain spectroscopy," Chem. Phys. Lett. 332, 389-395 (2000).
[CrossRef]

N. Nagai, R. Kumazawa, and R. Fukuyama, "Direct evidence of inter-molecular vibrations by THz spectroscopy," Chem. Phys. Lett. 413, 495-500 (2005).
[CrossRef]

J. Phys.: Condens. Matter (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

Nature (2)

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, "Terahertz semiconductor-heterostructure laser," Nature 417, 156-159 (2003).
[CrossRef]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

Opt. Commun. (1)

P. Yeh, "A new optical model for wire grid polarizers," Opt. Commun. 26, 289-292 (1978).
[CrossRef]

Opt. Express. (2)

H.-T. Chen, J. F. O'Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, "Complementary planar terahertz metamaterials," Opt. Express. 15, 1084-1095 (2007).
[CrossRef] [PubMed]

K. Konishi, T. Sugimoto, B. Bai, Y. Svirko, and M. Kuwata-Gonokami, "Effect of surface plasmon resonance on the optical activity of chiral metal nanogratings," Opt. Express. 15, 9575-9583 (2007).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. B (2)

Y. Ino, R. Shimano, Yu. P. Svirko and M. Kuwata-Gonokami, "Terahertz time domain magneto-optical ellipsometry in reflection geometry," Phys. Rev. B 70, 155101 (2004).
[CrossRef]

B. Parks, S. Spielman, and J. Orenstein, "High-frequency Hall effect in the normal state of YBa2Cu3O7," Phys. Rev. B 56, 115-117 (1997).
[CrossRef]

Phys. Rev. Lett. (3)

A. Papakostas, A. Potts, D.M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, "Optical Manifestations of Planar Chirality," Phys. Rev. Lett. 90, 107404 (2003).
[CrossRef] [PubMed]

A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, "Giant Gyrotropy due to Electromagnetic-Field Coupling in a Bilayered Chiral Structure," Phys. Rev. Lett. 97, 177401 (2006).
[CrossRef] [PubMed]

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, "Giant Optical Activity in Quasi-Two-Dimensional Planar Nanostructures," Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Physics in Medicine and Biology (1)

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H Linfield, and M. Pepper, "Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue," Physics in Medicine and Biology 47, 3853-3863 (2002).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

T. Hofmann, U. Schade, C. M. Herzinger, P. Esquinazi, and M. Schubert, "Terahertz magneto-optic generalized ellipsometry using synchrotron and blackbody radiation," Rev. Sci. Instrum. 77, 063902 (2006).
[CrossRef]

Science (2)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum Cascade Laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

Other (1)

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, 1975) 2nd Edition.

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Figures (3)

Fig. 1.
Fig. 1.

(a). Experimental scheme and achiral, right- and left-twisted gammadion grating structures. When the linearly polarized incident THz wave is transmitted through the sample, the transmitted wave is polarized elliptically. Definition of the elliptical polarization with the polarization azimuth rotation angle θ and ellipticity η, which are defined in this figure. (b) Schematic figure of sample structure. Cross section of left-twisted structure is shown. (c) The three measurement configurations of the THz polarimetry with three wire grid polarizers (WGP’s).

Fig. 2.
Fig. 2.

Time domain THz waveforms of transmitted waves obtained in the cross-Nichol arrangement (a), with WGP2 -45°(b) and +45°(c). The green curves show a reference signal measured without sample. The red, blue and black curves show the signal for right- and left-twisted gammadion samples and cross-patterned samples, respectively. By Fourier transform, the x- and y- elements of the electric field in frequency domain are calculated and shown in (d) and (e). Absolute value of electric fields is shown in Fig. (d)

Fig. 3.
Fig. 3.

Absolute values of diagonal (a) and off-diagonal (b) elements of the Jones matrix of the sample. Spectra of rotation angle (c) and ellipticity (d). Effective complex dielectric tensor of the sample for left (blue) and right-twisted (red) gammadion samples and cross-patterned sample (black). Green curves show the results of the Si substrate. ((e)–(h))

Equations (6)

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

E ˜ sam = T ˜ E ˜ ref
[ t ˜ 1 t ˜ 2 ] = [ E ˜ x ref E ˜ y ref E ˜ y ref E ˜ x ref ] 1 [ E ˜ x sam E ˜ y sam ] .
θ = 1 2 arctan 2 Re ( t ˜ 1 t ˜ 2 * ) t ˜ 1 2 + t ˜ 2 2
η = 1 2 arcsin 2 Im ( t ˜ 1 t ˜ 2 * ) t ˜ 1 2 + t ˜ 2 2
t ˜ 1 = 2 1 + n ˜ 2 n ˜ 1 + n ˜ exp ( i ω ( n ˜ 1 ) L c ) ,
δ ˜ ε 0 = t ˜ 2 t ˜ 1 [ 1 2 1 n ˜ ( 1 + n ˜ ) + 1 2 1 n ˜ 2 ( 1 + n ˜ ) + 1 2 i ω L c n ˜ ] 1

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