Abstract

We report the development of new terahertz (THz) techniques for rapidly measuring the complex Faraday angle in systems with broken time-reversal symmetry. Using the cyclotron resonance of a GaAs two-dimensional electron gas in a magnetic field, we have tested the performance of the techniques. We have made polarization modulation, high sensitivity (<1mrad) narrowband rotation measurements with a cw optically pumped molecular gas laser, and, by combining the distinct advantages of THz time domain spectroscopy and polarization modulation techniques, we have demonstrated rapid broadband rotation measurements to <5mrad precision.

© 2012 Optical Society of America

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  1. T. Morimoto, Y. Hatsugai, and H. Aoki, “Optical Hall conductivity in ordinary and graphene quantum Hall systems,” Phys. Rev. Lett. 103, 116803 (2009).
    [CrossRef]
  2. T. Morimoto, Y. Avishai, and H. Aoki, “Dynamical scaling analysis of the optical Hall conductivity in the quantum Hall regime,” Phys. Rev. B 82081404 (2010).
    [CrossRef]
  3. Y. Ikebe, T. Morimoto, R. Masutomi, T. Okamoto, H. Aoki, and R. Shimano, “Optical Hall effect in the integer quantum Hall regime,” Phys. Rev. Lett. 104, 256802 (2010).
    [CrossRef]
  4. W.-K. Tse and A. H. MacDonald, “Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators,” Phys. Rev. Lett. 105, 057401 (2010).
    [CrossRef]
  5. R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).
  6. G. S. Jenkins, D. C. Schmadel, and H. D. Drew, “Simultaneous measurement of circular dichroism and Faraday rotation at terahertz frequencies utilizing electric field sensitive detection via polarization,” Rev. Sci. Instrum. 81083903 (2010).
    [CrossRef]
  7. D. C. Schmadel, G. S. Jenkins, J. J. Tu, G. D. Gu, H. Kontani, and H. D. Drew, “Infrared Hall conductivity in optimally doped Bi2Sr2CaCu2O8+δ: Drude behavior examined by experiment and fluctuation-exchange-model calculations,” Phys. Rev. B 75, 140506 (2007).
    [CrossRef]
  8. M.-H. Kim, G. Acbas, M.-H. Yang, I. Ohkubo, H. Christen, D. Mandrus, M. A. Scarpulla, O. D. Dubon, Z. Schlesinger, P. Khalifah, and J. Cerne, “Determination of the infrared complex magnetoconductivity tensor in itinerant ferromagnets from Faraday and Kerr measurements,” Phys. Rev. B 75, 214416 (2007).
  9. J. Černe, D. C. Schmadel, M. Grayson, G. S. Jenkins, J. R. Simpson, and H. D. Drew, “Midinfrared Hall effect in thin-film metals: probing the Fermi surface anisotropy in Au and Cu,” Phys. Rev. B 61, 8133–8140 (2000).
  10. I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).
  11. A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, and J. Cerne, “THz quantum Hall conductivity studies in a GaAs heterojunction,” AIP Conference Proceedings, Vol. 1399 (American Institute of Physics, 2011), pp. 627–628.
    [CrossRef]
  12. A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, T. Morimoto, H. Aoki, and J. Cerne, “Terahertz dynamics of a topologically protected state: quantum Hall effect plateaus near cyclotron resonance in a GaAs/AlGaAs heterojunction,” Phys. Rev. Lett. (to be published), http://arxiv.org/abs/1201.0182 .
  13. H. Sumikura, T. Nagashima, H. Kitahara, and M. Hangyo, “Development of a cryogen-free terahertz time-domain magnetooptical measurement system,” Jpn. J. Appl. Phys. 46, 1739 (2007).
    [CrossRef]
  14. 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]
  15. M. B. Byrne, M. U. Shaukat, J. E. Cunningham, E. H. Linfield, and A. G. Davies, “Simultaneous measurement of orthogonal components of polarization in a free-space propagating terahertz signal using electro-optic detection,” Appl. Phys. Lett. 98, 151104 (2011).
    [CrossRef]
  16. M. Grayson, L. B. Rigal, D. C. Schmadel, H. D. Drew, and P.-J. Kung, “Spectral measurement of the Hall angle response in normal state cuprate superconductors,” Phys. Rev. Lett. 89, 037003 (2002).
    [CrossRef]
  17. K. W. Chiu, T. K. Lee, and J. J. Quinn, “Infrared magneto-transmittance of a two-dimensional electron gas,” Surf. Sci. 58, 182–184 (1976).
    [CrossRef]
  18. H. Piller, “Effect of internal reflection on optical Faraday rotation,” J. Appl. Phys. 37, 763–767 (1966).
    [CrossRef]
  19. H. Piller, “Far infrared Faraday rotation in a two-dimensional electron gas,” J. Vac. Sci. Technol. 16, 2096–2100 (1979).
    [CrossRef]
  20. J. P. Cheng, Y. J. Wang, B. D. McCombe, and W. Schaff, “Many-electron effects on quasi-two-dimensional shallow-donor impurity states in high magnetic fields,” Phys. Rev. Lett. 70, 489–492 (1993).
    [CrossRef]
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    [CrossRef]
  22. J. Kono, S. T. Lee, M. S. Salib, G. S. Herold, A. Petrou, and B. D. McCombe, “Optically detected far-infrared resonances in doped GaAs quantum wells,” Phys. Rev. B 52, R8654–R8657 (1995).
    [CrossRef]
  23. D. Grischkowsky, S. Keiding, M. VanExter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990).
  24. Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
    [CrossRef]
  25. P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18, 313–317 (2001).
    [CrossRef]
  26. S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, “Observation of the quasiparticle Hall effect in superconducting YBa2Cu3O7−δ,” Phys. Rev. Lett. 73, 1537–1540 (1994).
    [CrossRef]
  27. K. Yatsugi, N. Matsumoto, T. Nagashima, and M. Hangyo, “Transport properties of free carriers in semiconductors studied by terahertz time-domain magneto-optical ellipsometry,” Appl. Phys. Lett. 98, 212108 (2011).
    [CrossRef]

2012 (1)

R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).

2011 (3)

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).

M. B. Byrne, M. U. Shaukat, J. E. Cunningham, E. H. Linfield, and A. G. Davies, “Simultaneous measurement of orthogonal components of polarization in a free-space propagating terahertz signal using electro-optic detection,” Appl. Phys. Lett. 98, 151104 (2011).
[CrossRef]

K. Yatsugi, N. Matsumoto, T. Nagashima, and M. Hangyo, “Transport properties of free carriers in semiconductors studied by terahertz time-domain magneto-optical ellipsometry,” Appl. Phys. Lett. 98, 212108 (2011).
[CrossRef]

2010 (4)

T. Morimoto, Y. Avishai, and H. Aoki, “Dynamical scaling analysis of the optical Hall conductivity in the quantum Hall regime,” Phys. Rev. B 82081404 (2010).
[CrossRef]

Y. Ikebe, T. Morimoto, R. Masutomi, T. Okamoto, H. Aoki, and R. Shimano, “Optical Hall effect in the integer quantum Hall regime,” Phys. Rev. Lett. 104, 256802 (2010).
[CrossRef]

W.-K. Tse and A. H. MacDonald, “Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators,” Phys. Rev. Lett. 105, 057401 (2010).
[CrossRef]

G. S. Jenkins, D. C. Schmadel, and H. D. Drew, “Simultaneous measurement of circular dichroism and Faraday rotation at terahertz frequencies utilizing electric field sensitive detection via polarization,” Rev. Sci. Instrum. 81083903 (2010).
[CrossRef]

2009 (1)

T. Morimoto, Y. Hatsugai, and H. Aoki, “Optical Hall conductivity in ordinary and graphene quantum Hall systems,” Phys. Rev. Lett. 103, 116803 (2009).
[CrossRef]

2007 (3)

D. C. Schmadel, G. S. Jenkins, J. J. Tu, G. D. Gu, H. Kontani, and H. D. Drew, “Infrared Hall conductivity in optimally doped Bi2Sr2CaCu2O8+δ: Drude behavior examined by experiment and fluctuation-exchange-model calculations,” Phys. Rev. B 75, 140506 (2007).
[CrossRef]

M.-H. Kim, G. Acbas, M.-H. Yang, I. Ohkubo, H. Christen, D. Mandrus, M. A. Scarpulla, O. D. Dubon, Z. Schlesinger, P. Khalifah, and J. Cerne, “Determination of the infrared complex magnetoconductivity tensor in itinerant ferromagnets from Faraday and Kerr measurements,” Phys. Rev. B 75, 214416 (2007).

H. Sumikura, T. Nagashima, H. Kitahara, and M. Hangyo, “Development of a cryogen-free terahertz time-domain magnetooptical measurement system,” Jpn. J. Appl. Phys. 46, 1739 (2007).
[CrossRef]

2002 (1)

M. Grayson, L. B. Rigal, D. C. Schmadel, H. D. Drew, and P.-J. Kung, “Spectral measurement of the Hall angle response in normal state cuprate superconductors,” Phys. Rev. Lett. 89, 037003 (2002).
[CrossRef]

2001 (1)

2000 (1)

J. Černe, D. C. Schmadel, M. Grayson, G. S. Jenkins, J. R. Simpson, and H. D. Drew, “Midinfrared Hall effect in thin-film metals: probing the Fermi surface anisotropy in Au and Cu,” Phys. Rev. B 61, 8133–8140 (2000).

1997 (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]

1995 (2)

J. Kono, S. T. Lee, M. S. Salib, G. S. Herold, A. Petrou, and B. D. McCombe, “Optically detected far-infrared resonances in doped GaAs quantum wells,” Phys. Rev. B 52, R8654–R8657 (1995).
[CrossRef]

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

1994 (1)

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, “Observation of the quasiparticle Hall effect in superconducting YBa2Cu3O7−δ,” Phys. Rev. Lett. 73, 1537–1540 (1994).
[CrossRef]

1993 (1)

J. P. Cheng, Y. J. Wang, B. D. McCombe, and W. Schaff, “Many-electron effects on quasi-two-dimensional shallow-donor impurity states in high magnetic fields,” Phys. Rev. Lett. 70, 489–492 (1993).
[CrossRef]

1990 (2)

1979 (1)

H. Piller, “Far infrared Faraday rotation in a two-dimensional electron gas,” J. Vac. Sci. Technol. 16, 2096–2100 (1979).
[CrossRef]

1976 (1)

K. W. Chiu, T. K. Lee, and J. J. Quinn, “Infrared magneto-transmittance of a two-dimensional electron gas,” Surf. Sci. 58, 182–184 (1976).
[CrossRef]

1966 (1)

H. Piller, “Effect of internal reflection on optical Faraday rotation,” J. Appl. Phys. 37, 763–767 (1966).
[CrossRef]

Acbas, G.

M.-H. Kim, G. Acbas, M.-H. Yang, I. Ohkubo, H. Christen, D. Mandrus, M. A. Scarpulla, O. D. Dubon, Z. Schlesinger, P. Khalifah, and J. Cerne, “Determination of the infrared complex magnetoconductivity tensor in itinerant ferromagnets from Faraday and Kerr measurements,” Phys. Rev. B 75, 214416 (2007).

Aguilar, R. Valdés

R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).

Aoki, H.

Y. Ikebe, T. Morimoto, R. Masutomi, T. Okamoto, H. Aoki, and R. Shimano, “Optical Hall effect in the integer quantum Hall regime,” Phys. Rev. Lett. 104, 256802 (2010).
[CrossRef]

T. Morimoto, Y. Avishai, and H. Aoki, “Dynamical scaling analysis of the optical Hall conductivity in the quantum Hall regime,” Phys. Rev. B 82081404 (2010).
[CrossRef]

T. Morimoto, Y. Hatsugai, and H. Aoki, “Optical Hall conductivity in ordinary and graphene quantum Hall systems,” Phys. Rev. Lett. 103, 116803 (2009).
[CrossRef]

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, T. Morimoto, H. Aoki, and J. Cerne, “Terahertz dynamics of a topologically protected state: quantum Hall effect plateaus near cyclotron resonance in a GaAs/AlGaAs heterojunction,” Phys. Rev. Lett. (to be published), http://arxiv.org/abs/1201.0182 .

Armitage, N. P.

R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).

Avishai, Y.

T. Morimoto, Y. Avishai, and H. Aoki, “Dynamical scaling analysis of the optical Hall conductivity in the quantum Hall regime,” Phys. Rev. B 82081404 (2010).
[CrossRef]

Bakker, H. J.

Bansal, N.

R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).

Bilbro, L. S.

R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).

Bostwick, A.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).

Byrne, M. B.

M. B. Byrne, M. U. Shaukat, J. E. Cunningham, E. H. Linfield, and A. G. Davies, “Simultaneous measurement of orthogonal components of polarization in a free-space propagating terahertz signal using electro-optic detection,” Appl. Phys. Lett. 98, 151104 (2011).
[CrossRef]

Cerne, J.

R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).

M.-H. Kim, G. Acbas, M.-H. Yang, I. Ohkubo, H. Christen, D. Mandrus, M. A. Scarpulla, O. D. Dubon, Z. Schlesinger, P. Khalifah, and J. Cerne, “Determination of the infrared complex magnetoconductivity tensor in itinerant ferromagnets from Faraday and Kerr measurements,” Phys. Rev. B 75, 214416 (2007).

J. Černe, D. C. Schmadel, M. Grayson, G. S. Jenkins, J. R. Simpson, and H. D. Drew, “Midinfrared Hall effect in thin-film metals: probing the Fermi surface anisotropy in Au and Cu,” Phys. Rev. B 61, 8133–8140 (2000).

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, and J. Cerne, “THz quantum Hall conductivity studies in a GaAs heterojunction,” AIP Conference Proceedings, Vol. 1399 (American Institute of Physics, 2011), pp. 627–628.
[CrossRef]

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, T. Morimoto, H. Aoki, and J. Cerne, “Terahertz dynamics of a topologically protected state: quantum Hall effect plateaus near cyclotron resonance in a GaAs/AlGaAs heterojunction,” Phys. Rev. Lett. (to be published), http://arxiv.org/abs/1201.0182 .

Cheng, J. P.

J. P. Cheng, Y. J. Wang, B. D. McCombe, and W. Schaff, “Many-electron effects on quasi-two-dimensional shallow-donor impurity states in high magnetic fields,” Phys. Rev. Lett. 70, 489–492 (1993).
[CrossRef]

Chiu, K. W.

K. W. Chiu, T. K. Lee, and J. J. Quinn, “Infrared magneto-transmittance of a two-dimensional electron gas,” Surf. Sci. 58, 182–184 (1976).
[CrossRef]

Christen, H.

M.-H. Kim, G. Acbas, M.-H. Yang, I. Ohkubo, H. Christen, D. Mandrus, M. A. Scarpulla, O. D. Dubon, Z. Schlesinger, P. Khalifah, and J. Cerne, “Determination of the infrared complex magnetoconductivity tensor in itinerant ferromagnets from Faraday and Kerr measurements,” Phys. Rev. B 75, 214416 (2007).

Clarke, J.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, “Observation of the quasiparticle Hall effect in superconducting YBa2Cu3O7−δ,” Phys. Rev. Lett. 73, 1537–1540 (1994).
[CrossRef]

Crassee, I.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).

Cunningham, J.

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]

Cunningham, J. E.

M. B. Byrne, M. U. Shaukat, J. E. Cunningham, E. H. Linfield, and A. G. Davies, “Simultaneous measurement of orthogonal components of polarization in a free-space propagating terahertz signal using electro-optic detection,” Appl. Phys. Lett. 98, 151104 (2011).
[CrossRef]

Davies, A. G.

M. B. Byrne, M. U. Shaukat, J. E. Cunningham, E. H. Linfield, and A. G. Davies, “Simultaneous measurement of orthogonal components of polarization in a free-space propagating terahertz signal using electro-optic detection,” Appl. Phys. Lett. 98, 151104 (2011).
[CrossRef]

Drew, H. D.

G. S. Jenkins, D. C. Schmadel, and H. D. Drew, “Simultaneous measurement of circular dichroism and Faraday rotation at terahertz frequencies utilizing electric field sensitive detection via polarization,” Rev. Sci. Instrum. 81083903 (2010).
[CrossRef]

D. C. Schmadel, G. S. Jenkins, J. J. Tu, G. D. Gu, H. Kontani, and H. D. Drew, “Infrared Hall conductivity in optimally doped Bi2Sr2CaCu2O8+δ: Drude behavior examined by experiment and fluctuation-exchange-model calculations,” Phys. Rev. B 75, 140506 (2007).
[CrossRef]

M. Grayson, L. B. Rigal, D. C. Schmadel, H. D. Drew, and P.-J. Kung, “Spectral measurement of the Hall angle response in normal state cuprate superconductors,” Phys. Rev. Lett. 89, 037003 (2002).
[CrossRef]

J. Černe, D. C. Schmadel, M. Grayson, G. S. Jenkins, J. R. Simpson, and H. D. Drew, “Midinfrared Hall effect in thin-film metals: probing the Fermi surface anisotropy in Au and Cu,” Phys. Rev. B 61, 8133–8140 (2000).

Dubon, O. D.

M.-H. Kim, G. Acbas, M.-H. Yang, I. Ohkubo, H. Christen, D. Mandrus, M. A. Scarpulla, O. D. Dubon, Z. Schlesinger, P. Khalifah, and J. Cerne, “Determination of the infrared complex magnetoconductivity tensor in itinerant ferromagnets from Faraday and Kerr measurements,” Phys. Rev. B 75, 214416 (2007).

Eason, D.

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, and J. Cerne, “THz quantum Hall conductivity studies in a GaAs heterojunction,” AIP Conference Proceedings, Vol. 1399 (American Institute of Physics, 2011), pp. 627–628.
[CrossRef]

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, T. Morimoto, H. Aoki, and J. Cerne, “Terahertz dynamics of a topologically protected state: quantum Hall effect plateaus near cyclotron resonance in a GaAs/AlGaAs heterojunction,” Phys. Rev. Lett. (to be published), http://arxiv.org/abs/1201.0182 .

Ellis, C. T.

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, T. Morimoto, H. Aoki, and J. Cerne, “Terahertz dynamics of a topologically protected state: quantum Hall effect plateaus near cyclotron resonance in a GaAs/AlGaAs heterojunction,” Phys. Rev. Lett. (to be published), http://arxiv.org/abs/1201.0182 .

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, and J. Cerne, “THz quantum Hall conductivity studies in a GaAs heterojunction,” AIP Conference Proceedings, Vol. 1399 (American Institute of Physics, 2011), pp. 627–628.
[CrossRef]

Etienne, B.

S. Huant, S. P. Najda, and B. Etienne, “Two-dimensional D− centers,” Phys. Rev. Lett. 65, 1486–1489 (1990).
[CrossRef]

Fattinger, C.

George, D. K.

R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).

Geva, M.

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]

Grayson, M.

M. Grayson, L. B. Rigal, D. C. Schmadel, H. D. Drew, and P.-J. Kung, “Spectral measurement of the Hall angle response in normal state cuprate superconductors,” Phys. Rev. Lett. 89, 037003 (2002).
[CrossRef]

J. Černe, D. C. Schmadel, M. Grayson, G. S. Jenkins, J. R. Simpson, and H. D. Drew, “Midinfrared Hall effect in thin-film metals: probing the Fermi surface anisotropy in Au and Cu,” Phys. Rev. B 61, 8133–8140 (2000).

Grischkowsky, D.

Gu, G. D.

D. C. Schmadel, G. S. Jenkins, J. J. Tu, G. D. Gu, H. Kontani, and H. D. Drew, “Infrared Hall conductivity in optimally doped Bi2Sr2CaCu2O8+δ: Drude behavior examined by experiment and fluctuation-exchange-model calculations,” Phys. Rev. B 75, 140506 (2007).
[CrossRef]

Hangyo, M.

K. Yatsugi, N. Matsumoto, T. Nagashima, and M. Hangyo, “Transport properties of free carriers in semiconductors studied by terahertz time-domain magneto-optical ellipsometry,” Appl. Phys. Lett. 98, 212108 (2011).
[CrossRef]

H. Sumikura, T. Nagashima, H. Kitahara, and M. Hangyo, “Development of a cryogen-free terahertz time-domain magnetooptical measurement system,” Jpn. J. Appl. Phys. 46, 1739 (2007).
[CrossRef]

Hatsugai, Y.

T. Morimoto, Y. Hatsugai, and H. Aoki, “Optical Hall conductivity in ordinary and graphene quantum Hall systems,” Phys. Rev. Lett. 103, 116803 (2009).
[CrossRef]

Herold, G. S.

J. Kono, S. T. Lee, M. S. Salib, G. S. Herold, A. Petrou, and B. D. McCombe, “Optically detected far-infrared resonances in doped GaAs quantum wells,” Phys. Rev. B 52, R8654–R8657 (1995).
[CrossRef]

Huant, S.

S. Huant, S. P. Najda, and B. Etienne, “Two-dimensional D− centers,” Phys. Rev. Lett. 65, 1486–1489 (1990).
[CrossRef]

Ikebe, Y.

Y. Ikebe, T. Morimoto, R. Masutomi, T. Okamoto, H. Aoki, and R. Shimano, “Optical Hall effect in the integer quantum Hall regime,” Phys. Rev. Lett. 104, 256802 (2010).
[CrossRef]

Jenkins, G. S.

G. S. Jenkins, D. C. Schmadel, and H. D. Drew, “Simultaneous measurement of circular dichroism and Faraday rotation at terahertz frequencies utilizing electric field sensitive detection via polarization,” Rev. Sci. Instrum. 81083903 (2010).
[CrossRef]

D. C. Schmadel, G. S. Jenkins, J. J. Tu, G. D. Gu, H. Kontani, and H. D. Drew, “Infrared Hall conductivity in optimally doped Bi2Sr2CaCu2O8+δ: Drude behavior examined by experiment and fluctuation-exchange-model calculations,” Phys. Rev. B 75, 140506 (2007).
[CrossRef]

J. Černe, D. C. Schmadel, M. Grayson, G. S. Jenkins, J. R. Simpson, and H. D. Drew, “Midinfrared Hall effect in thin-film metals: probing the Fermi surface anisotropy in Au and Cu,” Phys. Rev. B 61, 8133–8140 (2000).

Keiding, S.

Khalifah, P.

M.-H. Kim, G. Acbas, M.-H. Yang, I. Ohkubo, H. Christen, D. Mandrus, M. A. Scarpulla, O. D. Dubon, Z. Schlesinger, P. Khalifah, and J. Cerne, “Determination of the infrared complex magnetoconductivity tensor in itinerant ferromagnets from Faraday and Kerr measurements,” Phys. Rev. B 75, 214416 (2007).

Kim, M.-H.

M.-H. Kim, G. Acbas, M.-H. Yang, I. Ohkubo, H. Christen, D. Mandrus, M. A. Scarpulla, O. D. Dubon, Z. Schlesinger, P. Khalifah, and J. Cerne, “Determination of the infrared complex magnetoconductivity tensor in itinerant ferromagnets from Faraday and Kerr measurements,” Phys. Rev. B 75, 214416 (2007).

Kitahara, H.

H. Sumikura, T. Nagashima, H. Kitahara, and M. Hangyo, “Development of a cryogen-free terahertz time-domain magnetooptical measurement system,” Jpn. J. Appl. Phys. 46, 1739 (2007).
[CrossRef]

Kono, J.

J. Kono, S. T. Lee, M. S. Salib, G. S. Herold, A. Petrou, and B. D. McCombe, “Optically detected far-infrared resonances in doped GaAs quantum wells,” Phys. Rev. B 52, R8654–R8657 (1995).
[CrossRef]

Kontani, H.

D. C. Schmadel, G. S. Jenkins, J. J. Tu, G. D. Gu, H. Kontani, and H. D. Drew, “Infrared Hall conductivity in optimally doped Bi2Sr2CaCu2O8+δ: Drude behavior examined by experiment and fluctuation-exchange-model calculations,” Phys. Rev. B 75, 140506 (2007).
[CrossRef]

Kung, P.-J.

M. Grayson, L. B. Rigal, D. C. Schmadel, H. D. Drew, and P.-J. Kung, “Spectral measurement of the Hall angle response in normal state cuprate superconductors,” Phys. Rev. Lett. 89, 037003 (2002).
[CrossRef]

Kuzmenko, A. B.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).

Lee, S. T.

J. Kono, S. T. Lee, M. S. Salib, G. S. Herold, A. Petrou, and B. D. McCombe, “Optically detected far-infrared resonances in doped GaAs quantum wells,” Phys. Rev. B 52, R8654–R8657 (1995).
[CrossRef]

Lee, T. K.

K. W. Chiu, T. K. Lee, and J. J. Quinn, “Infrared magneto-transmittance of a two-dimensional electron gas,” Surf. Sci. 58, 182–184 (1976).
[CrossRef]

Levallois, J.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).

Lew, D. J.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, “Observation of the quasiparticle Hall effect in superconducting YBa2Cu3O7−δ,” Phys. Rev. Lett. 73, 1537–1540 (1994).
[CrossRef]

Linfield, E. H.

M. B. Byrne, M. U. Shaukat, J. E. Cunningham, E. H. Linfield, and A. G. Davies, “Simultaneous measurement of orthogonal components of polarization in a free-space propagating terahertz signal using electro-optic detection,” Appl. Phys. Lett. 98, 151104 (2011).
[CrossRef]

Liu, W.

R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).

Ludwig, F.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, “Observation of the quasiparticle Hall effect in superconducting YBa2Cu3O7−δ,” Phys. Rev. Lett. 73, 1537–1540 (1994).
[CrossRef]

MacDonald, A. H.

W.-K. Tse and A. H. MacDonald, “Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators,” Phys. Rev. Lett. 105, 057401 (2010).
[CrossRef]

Mandrus, D.

M.-H. Kim, G. Acbas, M.-H. Yang, I. Ohkubo, H. Christen, D. Mandrus, M. A. Scarpulla, O. D. Dubon, Z. Schlesinger, P. Khalifah, and J. Cerne, “Determination of the infrared complex magnetoconductivity tensor in itinerant ferromagnets from Faraday and Kerr measurements,” Phys. Rev. B 75, 214416 (2007).

Markelz, A. G.

R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).

Masutomi, R.

Y. Ikebe, T. Morimoto, R. Masutomi, T. Okamoto, H. Aoki, and R. Shimano, “Optical Hall effect in the integer quantum Hall regime,” Phys. Rev. Lett. 104, 256802 (2010).
[CrossRef]

Matsumoto, N.

K. Yatsugi, N. Matsumoto, T. Nagashima, and M. Hangyo, “Transport properties of free carriers in semiconductors studied by terahertz time-domain magneto-optical ellipsometry,” Appl. Phys. Lett. 98, 212108 (2011).
[CrossRef]

McCombe, B. D.

J. Kono, S. T. Lee, M. S. Salib, G. S. Herold, A. Petrou, and B. D. McCombe, “Optically detected far-infrared resonances in doped GaAs quantum wells,” Phys. Rev. B 52, R8654–R8657 (1995).
[CrossRef]

J. P. Cheng, Y. J. Wang, B. D. McCombe, and W. Schaff, “Many-electron effects on quasi-two-dimensional shallow-donor impurity states in high magnetic fields,” Phys. Rev. Lett. 70, 489–492 (1993).
[CrossRef]

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, and J. Cerne, “THz quantum Hall conductivity studies in a GaAs heterojunction,” AIP Conference Proceedings, Vol. 1399 (American Institute of Physics, 2011), pp. 627–628.
[CrossRef]

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, T. Morimoto, H. Aoki, and J. Cerne, “Terahertz dynamics of a topologically protected state: quantum Hall effect plateaus near cyclotron resonance in a GaAs/AlGaAs heterojunction,” Phys. Rev. Lett. (to be published), http://arxiv.org/abs/1201.0182 .

Merchant, P.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, “Observation of the quasiparticle Hall effect in superconducting YBa2Cu3O7−δ,” Phys. Rev. Lett. 73, 1537–1540 (1994).
[CrossRef]

Mittleman, D. M.

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]

Morimoto, T.

Y. Ikebe, T. Morimoto, R. Masutomi, T. Okamoto, H. Aoki, and R. Shimano, “Optical Hall effect in the integer quantum Hall regime,” Phys. Rev. Lett. 104, 256802 (2010).
[CrossRef]

T. Morimoto, Y. Avishai, and H. Aoki, “Dynamical scaling analysis of the optical Hall conductivity in the quantum Hall regime,” Phys. Rev. B 82081404 (2010).
[CrossRef]

T. Morimoto, Y. Hatsugai, and H. Aoki, “Optical Hall conductivity in ordinary and graphene quantum Hall systems,” Phys. Rev. Lett. 103, 116803 (2009).
[CrossRef]

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, T. Morimoto, H. Aoki, and J. Cerne, “Terahertz dynamics of a topologically protected state: quantum Hall effect plateaus near cyclotron resonance in a GaAs/AlGaAs heterojunction,” Phys. Rev. Lett. (to be published), http://arxiv.org/abs/1201.0182 .

Nagashima, T.

K. Yatsugi, N. Matsumoto, T. Nagashima, and M. Hangyo, “Transport properties of free carriers in semiconductors studied by terahertz time-domain magneto-optical ellipsometry,” Appl. Phys. Lett. 98, 212108 (2011).
[CrossRef]

H. Sumikura, T. Nagashima, H. Kitahara, and M. Hangyo, “Development of a cryogen-free terahertz time-domain magnetooptical measurement system,” Jpn. J. Appl. Phys. 46, 1739 (2007).
[CrossRef]

Najda, S. P.

S. Huant, S. P. Najda, and B. Etienne, “Two-dimensional D− centers,” Phys. Rev. Lett. 65, 1486–1489 (1990).
[CrossRef]

Nemeth, D. T.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, “Observation of the quasiparticle Hall effect in superconducting YBa2Cu3O7−δ,” Phys. Rev. Lett. 73, 1537–1540 (1994).
[CrossRef]

Nienhuys, H.-K.

Nuss, M. C.

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]

Oh, S.

R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).

Ohkubo, I.

M.-H. Kim, G. Acbas, M.-H. Yang, I. Ohkubo, H. Christen, D. Mandrus, M. A. Scarpulla, O. D. Dubon, Z. Schlesinger, P. Khalifah, and J. Cerne, “Determination of the infrared complex magnetoconductivity tensor in itinerant ferromagnets from Faraday and Kerr measurements,” Phys. Rev. B 75, 214416 (2007).

Okamoto, T.

Y. Ikebe, T. Morimoto, R. Masutomi, T. Okamoto, H. Aoki, and R. Shimano, “Optical Hall effect in the integer quantum Hall regime,” Phys. Rev. Lett. 104, 256802 (2010).
[CrossRef]

Orenstein, J.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, “Observation of the quasiparticle Hall effect in superconducting YBa2Cu3O7−δ,” Phys. Rev. Lett. 73, 1537–1540 (1994).
[CrossRef]

Ostler, M.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).

Parks, B.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, “Observation of the quasiparticle Hall effect in superconducting YBa2Cu3O7−δ,” Phys. Rev. Lett. 73, 1537–1540 (1994).
[CrossRef]

Petrou, A.

J. Kono, S. T. Lee, M. S. Salib, G. S. Herold, A. Petrou, and B. D. McCombe, “Optically detected far-infrared resonances in doped GaAs quantum wells,” Phys. Rev. B 52, R8654–R8657 (1995).
[CrossRef]

Piller, H.

H. Piller, “Far infrared Faraday rotation in a two-dimensional electron gas,” J. Vac. Sci. Technol. 16, 2096–2100 (1979).
[CrossRef]

H. Piller, “Effect of internal reflection on optical Faraday rotation,” J. Appl. Phys. 37, 763–767 (1966).
[CrossRef]

Planken, P. C. M.

Quinn, J. J.

K. W. Chiu, T. K. Lee, and J. J. Quinn, “Infrared magneto-transmittance of a two-dimensional electron gas,” Surf. Sci. 58, 182–184 (1976).
[CrossRef]

Rigal, L. B.

M. Grayson, L. B. Rigal, D. C. Schmadel, H. D. Drew, and P.-J. Kung, “Spectral measurement of the Hall angle response in normal state cuprate superconductors,” Phys. Rev. Lett. 89, 037003 (2002).
[CrossRef]

Rotenberg, E.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).

Salib, M. S.

J. Kono, S. T. Lee, M. S. Salib, G. S. Herold, A. Petrou, and B. D. McCombe, “Optically detected far-infrared resonances in doped GaAs quantum wells,” Phys. Rev. B 52, R8654–R8657 (1995).
[CrossRef]

Scarpulla, M. A.

M.-H. Kim, G. Acbas, M.-H. Yang, I. Ohkubo, H. Christen, D. Mandrus, M. A. Scarpulla, O. D. Dubon, Z. Schlesinger, P. Khalifah, and J. Cerne, “Determination of the infrared complex magnetoconductivity tensor in itinerant ferromagnets from Faraday and Kerr measurements,” Phys. Rev. B 75, 214416 (2007).

Schaff, W.

J. P. Cheng, Y. J. Wang, B. D. McCombe, and W. Schaff, “Many-electron effects on quasi-two-dimensional shallow-donor impurity states in high magnetic fields,” Phys. Rev. Lett. 70, 489–492 (1993).
[CrossRef]

Schlesinger, Z.

M.-H. Kim, G. Acbas, M.-H. Yang, I. Ohkubo, H. Christen, D. Mandrus, M. A. Scarpulla, O. D. Dubon, Z. Schlesinger, P. Khalifah, and J. Cerne, “Determination of the infrared complex magnetoconductivity tensor in itinerant ferromagnets from Faraday and Kerr measurements,” Phys. Rev. B 75, 214416 (2007).

Schmadel, D. C.

G. S. Jenkins, D. C. Schmadel, and H. D. Drew, “Simultaneous measurement of circular dichroism and Faraday rotation at terahertz frequencies utilizing electric field sensitive detection via polarization,” Rev. Sci. Instrum. 81083903 (2010).
[CrossRef]

D. C. Schmadel, G. S. Jenkins, J. J. Tu, G. D. Gu, H. Kontani, and H. D. Drew, “Infrared Hall conductivity in optimally doped Bi2Sr2CaCu2O8+δ: Drude behavior examined by experiment and fluctuation-exchange-model calculations,” Phys. Rev. B 75, 140506 (2007).
[CrossRef]

M. Grayson, L. B. Rigal, D. C. Schmadel, H. D. Drew, and P.-J. Kung, “Spectral measurement of the Hall angle response in normal state cuprate superconductors,” Phys. Rev. Lett. 89, 037003 (2002).
[CrossRef]

J. Černe, D. C. Schmadel, M. Grayson, G. S. Jenkins, J. R. Simpson, and H. D. Drew, “Midinfrared Hall effect in thin-film metals: probing the Fermi surface anisotropy in Au and Cu,” Phys. Rev. B 61, 8133–8140 (2000).

Seyller, T.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).

Shaukat, M. U.

M. B. Byrne, M. U. Shaukat, J. E. Cunningham, E. H. Linfield, and A. G. Davies, “Simultaneous measurement of orthogonal components of polarization in a free-space propagating terahertz signal using electro-optic detection,” Appl. Phys. Lett. 98, 151104 (2011).
[CrossRef]

Shimano, R.

Y. Ikebe, T. Morimoto, R. Masutomi, T. Okamoto, H. Aoki, and R. Shimano, “Optical Hall effect in the integer quantum Hall regime,” Phys. Rev. Lett. 104, 256802 (2010).
[CrossRef]

Simpson, J. R.

J. Černe, D. C. Schmadel, M. Grayson, G. S. Jenkins, J. R. Simpson, and H. D. Drew, “Midinfrared Hall effect in thin-film metals: probing the Fermi surface anisotropy in Au and Cu,” Phys. Rev. B 61, 8133–8140 (2000).

Spielman, S.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, “Observation of the quasiparticle Hall effect in superconducting YBa2Cu3O7−δ,” Phys. Rev. Lett. 73, 1537–1540 (1994).
[CrossRef]

Stier, A. V.

R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, and J. Cerne, “THz quantum Hall conductivity studies in a GaAs heterojunction,” AIP Conference Proceedings, Vol. 1399 (American Institute of Physics, 2011), pp. 627–628.
[CrossRef]

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, T. Morimoto, H. Aoki, and J. Cerne, “Terahertz dynamics of a topologically protected state: quantum Hall effect plateaus near cyclotron resonance in a GaAs/AlGaAs heterojunction,” Phys. Rev. Lett. (to be published), http://arxiv.org/abs/1201.0182 .

Strasser, G.

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, T. Morimoto, H. Aoki, and J. Cerne, “Terahertz dynamics of a topologically protected state: quantum Hall effect plateaus near cyclotron resonance in a GaAs/AlGaAs heterojunction,” Phys. Rev. Lett. (to be published), http://arxiv.org/abs/1201.0182 .

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, and J. Cerne, “THz quantum Hall conductivity studies in a GaAs heterojunction,” AIP Conference Proceedings, Vol. 1399 (American Institute of Physics, 2011), pp. 627–628.
[CrossRef]

Sumikura, H.

H. Sumikura, T. Nagashima, H. Kitahara, and M. Hangyo, “Development of a cryogen-free terahertz time-domain magnetooptical measurement system,” Jpn. J. Appl. Phys. 46, 1739 (2007).
[CrossRef]

Tse, W.-K.

W.-K. Tse and A. H. MacDonald, “Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators,” Phys. Rev. Lett. 105, 057401 (2010).
[CrossRef]

Tu, J. J.

D. C. Schmadel, G. S. Jenkins, J. J. Tu, G. D. Gu, H. Kontani, and H. D. Drew, “Infrared Hall conductivity in optimally doped Bi2Sr2CaCu2O8+δ: Drude behavior examined by experiment and fluctuation-exchange-model calculations,” Phys. Rev. B 75, 140506 (2007).
[CrossRef]

van der Marel, D.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).

VanExter, M.

Walter, A. L.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).

Wang, Y. J.

J. P. Cheng, Y. J. Wang, B. D. McCombe, and W. Schaff, “Many-electron effects on quasi-two-dimensional shallow-donor impurity states in high magnetic fields,” Phys. Rev. Lett. 70, 489–492 (1993).
[CrossRef]

Wenckebach, T.

Wu, L.

R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).

Wu, Q.

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

Yang, M.-H.

M.-H. Kim, G. Acbas, M.-H. Yang, I. Ohkubo, H. Christen, D. Mandrus, M. A. Scarpulla, O. D. Dubon, Z. Schlesinger, P. Khalifah, and J. Cerne, “Determination of the infrared complex magnetoconductivity tensor in itinerant ferromagnets from Faraday and Kerr measurements,” Phys. Rev. B 75, 214416 (2007).

Yatsugi, K.

K. Yatsugi, N. Matsumoto, T. Nagashima, and M. Hangyo, “Transport properties of free carriers in semiconductors studied by terahertz time-domain magneto-optical ellipsometry,” Appl. Phys. Lett. 98, 212108 (2011).
[CrossRef]

Zhang, H.

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, and J. Cerne, “THz quantum Hall conductivity studies in a GaAs heterojunction,” AIP Conference Proceedings, Vol. 1399 (American Institute of Physics, 2011), pp. 627–628.
[CrossRef]

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, T. Morimoto, H. Aoki, and J. Cerne, “Terahertz dynamics of a topologically protected state: quantum Hall effect plateaus near cyclotron resonance in a GaAs/AlGaAs heterojunction,” Phys. Rev. Lett. (to be published), http://arxiv.org/abs/1201.0182 .

Zhang, X.-C.

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

Appl. Phys. Lett. (4)

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]

M. B. Byrne, M. U. Shaukat, J. E. Cunningham, E. H. Linfield, and A. G. Davies, “Simultaneous measurement of orthogonal components of polarization in a free-space propagating terahertz signal using electro-optic detection,” Appl. Phys. Lett. 98, 151104 (2011).
[CrossRef]

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[CrossRef]

K. Yatsugi, N. Matsumoto, T. Nagashima, and M. Hangyo, “Transport properties of free carriers in semiconductors studied by terahertz time-domain magneto-optical ellipsometry,” Appl. Phys. Lett. 98, 212108 (2011).
[CrossRef]

J. Appl. Phys. (1)

H. Piller, “Effect of internal reflection on optical Faraday rotation,” J. Appl. Phys. 37, 763–767 (1966).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Vac. Sci. Technol. (1)

H. Piller, “Far infrared Faraday rotation in a two-dimensional electron gas,” J. Vac. Sci. Technol. 16, 2096–2100 (1979).
[CrossRef]

Jpn. J. Appl. Phys. (1)

H. Sumikura, T. Nagashima, H. Kitahara, and M. Hangyo, “Development of a cryogen-free terahertz time-domain magnetooptical measurement system,” Jpn. J. Appl. Phys. 46, 1739 (2007).
[CrossRef]

Nat. Phys. (1)

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).

Phys. Rev. B (5)

D. C. Schmadel, G. S. Jenkins, J. J. Tu, G. D. Gu, H. Kontani, and H. D. Drew, “Infrared Hall conductivity in optimally doped Bi2Sr2CaCu2O8+δ: Drude behavior examined by experiment and fluctuation-exchange-model calculations,” Phys. Rev. B 75, 140506 (2007).
[CrossRef]

M.-H. Kim, G. Acbas, M.-H. Yang, I. Ohkubo, H. Christen, D. Mandrus, M. A. Scarpulla, O. D. Dubon, Z. Schlesinger, P. Khalifah, and J. Cerne, “Determination of the infrared complex magnetoconductivity tensor in itinerant ferromagnets from Faraday and Kerr measurements,” Phys. Rev. B 75, 214416 (2007).

J. Černe, D. C. Schmadel, M. Grayson, G. S. Jenkins, J. R. Simpson, and H. D. Drew, “Midinfrared Hall effect in thin-film metals: probing the Fermi surface anisotropy in Au and Cu,” Phys. Rev. B 61, 8133–8140 (2000).

T. Morimoto, Y. Avishai, and H. Aoki, “Dynamical scaling analysis of the optical Hall conductivity in the quantum Hall regime,” Phys. Rev. B 82081404 (2010).
[CrossRef]

J. Kono, S. T. Lee, M. S. Salib, G. S. Herold, A. Petrou, and B. D. McCombe, “Optically detected far-infrared resonances in doped GaAs quantum wells,” Phys. Rev. B 52, R8654–R8657 (1995).
[CrossRef]

Phys. Rev. Lett. (8)

T. Morimoto, Y. Hatsugai, and H. Aoki, “Optical Hall conductivity in ordinary and graphene quantum Hall systems,” Phys. Rev. Lett. 103, 116803 (2009).
[CrossRef]

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Rev. Sci. Instrum. (1)

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Other (2)

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[CrossRef]

A. V. Stier, H. Zhang, C. T. Ellis, D. Eason, G. Strasser, B. D. McCombe, T. Morimoto, H. Aoki, and J. Cerne, “Terahertz dynamics of a topologically protected state: quantum Hall effect plateaus near cyclotron resonance in a GaAs/AlGaAs heterojunction,” Phys. Rev. Lett. (to be published), http://arxiv.org/abs/1201.0182 .

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Figures (7)

Fig. 1.
Fig. 1.

Schematics of the polarization change for a sample with off-diagonal transmission coefficients. a) Shows that for complex t˜ab=tabeiϕab, Et has a component perpendicular to the incident polarization and this Ety=E0tyx is shifted by a distance ΔL, which produces a phase delay relative to Et. Re(θ˜) is the rotation and Im(θ˜) is the ellipticity of the transmitted polarization. b) Shows that when all tab are real, there is a net magnitude change and a pure rotation.

Fig. 2.
Fig. 2.

Schematic of the NB-PMOTS.

Fig. 3.
Fig. 3.

The intensity at the detector, Idet, as a function of time is shown for two different incident polarization orientations. Prot indicates the orientation of the rotating polarizer. For a), the incident polarization is vertical corresponding to the t=0 orientation of the rotating polarizer and the phase of the 2ωrot signal ϕ=0. For b), the incident polarization is rotated from vertical by θ and the phase of the 2ωrot signal ϕ=2θ; see Eq. (9).

Fig. 4.
Fig. 4.

Data for NB-PMOTS. a) Calibration of the detected polarization rotation using a static polarizer at fixed angles. Note there is no noticeable transmission change for the 1° rotation occurring at 0.1 min; however, the Faraday rotation determined from the lock-in phase clearly resolves this rotation to 0.05° sensitivity. b) NB-PMOTS for a GaAs 2DEG as a function of magnetic field. Both a low field defect state (3.9 T) and the cyclotron resonance (6.3 T) are observed. Note that while the 3.9 T feature is barely resolved in the transmittance, it is clearly shown in the Faraday rotation.

Fig. 5.
Fig. 5.

a) Experimental setup for BB-PMOTS and b) extraction of frequency spectrum from THz pulse.

Fig. 6.
Fig. 6.

Measured rotation spectra using BB-PMOTS for three static polarizer orientations. The label on the curve is the actual rotation of the static polarizer.

Fig. 7.
Fig. 7.

Rotation a) and ellipticity b) near the cyclotron frequency for 2DEG in GaAs at ±3T: solid curves, BB-PMOTS; dashed curves, static crossed polarizer measurements.

Equations (14)

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E⃗t=(t˜xxt˜xyt˜yxt˜yy)(Eo0)=(txxeiϕxxtxyeiϕxytyxeiϕyxtyyeiϕyy)(Eo0)=Eo(txxeiϕxxtyxeiϕyx).
tan(θ˜)=t˜yxt˜xxθ˜.
tan(θ˜F)=σ˜xyσ˜xx(1+n˜s+1Z0σ˜xxd)1,
tan(θ˜K)=r˜xyr˜xxσ˜xyσ˜xx2.
Edet=(1000)(cos(ωrott)sin(ωrott)sin(ωrott)cos(ωrott))(t˜xxt˜xyt˜yxt˜yy)(E00).
IdetE02txx2cos2(ωrott)+2E02txxtyxcos(ϕxxϕxy)cos(ωrott)sin(ωrott)+E02tyxsin2(ωrott)(E02txx22+E02tyx22)+(E02txx22E02tyx22)cos(2ωrott)+E02txxtyxcos(ϕxxϕxy)sin(2ωrott).
S2ω,X=E022(txx2tyx2),
S2ω,Y=E02tyxtxxcos(ϕxxϕyx).
S2ω,YS2ω,X=tan(ϕ)=tan(2θ).
tan(ϕ)=2txxtyx(txx2tyx2)cos(ϕxxϕxy)2tyxtxxcos(ϕxxϕyx)=2Re(t˜yxt˜xx)=2Re(θ˜).
Edet=(1000)(t˜xxt˜xyt˜yxt˜yy)(cosωrottsinωrottsinωrottcosωrott)(1000)(cosωrottsinωrottsinωrottcosωrott)(E00).
Edet=t˜xxEcos2(ωrott)t˜xyEsin(ωrott)cos(ωrott)=t˜xxE2+t˜xxE2cos(2ωrott)t˜xyE 2sin(2ωrott).
X(ν)=txx(ν)E0(ν)eiϕxx(ν)Y(ν)=txy(ν)E0(ν)eiϕxy(ν),
Y(ν)X(ν)=txy(ν)txx(ν)ei(ϕxy(ν)ϕxx(ν)).

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