Abstract

We have developed a terahertz time-domain polarimetry (THz-TDP) system by applying frequency modulation to electro-optic sampling detection in a nonlinear crystal. We characterized the precision of this system in determining the polarization angles to be 1.3° for fixed time delay, and 0.5° for complete time-domain waveform. Furthermore, we calculated the Jones matrix of the optical components used for beam propagation to calibrate the induced systematic error. The advantages of employing this calibration approach are demonstrated on a sapphire crystal investigated at different sample test positions in transmission configuration, and using high resistivity Si, AlN and quartz in reflection geometry. The new THz-TDP technique has the advantage of not using any external polarizers, and therefore is not constrained by their optical performance limitations, such as restricted bandwidths and frequency-dependent extinction ratio. Finally, the THz-TDP technique can be easily implemented on existing time-domain spectroscopy (TDS) systems.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (4)

K. A. Niessen, M. Xu, D. K. George, M. C. Chen, A. R. Ferré-D’Amaré, E. H. Snell, V. Cody, J. Pace, M. Schmidt, and A. G. Markelz, “Protein and RNA dynamical fingerprinting,” Nat. Commun. 10(1), 1026 (2019).
[Crossref]

W. J. Choi, G. Cheng, Z. Huang, S. Zhang, T. B. Norris, and N. A. Kotov, “Terahertz circular dichroism spectroscopy of biomaterials enabled by kirigami polarization modulators,” Nat. Mater. 18(8), 820–826 (2019).
[Crossref]

N. Sirica, R. I. Tobey, L. X. Zhao, G. F. Chen, B. Xu, R. Yang, B. Shen, D. A. Yarotski, P. Bowlan, S. A. Trugman, J. X. Zhu, Y. M. Dai, A. K. Azad, N. Ni, X. G. Qiu, A. J. Taylor, and R. P. Prasankumar, “Tracking Ultrafast Photocurrents in the Weyl Semimetal TaAs Using THz Emission Spectroscopy,” Phys. Rev. Lett. 122(19), 197401 (2019).
[Crossref]

M. A. Báez-Chorro and B. Vidal, “Single trace terahertz spectroscopic ellipsometry,” Opt. Express 27(24), 35468–35474 (2019).
[Crossref]

2018 (4)

X. Chen, E. P. J. Parrott, Z. Huang, H.-P. Chan, and E. Pickwell-MacPherson, “Robust and accurate terahertz time-domain spectroscopic ellipsometry,” Photonics Res. 6(8), 768–775 (2018).
[Crossref]

F. Sanjuan, G. Gaborit, and J.-L. Coutaz, “Full electro-optic terahertz time-domain spectrometer for polarimetric studies,” Appl. Opt. 57(21), 6055–6060 (2018).
[Crossref]

A. Pal, S. N. Shirodkar, P. Deshmukh, H. Surdi, B. R. Sangala, S. S. Prabhu, K. C. Rustagi, U. V. Waghmare, and P. Ayyub, “Rotation of terahertz radiation due to phonon-mediated magnetoelectric coupling in chiral selenium,” Phys. Rev. B 98(23), 235141 (2018).
[Crossref]

H. Plank, J. Pernul, S. Gebert, S. N. Danilov, J. König-Otto, S. Winnerl, M. Lanius, J. Kampmeier, G. Mussler, I. Aguilera, D. Grützmacher, and S. D. Ganichev, “Infrared/terahertz spectra of the photogalvanic effect in (Bi,Sb)Te based three-dimensional topological insulators,” Phys. Rev. Mater. 2(2), 024202 (2018).
[Crossref]

2017 (3)

A. Moriwaki, M. Okano, and S. Watanabe, “Internal triaxial strain imaging of visibly opaque black rubbers with terahertz polarization spectroscopy,” APL Photonics 2(10), 106101 (2017).
[Crossref]

Q. Jin, E. Yiwen, K. Williams, J. M. Dai, and X. C. Zhang, “Observation of broadband terahertz wave generation from liquid water,” Appl. Phys. Lett. 111(7), 071103 (2017).
[Crossref]

M. Okano, M. Fujii, and S. Watanabe, “Anisotropic percolation conduction in elastomer-carbon black composites investigated by polarization-sensitive terahertz time-domain spectroscopy,” Appl. Phys. Lett. 111(22), 221902 (2017).
[Crossref]

2016 (2)

M. Okano and S. Watanabe, “Anisotropic optical response of optically opaque elastomers with conductive fillers as revealed by terahertz polarization spectroscopy,” Sci. Rep. 6(1), 39079 (2016).
[Crossref]

K. Oguchi, H. Iwasaki, M. Okano, and S. Watanabe, “Polarization-sensitive electro-optic detection of terahertz wave using three different types of crystal symmetry: Toward broadband polarization spectroscopy,” Appl. Phys. Lett. 108(1), 011105 (2016).
[Crossref]

2015 (1)

2014 (4)

D. S. Bulgarevich, M. Watanabe, M. Shiwa, G. Niehues, S. Nishizawa, and M. Tani, “A polarization-sensitive 4-contact detector for terahertz time-domain spectroscopy,” Opt. Express 22(9), 10332–10340 (2014).
[Crossref]

N. Nemoto, T. Higuchi, N. Kanda, K. Konishi, and M. Kuwata-Gonokami, “Highly precise and accurate terahertz polarization measurements based on electro-optic sampling with polarization modulation of probe pulses,” Opt. Express 22(15), 17915–17929 (2014).
[Crossref]

N. Yasumatsu, A. Kasatani, K. Oguchi, and S. Watanabe, “High-speed terahertz time-domain polarimeter based on an electro-optic modulation technique,” Appl. Phys. Express 7(9), 092401 (2014).
[Crossref]

G. Acbas, K. A. Niessen, E. H. Snell, and A. G. Markelz, “Optical measurements of long-range protein vibrations,” Nat. Commun. 5(1), 3076 (2014).
[Crossref]

2013 (5)

Y. S. You, T. I. Oh, and K.-Y. Kim, “Mechanism of elliptically polarized terahertz generation in two-color laser filamentation,” Opt. Lett. 38(7), 1034–1036 (2013).
[Crossref]

T. Nagashima, M. Tani, and M. Hangyo, “Polarization-sensitive THz-TDS and its Application to Anisotropy Sensing,” J. Infrared, Millimeter, Terahertz Waves 34(11), 740–775 (2013).
[Crossref]

R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum Faraday and Kerr rotations in graphene,” Nat. Commun. 4(1), 1841 (2013).
[Crossref]

S. Watanabe, N. Yasumatsu, K. Oguchi, M. Takeda, T. Suzuki, and T. Tachizaki, “A Real-Time Terahertz Time-Domain Polarization Analyzer with 80-MHz Repetition-Rate Femtosecond Laser Pulses,” Sensors 13(3), 3299–3312 (2013).
[Crossref]

N. Yasumatsu and S. Watanabe, “Robustness of electric field vector sensing of electromagnetic waves by analyzing crystal angle dependence of the electro-optic effect,” J. Opt. Soc. Am. B 30(11), 2940–2951 (2013).
[Crossref]

2012 (9)

M. Neshat and N. P. Armitage, “Improved measurement of polarization state in terahertz polarization spectroscopy,” Opt. Lett. 37(11), 1811–1813 (2012).
[Crossref]

N. Yasumatsu and S. Watanabe, “Precise real-time polarization measurement of terahertz electromagnetic waves by a spinning electro-optic sensor,” Rev. Sci. Instrum. 83(2), 023104 (2012).
[Crossref]

D. K. George, A. V. Stier, C. T. Ellis, B. D. McCombe, J. Černe, and A. G. Markelz, “Terahertz magneto-optical polarization modulation spectroscopy,” J. Opt. Soc. Am. B 29(6), 1406–1412 (2012).
[Crossref]

C. M. Morris, R. V. Aguilar, A. V. Stier, and N. P. Armitage, “Polarization modulation time-domain terahertz polarimetry,” Opt. Express 20(11), 12303–12317 (2012).
[Crossref]

Z. Lü, D. Zhang, C. Meng, L. Sun, Z. Zhou, Z. Zhao, and J. Yuan, “Polarization-sensitive air-biased-coherent-detection for terahertz wave,” Appl. Phys. Lett. 101(8), 081119 (2012).
[Crossref]

E. Castro-Camus, “Polarization-Resolved Terahertz Time-Domain Spectroscopy,” J. Infrared, Millimeter, Terahertz Waves 33(4), 418–430 (2012).
[Crossref]

D. J. Aschaffenburg, M. R. C. Williams, D. Talbayev, D. F. Santavicca, D. E. Prober, and C. A. Schmuttenmaer, “Efficient measurement of broadband terahertz optical activity,” Appl. Phys. Lett. 100(24), 241114 (2012).
[Crossref]

J. F. Zhou, D. R. Chowdhury, R. K. Zhao, A. K. Azad, H. T. Chen, C. M. Soukoulis, A. J. Taylor, and J. F. O’Hara, “Terahertz chiral metamaterials with giant and dynamically tunable optical activity,” Phys. Rev. B 86(3), 035448 (2012).
[Crossref]

M. Neshat and N. P. Armitage, “Terahertz time-domain spectroscopic ellipsometry: instrumentation and calibration,” Opt. Express 20(27), 29063–29075 (2012).
[Crossref]

2011 (5)

A. M. Shuvaev, G. V. Astakhov, A. Pimenov, C. Brune, H. Buhmann, and L. W. Molenkamp, “Giant Magneto-Optical Faraday Effect in HgTe Thin Films in the Terahertz Spectral Range,” Phys. Rev. Lett. 106(10), 107404 (2011).
[Crossref]

N. Matsumoto, T. Hosokura, T. Nagashima, and M. Hangyo, “Measurement of the dielectric constant of thin films by terahertz time-domain spectroscopic ellipsometry,” Opt. Lett. 36(2), 265–267 (2011).
[Crossref]

Y. Kim, M. Yi, B. G. Kim, and J. Ahn, “Investigation of THz birefringence measurement and calculation in Al2O3 and LiNbO3,” Appl. Opt. 50(18), 2906–2910 (2011).
[Crossref]

H. Hoshina, Y. Morisawa, H. Sato, H. Minamide, I. Noda, Y. Ozaki, and C. Otani, “Polarization and temperature dependent spectra of poly(3-hydroxyalkanoate)s measured at terahertz frequencies,” Phys. Chem. Chem. Phys. 13(20), 9173–9179 (2011).
[Crossref]

R. Shimano, Y. Ikebe, K. S. Takahashi, M. Kawasaki, N. Nagaosa, and Y. Tokura, “Terahertz Faraday rotation induced by an anomalous Hall effect in the itinerant ferromagnet SrRuO3,” EPL 95(1), 17002 (2011).
[Crossref]

2010 (3)

X. Wang, Y. Cui, W. Sun, J. Ye, and Y. Zhang, “Terahertz polarization real-time imaging based on balanced electro-optic detection,” J. Opt. Soc. Am. A 27(11), 2387–2393 (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 modulation,” Rev. Sci. Instrum. 81(8), 083903 (2010).
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R. Singh, E. Plum, W. L. Zhang, and N. I. Zheludev, “Highly tunable optical activity in planar achiral terahertz metamaterials,” Opt. Express 18(13), 13425–13430 (2010).
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2009 (4)

L. Ren, C. L. Pint, L. G. Booshenri, W. D. Rice, X. F. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon Nanotube Terahertz Polarizer,” Nano Lett. 9(7), 2610–2613 (2009).
[Crossref]

Y. P. Chen, C. Marceau, S. Genier, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized Terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282(21), 4283–4287 (2009).
[Crossref]

J. M. Dai, N. Karpowicz, and X. C. Zhang, “Coherent Polarization Control of Terahertz Waves Generated from Two-Color Laser-Induced Gas Plasma,” Phys. Rev. Lett. 103(2), 023001 (2009).
[Crossref]

A. Y. Elezzabi and S. Sederberg, “Optical activity in an artificial chiral media: a terahertz time-domain investigation of Karl F. Lindman’s 1920 pioneering experiment,” Opt. Express 17(8), 6600–6612 (2009).
[Crossref]

2008 (3)

S. D. Ganichev, W. Weber, J. Kiermaier, S. N. Danilov, P. Olbrich, D. Schuh, W. Wegscheider, D. Bougeard, G. Abstreiter, and W. Prettl, “All-electric detection of the polarization state of terahertz laser radiation,” J. Appl. Phys. 103(11), 114504 (2008).
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R. Zhang, Y. Cui, W. Sun, and Y. Zhang, “Polarization information for terahertz imaging,” Appl. Opt. 47(34), 6422–6427 (2008).
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Y. Ikebe and R. Shimano, “Characterization of doped silicon in low carrier density region by terahertz frequency Faraday effect,” Appl. Phys. Lett. 92(1), 012111 (2008).
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2006 (4)

2005 (2)

E. Castro-Camus, J. Lloyd-Hughes, M. B. Johnston, M. D. Fraser, H. H. Tan, and C. Jagadish, “Polarization-sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86(25), 254102 (2005).
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N. C. J. van der Valk, W. A. M. van der Marel, and P. C. M. Planken, “Terahertz polarization imaging,” Opt. Lett. 30(20), 2802–2804 (2005).
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2004 (1)

2002 (2)

R. Shimano, Y. Ino, Y. P. Svirko, and M. Kuwata-Gonokami, “Terahertz frequency Hall measurement by magneto-optical Kerr spectroscopy in InAs,” Appl. Phys. Lett. 81(2), 199–201 (2002).
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M. Herrmann, M. Tani, K. Sakai, and R. Fukasawa, “Terahertz imaging of silicon wafers,” J. Appl. Phys. 91(3), 1247–1250 (2002).
[Crossref]

2001 (2)

T. Nagashima and M. Hangyo, “Measurement of complex optical constants of a highly doped Si wafer using terahertz ellipsometry,” Appl. Phys. Lett. 79(24), 3917–3919 (2001).
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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(3), 313–317 (2001).
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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(1), 16–18 (1997).
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1994 (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(11), 1324–1326 (1994).
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1990 (1)

1973 (1)

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S. D. Ganichev, W. Weber, J. Kiermaier, S. N. Danilov, P. Olbrich, D. Schuh, W. Wegscheider, D. Bougeard, G. Abstreiter, and W. Prettl, “All-electric detection of the polarization state of terahertz laser radiation,” J. Appl. Phys. 103(11), 114504 (2008).
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Acbas, G.

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Ahn, J.

Alexander, M.

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(11), 1324–1326 (1994).
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Aoki, H.

R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum Faraday and Kerr rotations in graphene,” Nat. Commun. 4(1), 1841 (2013).
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A. Pal, S. N. Shirodkar, P. Deshmukh, H. Surdi, B. R. Sangala, S. S. Prabhu, K. C. Rustagi, U. V. Waghmare, and P. Ayyub, “Rotation of terahertz radiation due to phonon-mediated magnetoelectric coupling in chiral selenium,” Phys. Rev. B 98(23), 235141 (2018).
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Azad, A. K.

N. Sirica, R. I. Tobey, L. X. Zhao, G. F. Chen, B. Xu, R. Yang, B. Shen, D. A. Yarotski, P. Bowlan, S. A. Trugman, J. X. Zhu, Y. M. Dai, A. K. Azad, N. Ni, X. G. Qiu, A. J. Taylor, and R. P. Prasankumar, “Tracking Ultrafast Photocurrents in the Weyl Semimetal TaAs Using THz Emission Spectroscopy,” Phys. Rev. Lett. 122(19), 197401 (2019).
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J. F. Zhou, D. R. Chowdhury, R. K. Zhao, A. K. Azad, H. T. Chen, C. M. Soukoulis, A. J. Taylor, and J. F. O’Hara, “Terahertz chiral metamaterials with giant and dynamically tunable optical activity,” Phys. Rev. B 86(3), 035448 (2012).
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Báez-Chorro, M. A.

Bakker, H. J.

Bliss, D.

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(11), 1324–1326 (1994).
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Booshenri, L. G.

L. Ren, C. L. Pint, L. G. Booshenri, W. D. Rice, X. F. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon Nanotube Terahertz Polarizer,” Nano Lett. 9(7), 2610–2613 (2009).
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N. Sirica, R. I. Tobey, L. X. Zhao, G. F. Chen, B. Xu, R. Yang, B. Shen, D. A. Yarotski, P. Bowlan, S. A. Trugman, J. X. Zhu, Y. M. Dai, A. K. Azad, N. Ni, X. G. Qiu, A. J. Taylor, and R. P. Prasankumar, “Tracking Ultrafast Photocurrents in the Weyl Semimetal TaAs Using THz Emission Spectroscopy,” Phys. Rev. Lett. 122(19), 197401 (2019).
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A. M. Shuvaev, G. V. Astakhov, A. Pimenov, C. Brune, H. Buhmann, and L. W. Molenkamp, “Giant Magneto-Optical Faraday Effect in HgTe Thin Films in the Terahertz Spectral Range,” Phys. Rev. Lett. 106(10), 107404 (2011).
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Buhmann, H.

A. M. Shuvaev, G. V. Astakhov, A. Pimenov, C. Brune, H. Buhmann, and L. W. Molenkamp, “Giant Magneto-Optical Faraday Effect in HgTe Thin Films in the Terahertz Spectral Range,” Phys. Rev. Lett. 106(10), 107404 (2011).
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Bulgarevich, D. S.

Castro-Camus, E.

E. Castro-Camus, “Polarization-Resolved Terahertz Time-Domain Spectroscopy,” J. Infrared, Millimeter, Terahertz Waves 33(4), 418–430 (2012).
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E. Castro-Camus, J. Lloyd-Hughes, M. B. Johnston, M. D. Fraser, H. H. Tan, and C. Jagadish, “Polarization-sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86(25), 254102 (2005).
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Chan, H.-P.

X. Chen, E. P. J. Parrott, Z. Huang, H.-P. Chan, and E. Pickwell-MacPherson, “Robust and accurate terahertz time-domain spectroscopic ellipsometry,” Photonics Res. 6(8), 768–775 (2018).
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Chateauneuf, M.

Y. P. Chen, C. Marceau, S. Genier, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized Terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282(21), 4283–4287 (2009).
[Crossref]

Chen, G. F.

N. Sirica, R. I. Tobey, L. X. Zhao, G. F. Chen, B. Xu, R. Yang, B. Shen, D. A. Yarotski, P. Bowlan, S. A. Trugman, J. X. Zhu, Y. M. Dai, A. K. Azad, N. Ni, X. G. Qiu, A. J. Taylor, and R. P. Prasankumar, “Tracking Ultrafast Photocurrents in the Weyl Semimetal TaAs Using THz Emission Spectroscopy,” Phys. Rev. Lett. 122(19), 197401 (2019).
[Crossref]

Chen, H. L.

Chen, H. T.

J. F. Zhou, D. R. Chowdhury, R. K. Zhao, A. K. Azad, H. T. Chen, C. M. Soukoulis, A. J. Taylor, and J. F. O’Hara, “Terahertz chiral metamaterials with giant and dynamically tunable optical activity,” Phys. Rev. B 86(3), 035448 (2012).
[Crossref]

Chen, M. C.

K. A. Niessen, M. Xu, D. K. George, M. C. Chen, A. R. Ferré-D’Amaré, E. H. Snell, V. Cody, J. Pace, M. Schmidt, and A. G. Markelz, “Protein and RNA dynamical fingerprinting,” Nat. Commun. 10(1), 1026 (2019).
[Crossref]

Chen, X.

X. Chen, E. P. J. Parrott, Z. Huang, H.-P. Chan, and E. Pickwell-MacPherson, “Robust and accurate terahertz time-domain spectroscopic ellipsometry,” Photonics Res. 6(8), 768–775 (2018).
[Crossref]

Chen, Y. P.

Y. P. Chen, C. Marceau, S. Genier, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized Terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282(21), 4283–4287 (2009).
[Crossref]

Cheng, G.

W. J. Choi, G. Cheng, Z. Huang, S. Zhang, T. B. Norris, and N. A. Kotov, “Terahertz circular dichroism spectroscopy of biomaterials enabled by kirigami polarization modulators,” Nat. Mater. 18(8), 820–826 (2019).
[Crossref]

Chin, S. L.

Y. P. Chen, C. Marceau, S. Genier, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized Terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282(21), 4283–4287 (2009).
[Crossref]

Choi, W. J.

W. J. Choi, G. Cheng, Z. Huang, S. Zhang, T. B. Norris, and N. A. Kotov, “Terahertz circular dichroism spectroscopy of biomaterials enabled by kirigami polarization modulators,” Nat. Mater. 18(8), 820–826 (2019).
[Crossref]

Chowdhury, D. R.

J. F. Zhou, D. R. Chowdhury, R. K. Zhao, A. K. Azad, H. T. Chen, C. M. Soukoulis, A. J. Taylor, and J. F. O’Hara, “Terahertz chiral metamaterials with giant and dynamically tunable optical activity,” Phys. Rev. B 86(3), 035448 (2012).
[Crossref]

Chu, T. S.

T. S. Chu and R. H. Turrin, “Depolarization Properties of Offset Reflector Antennas,” IRE Trans. Antennas Propag. 21(3), 339–345 (1973).
[Crossref]

Cody, V.

K. A. Niessen, M. Xu, D. K. George, M. C. Chen, A. R. Ferré-D’Amaré, E. H. Snell, V. Cody, J. Pace, M. Schmidt, and A. G. Markelz, “Protein and RNA dynamical fingerprinting,” Nat. Commun. 10(1), 1026 (2019).
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Collazo, R.

Coutaz, J.-L.

Cui, Y.

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(1), 16–18 (1997).
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Dai, J. M.

Q. Jin, E. Yiwen, K. Williams, J. M. Dai, and X. C. Zhang, “Observation of broadband terahertz wave generation from liquid water,” Appl. Phys. Lett. 111(7), 071103 (2017).
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J. M. Dai, N. Karpowicz, and X. C. Zhang, “Coherent Polarization Control of Terahertz Waves Generated from Two-Color Laser-Induced Gas Plasma,” Phys. Rev. Lett. 103(2), 023001 (2009).
[Crossref]

Dai, Y. M.

N. Sirica, R. I. Tobey, L. X. Zhao, G. F. Chen, B. Xu, R. Yang, B. Shen, D. A. Yarotski, P. Bowlan, S. A. Trugman, J. X. Zhu, Y. M. Dai, A. K. Azad, N. Ni, X. G. Qiu, A. J. Taylor, and R. P. Prasankumar, “Tracking Ultrafast Photocurrents in the Weyl Semimetal TaAs Using THz Emission Spectroscopy,” Phys. Rev. Lett. 122(19), 197401 (2019).
[Crossref]

Danilov, S. N.

H. Plank, J. Pernul, S. Gebert, S. N. Danilov, J. König-Otto, S. Winnerl, M. Lanius, J. Kampmeier, G. Mussler, I. Aguilera, D. Grützmacher, and S. D. Ganichev, “Infrared/terahertz spectra of the photogalvanic effect in (Bi,Sb)Te based three-dimensional topological insulators,” Phys. Rev. Mater. 2(2), 024202 (2018).
[Crossref]

S. D. Ganichev, W. Weber, J. Kiermaier, S. N. Danilov, P. Olbrich, D. Schuh, W. Wegscheider, D. Bougeard, G. Abstreiter, and W. Prettl, “All-electric detection of the polarization state of terahertz laser radiation,” J. Appl. Phys. 103(11), 114504 (2008).
[Crossref]

Deshmukh, P.

A. Pal, S. N. Shirodkar, P. Deshmukh, H. Surdi, B. R. Sangala, S. S. Prabhu, K. C. Rustagi, U. V. Waghmare, and P. Ayyub, “Rotation of terahertz radiation due to phonon-mediated magnetoelectric coupling in chiral selenium,” Phys. Rev. B 98(23), 235141 (2018).
[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 modulation,” Rev. Sci. Instrum. 81(8), 083903 (2010).
[Crossref]

Dubois, J.

Y. P. Chen, C. Marceau, S. Genier, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized Terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282(21), 4283–4287 (2009).
[Crossref]

Elezzabi, A. Y.

Ellis, C. T.

Ewert, U.

F. Rutz, T. Hasek, M. Koch, H. Richter, and U. Ewert, “Terahertz birefringence of liquid crystal polymers,” Appl. Phys. Lett. 89(22), 221911 (2006).
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Ferré-D’Amaré, A. R.

K. A. Niessen, M. Xu, D. K. George, M. C. Chen, A. R. Ferré-D’Amaré, E. H. Snell, V. Cody, J. Pace, M. Schmidt, and A. G. Markelz, “Protein and RNA dynamical fingerprinting,” Nat. Commun. 10(1), 1026 (2019).
[Crossref]

Franke, A.

Fraser, M. D.

E. Castro-Camus, J. Lloyd-Hughes, M. B. Johnston, M. D. Fraser, H. H. Tan, and C. Jagadish, “Polarization-sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86(25), 254102 (2005).
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M. Okano, M. Fujii, and S. Watanabe, “Anisotropic percolation conduction in elastomer-carbon black composites investigated by polarization-sensitive terahertz time-domain spectroscopy,” Appl. Phys. Lett. 111(22), 221902 (2017).
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Fukasawa, R.

M. Herrmann, M. Tani, K. Sakai, and R. Fukasawa, “Terahertz imaging of silicon wafers,” J. Appl. Phys. 91(3), 1247–1250 (2002).
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Gaborit, G.

Gallot, G.

Ganichev, S. D.

H. Plank, J. Pernul, S. Gebert, S. N. Danilov, J. König-Otto, S. Winnerl, M. Lanius, J. Kampmeier, G. Mussler, I. Aguilera, D. Grützmacher, and S. D. Ganichev, “Infrared/terahertz spectra of the photogalvanic effect in (Bi,Sb)Te based three-dimensional topological insulators,” Phys. Rev. Mater. 2(2), 024202 (2018).
[Crossref]

S. D. Ganichev, W. Weber, J. Kiermaier, S. N. Danilov, P. Olbrich, D. Schuh, W. Wegscheider, D. Bougeard, G. Abstreiter, and W. Prettl, “All-electric detection of the polarization state of terahertz laser radiation,” J. Appl. Phys. 103(11), 114504 (2008).
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Gebert, S.

H. Plank, J. Pernul, S. Gebert, S. N. Danilov, J. König-Otto, S. Winnerl, M. Lanius, J. Kampmeier, G. Mussler, I. Aguilera, D. Grützmacher, and S. D. Ganichev, “Infrared/terahertz spectra of the photogalvanic effect in (Bi,Sb)Te based three-dimensional topological insulators,” Phys. Rev. Mater. 2(2), 024202 (2018).
[Crossref]

Genier, S.

Y. P. Chen, C. Marceau, S. Genier, F. Theberge, M. Chateauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized Terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282(21), 4283–4287 (2009).
[Crossref]

George, D. K.

K. A. Niessen, M. Xu, D. K. George, M. C. Chen, A. R. Ferré-D’Amaré, E. H. Snell, V. Cody, J. Pace, M. Schmidt, and A. G. Markelz, “Protein and RNA dynamical fingerprinting,” Nat. Commun. 10(1), 1026 (2019).
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D. K. George, A. V. Stier, C. T. Ellis, B. D. McCombe, J. Černe, and A. G. Markelz, “Terahertz magneto-optical polarization modulation spectroscopy,” J. Opt. Soc. Am. B 29(6), 1406–1412 (2012).
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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(1), 16–18 (1997).
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Grischkowsky, D.

Grützmacher, D.

H. Plank, J. Pernul, S. Gebert, S. N. Danilov, J. König-Otto, S. Winnerl, M. Lanius, J. Kampmeier, G. Mussler, I. Aguilera, D. Grützmacher, and S. D. Ganichev, “Infrared/terahertz spectra of the photogalvanic effect in (Bi,Sb)Te based three-dimensional topological insulators,” Phys. Rev. Mater. 2(2), 024202 (2018).
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Hangyo, M.

T. Nagashima, M. Tani, and M. Hangyo, “Polarization-sensitive THz-TDS and its Application to Anisotropy Sensing,” J. Infrared, Millimeter, Terahertz Waves 34(11), 740–775 (2013).
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N. Matsumoto, T. Hosokura, T. Nagashima, and M. Hangyo, “Measurement of the dielectric constant of thin films by terahertz time-domain spectroscopic ellipsometry,” Opt. Lett. 36(2), 265–267 (2011).
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Y. Hirota, R. Hattori, M. Tani, and M. Hangyo, “Polarization modulation of terahertz electromagnetic radiation by four-contact photoconductive antenna,” Opt. Express 14(10), 4486–4493 (2006).
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T. Nagashima and M. Hangyo, “Measurement of complex optical constants of a highly doped Si wafer using terahertz ellipsometry,” Appl. Phys. Lett. 79(24), 3917–3919 (2001).
[Crossref]

Hasek, T.

F. Rutz, T. Hasek, M. Koch, H. Richter, and U. Ewert, “Terahertz birefringence of liquid crystal polymers,” Appl. Phys. Lett. 89(22), 221911 (2006).
[Crossref]

Hattori, R.

Hauge, R. H.

L. Ren, C. L. Pint, L. G. Booshenri, W. D. Rice, X. F. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon Nanotube Terahertz Polarizer,” Nano Lett. 9(7), 2610–2613 (2009).
[Crossref]

Herrmann, M.

M. Herrmann, M. Tani, K. Sakai, and R. Fukasawa, “Terahertz imaging of silicon wafers,” J. Appl. Phys. 91(3), 1247–1250 (2002).
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Hibino, H.

R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum Faraday and Kerr rotations in graphene,” Nat. Commun. 4(1), 1841 (2013).
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Higuchi, T.

Hilton, D. J.

L. Ren, C. L. Pint, L. G. Booshenri, W. D. Rice, X. F. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon Nanotube Terahertz Polarizer,” Nano Lett. 9(7), 2610–2613 (2009).
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Hirota, Y.

Hoshina, H.

H. Hoshina, Y. Morisawa, H. Sato, H. Minamide, I. Noda, Y. Ozaki, and C. Otani, “Polarization and temperature dependent spectra of poly(3-hydroxyalkanoate)s measured at terahertz frequencies,” Phys. Chem. Chem. Phys. 13(20), 9173–9179 (2011).
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Hosokura, T.

Hsieh, C. F.

Huang, Z.

W. J. Choi, G. Cheng, Z. Huang, S. Zhang, T. B. Norris, and N. A. Kotov, “Terahertz circular dichroism spectroscopy of biomaterials enabled by kirigami polarization modulators,” Nat. Mater. 18(8), 820–826 (2019).
[Crossref]

X. Chen, E. P. J. Parrott, Z. Huang, H.-P. Chan, and E. Pickwell-MacPherson, “Robust and accurate terahertz time-domain spectroscopic ellipsometry,” Photonics Res. 6(8), 768–775 (2018).
[Crossref]

Ikebe, Y.

R. Shimano, Y. Ikebe, K. S. Takahashi, M. Kawasaki, N. Nagaosa, and Y. Tokura, “Terahertz Faraday rotation induced by an anomalous Hall effect in the itinerant ferromagnet SrRuO3,” EPL 95(1), 17002 (2011).
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L. Ren, C. L. Pint, L. G. Booshenri, W. D. Rice, X. F. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon Nanotube Terahertz Polarizer,” Nano Lett. 9(7), 2610–2613 (2009).
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Plum, E.

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S. D. Ganichev, W. Weber, J. Kiermaier, S. N. Danilov, P. Olbrich, D. Schuh, W. Wegscheider, D. Bougeard, G. Abstreiter, and W. Prettl, “All-electric detection of the polarization state of terahertz laser radiation,” J. Appl. Phys. 103(11), 114504 (2008).
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L. Ren, C. L. Pint, L. G. Booshenri, W. D. Rice, X. F. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon Nanotube Terahertz Polarizer,” Nano Lett. 9(7), 2610–2613 (2009).
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F. Rutz, T. Hasek, M. Koch, H. Richter, and U. Ewert, “Terahertz birefringence of liquid crystal polymers,” Appl. Phys. Lett. 89(22), 221911 (2006).
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A. Pal, S. N. Shirodkar, P. Deshmukh, H. Surdi, B. R. Sangala, S. S. Prabhu, K. C. Rustagi, U. V. Waghmare, and P. Ayyub, “Rotation of terahertz radiation due to phonon-mediated magnetoelectric coupling in chiral selenium,” Phys. Rev. B 98(23), 235141 (2018).
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Santavicca, D. F.

D. J. Aschaffenburg, M. R. C. Williams, D. Talbayev, D. F. Santavicca, D. E. Prober, and C. A. Schmuttenmaer, “Efficient measurement of broadband terahertz optical activity,” Appl. Phys. Lett. 100(24), 241114 (2012).
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H. Hoshina, Y. Morisawa, H. Sato, H. Minamide, I. Noda, Y. Ozaki, and C. Otani, “Polarization and temperature dependent spectra of poly(3-hydroxyalkanoate)s measured at terahertz frequencies,” Phys. Chem. Chem. Phys. 13(20), 9173–9179 (2011).
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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 modulation,” Rev. Sci. Instrum. 81(8), 083903 (2010).
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APL Photonics (1)

A. Moriwaki, M. Okano, and S. Watanabe, “Internal triaxial strain imaging of visibly opaque black rubbers with terahertz polarization spectroscopy,” APL Photonics 2(10), 106101 (2017).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Express (1)

N. Yasumatsu, A. Kasatani, K. Oguchi, and S. Watanabe, “High-speed terahertz time-domain polarimeter based on an electro-optic modulation technique,” Appl. Phys. Express 7(9), 092401 (2014).
[Crossref]

Appl. Phys. Lett. (12)

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(11), 1324–1326 (1994).
[Crossref]

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[Crossref]

Z. Lü, D. Zhang, C. Meng, L. Sun, Z. Zhou, Z. Zhao, and J. Yuan, “Polarization-sensitive air-biased-coherent-detection for terahertz wave,” Appl. Phys. Lett. 101(8), 081119 (2012).
[Crossref]

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[Crossref]

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Figures (8)

Fig. 1.
Fig. 1. Schematic of the THz Time-Domain Polarimetry (THz-TDP) system. The ZnTe detector is rotating at a constant frequency, ω. BS1-BS2: beam splitters; ND: a variable neutral density filter wheel; GT1-GT2: Glan-Thompson polarizers; QWP1-QWP2: quarter-wave plates; HWP: a half-wave plate; S: position of sample holder; PM1-PM2: off-axis parabolic mirrors; HR-Si: a high resistivity silicon wafer used to block the NIR pulses; L: a plano-convex lens; WP: a Wollaston prism. Inset: configuration of the electro-optic sampling. The polarization direction of the probe beam is set parallel to the x-axis in the laboratory frame. β is the orientation of the [-110] axis of the (110)-cut ZnTe crystal and γ is the polarization angle of the terahertz electric field vector with respect to the probe beam.
Fig. 2.
Fig. 2. Principle of the lock-in type readout in THz-TDP system. The E-O crystal is rotating at a period of 31 ms, and two revolutions of crystal rotation are taken as a complete measurement event. 62 data points are collected within a time interval of 1 ms, here 14 of them are illustrated and labeled with the index number $i$ The E-O crystal is at the same angle for indices $i$ and $i + 31$; Examples of the pairs of the same angles are shown such as (1, 32), (6, 37), (11, 42), (16, 47), (21, 52), (26, 57), and (31, 62). For even values of these two indices, the THz pulses are always blocked by the chopper. Therefore, we subtract the data of even indices (hollow) from those of odd indices (solid) to extract the net contribution by the THz waves.
Fig. 3.
Fig. 3. (a) Time-dependent balanced signal $\Delta I(i )\; $ obtained during two revolutions of the ZnTe detector. The time interval between each index of data $(i)$ is 1 ms. The THz waves are blocked at all even indices by an optical chopper rotating at $\textrm{f}/2 = 500\;{\textrm{Hz}}\,.\Delta I$ obtained at odd (solid) and even indices (open circle) are rearranged and plotted separately. (b) The net signal induced by the THz pulses is shown. We conducted $N = 3000$ measurements to calculate the mean value and standard deviation of data. (c) Distribution of deviations $\Delta \gamma $ of the measured polarization angle $\gamma $ from the mean value $\bar{\gamma }$ using data presented in (b).
Fig. 4.
Fig. 4. (a) Polarization-resolved time-domain waveform of a THz pulse polarized at $\gamma = {20^\circ }$. (b) The rotation angle $\Psi $ and (c) phase lag $\Delta $ obtained for the THz pulses polarized at $\gamma = {20^\circ }$. The average value (black line) is calculated for 10 separate instances of polarimetric measurements (red dots).
Fig. 5.
Fig. 5. (a) The real and (b) imaginary part of the normalized Jones matrix entry ${\tilde{t}_3}$. Matrix #1 and #2 are calculated when the polarization angle $\gamma $ equals -60° or -45°, respectively. Matrix #3 is obtained when the silicon wafer on the path of THz pulses is set at a smaller incident angle. (c-f) Comparison between the $\Psi $ before (red) and after calibration (blue) using Matrix #1 (Solid) and Matrix #2 (dashed), when $\gamma $ is set at (c) -80°, (d) -20°, (e) 20° and (f) 40°. Note that $\Psi $ is by definition a positive number. The error in $\Psi $ after calibrating with Jones Matrix #1 and #2 are shown separately in (g) and (h), represented by the mean value and range of the data in (c-f).
Fig. 6.
Fig. 6. (a) The measurement schematic of the birefringence of a sapphire crystal. (b) The THz waveform transmitted through the sample. The THz source is linearly polarized in the x-direction, while the sample’s optical axis is oriented at 45°. (c) Calculated birefringence of sapphire from polarimetry measurements with and without calibration. The results obtained from 2f and 4f arrangements are in agreement.
Fig. 7.
Fig. 7. Schematic of the 6f arrangement of the THz-TDP system. Samples can be placed in either transmission mode or reflection mode focus position. For calculating the Jones matrix of 4f arrangement, the polarimetry block is placed at the focal point of PM4. The inset shows the schematic of ellipsometry measurement used in reflection configuration.
Fig. 8.
Fig. 8. Ellipsometry measurements on the refractive indices of isotropic wafers made by (a) high-resistivity silicon, (b) aluminum nitride and (c) quartz. The results are extracted from both the uncalibrated (red) and calibrated (blue) THz-TDP measurements. The values obtained from transmission THz-TDS (black) are shown as references.

Equations (19)

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Δ I E THz { 1 2 cos ( β + γ ) + 3 2 cos ( 3 β γ ) } .
Δ I ( t ) E THz { 1 2 cos ( ω t + β 0 + γ ) + 3 2 cos ( 3 ω t + 3 β 0 γ ) } ,
E ω = C 2 E THz φ ω = β 0 + γ + 2 n 1 π E 3 ω = 3 C 2 E THz φ 3 ω = 3 β 0 γ + 2 n 2 π ,
Δ I ( i ) = { Δ I ( i ) Δ I ( i + 31 ) ( i = 1 , 3 , 31 ) Δ I ( i + 31 ) Δ I ( i ) ( i = 2 , 4 , 30 ) .
E THz = ( E x E y ) ( sin ( ψ ϕ 0 ) cos ( ψ ϕ 0 ) cos ψ + 1 2 co s 2 ( ψ ϕ 0 ) sin ψ sin ( ψ ϕ 0 ) cos ( ψ ϕ 0 ) sin ψ 1 2 co s 2 ( ψ ϕ 0 ) cos ψ ) ,
r ~ = E ~ y E ~ x = tan Ψ e i Δ ,
E ( ω ) = T ( ω ) E 0 ( ω ) ,
T ( ω ) = [ t ~ x x ( ω ) t ~ x y ( ω ) t ~ y x ( ω ) t ~ y y ( ω ) ] [ 1 t ~ 1 ( ω ) t ~ 2 ( ω ) t ~ 3 ( ω ) ] ,
[ E x E y ] = [ 1 t ~ 1 t ~ 2 t ~ 3 ] [ 1 0 ] = [ 1 t ~ 2 ] ,
[ E x E y ] = [ 1 t ~ 1 t ~ 2 t ~ 3 ] [ 0 1 ] = [ t ~ 1 t ~ 3 ] .
[ E x E y ] = [ 1 t ~ 1 t ~ 2 t ~ 3 ] [ E x 0 E y 0 ] = [ E x 0 + t ~ 1 E y 0 t ~ 2 E x 0 + t ~ 3 E y 0 ] .
T = [ 1 0.003 0.011 0.80 ] .
S = R ( α ) [ e i φ x 0 0 e i φ y ] R ( α ) = [ e i φ x cos 2 α + e i φ y sin 2 α ( e i φ x e i φ y ) cos α sin α ( e i φ x e i φ y ) cos α sin α e i φ x sin 2 α + e i φ y cos 2 α ] ,
E = S E 0 = [ e i φ x cos 2 α + e i φ y sin 2 α ( e i φ x e i φ y ) cos α sin α ] .
δ = φ x φ y r ~ = E x E y = e i δ + tan 2 α ( e i δ 1 ) tan α α = 1 2 tan 1 [ 1 Re ( r ~ ) ] δ = 2 tan 1 [ 1 sin ( 2 α ) Im ( r ~ ) ] ,
E  =  T 2 S T 1 E 0 ,
ρ = r p / r s = E p / E p 0 E s / E s 0 .
n ~ = n i κ = sin θ i 1 + tan 2 θ i ( 1 ρ 1 + ρ ) 2 ,
E  =  T 3 [ ρ 0 0 1 ] T 2 T 1 E 0 .

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