Abstract

The values of the nonlinear refractive index coefficient for various materials in the terahertz frequency range exceed the ones in both visible and NIR ranges by several orders of magnitude. This allows to create nonlinear switches, modulators, systems requiring lower control energies in the terahertz frequency range. We report the direct measurement of the nonlinear refractive index coefficient of liquid water by using the Z-scan method with broadband pulsed THz beam. Our experimental result shows that nonlinear refractive index coefficient in water is positive and can be as large as 7×10−10 cm2/W in the THz frequency range, which exceeds the values for the visible and NIR ranges by 6 orders of magnitude. To estimate n2, we use the theoretical model that takes into account ionic vibrational contribution to the third-order susceptibility. We show that the origins of the nonlinearity observed are the anharmonicity of molecular vibrations.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  25. Yiwen E, Q. Jin, A. Tcypkin, and X.-C. Zhang, “Terahertz wave generation from liquid water films via laser-induced breakdown,” Appl. Phys. Lett. 113, 181103 (2018).
    [Crossref]
  26. M. Paillette, “Recherches expérimentales sur les effets kerr induits par une onde lumineuse,” Ann. Phys.-Paris,  14, 671–712 (1969).
    [Crossref]
  27. W. L. Smith, P. Liu, and N. Bloembergen, “Superbroadening in h 2 o and d 2 o by self-focused picosecond pulses from a yalg: Nd laser,” Phys. Rev. A 15, 2396–2403 (1977).
    [Crossref]
  28. P. Ho and R. Alfano, “Optical kerr effect in liquids,” Phys. Rev. A 20, 2170 (1979).
    [Crossref]
  29. R. W. Boyd, Nonlinear optics (Elsevier, 2003).
  30. K. Yang, P. Richards, and Y. Shen, “Generation of far-infrared radiation by picosecond light pulses in linbo3,” Appl. Phys. Lett. 19, 320–323 (1971).
    [Crossref]
  31. C. Lombosi, G. Polonyi, M. Mechler, Z. Ollmann, J. Hebling, and J. A. Fulop, “Nonlinear distortion of intense THz beams,” New J. Phys. 17, 083041 (2015).
    [Crossref]
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    [Crossref]
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    [Crossref]
  34. X. Zheng, R. Chen, G. Shi, J. Zhang, Z. Xu, X. Cheng, and T. Jiang, “Characterization of nonlinear properties of black phosphorus nanoplatelets with femtosecond pulsed z-scan measurements,” Opt. Lett. 40, 3480–3483 (2015).
    [Crossref] [PubMed]
  35. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
    [Crossref]
  36. M. Yin, H. Li, S. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single z-scan method,” Appl. Phys. B 70, 587–591 (2000).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  40. G. Kell, “Precise representation of volume properties of water at one atmosphere,” JCED 12, 66–69 (1967).
  41. L. Thrane, R. H. Jacobsen, P. U. Jepsen, and S. Keiding, “Thz reflection spectroscopy of liquid water,” Chem. Phys. Lett. 240, 330–333 (1995).
    [Crossref]

2018 (8)

Y. V. Grachev, X. Liu, S. E. Putilin, A. N. Tsypkin, V. G. Bespalov, S. A. Kozlov, and X.-C. Zhang, “Wireless data transmission method using pulsed thz sliced spectral supercontinuum,” IEEE Photonics Technol. Lett. 30, 103–106 (2018).
[Crossref]

S. Lin, S. Yu, and D. Talbayev, “Measurement of quadratic terahertz optical nonlinearities using second-harmonic lock-in detection,” Phys. Rev. Appl. 10, 044007 (2018).
[Crossref]

A. Woldegeorgis, T. Kurihara, B. Beleites, J. Bossert, R. Grosse, G. G. Paulus, F. Ronneberger, and A. Gopal, “Thz induced nonlinear effects in materials at intensities above 26 gw/cm 2,” J. Infrared Millim. Terahertz Waves 39, 667–680 (2018).
[Crossref]

A. Tcypkin, S. Putilin, M. Kulya, M. Melnik, A. Drozdov, V. Bespalov, X.-C. Zhang, R. Boyd, and S. Kozlov, “Experimental estimate of the nonlinear refractive index of crystalline znse in the terahertz spectral range,” Bull. Russ. Acad. Sci.: Phys. 82, 1547–1549 (2018).
[Crossref]

Yiwen E, Q. Jin, A. Tcypkin, and X.-C. Zhang, “Terahertz wave generation from liquid water films via laser-induced breakdown,” Appl. Phys. Lett. 113, 181103 (2018).
[Crossref]

D. A. Kislin, M. A. Knyazev, Y. A. Shpolyanskii, and S. A. Kozlov, “Self-action of nonparaxial few-cycle optical waves in dielectric media,” JETP Letters 107, 753–760 (2018).
[Crossref]

O. Smolyanskaya, I. Schelkanova, M. Kulya, E. Odlyanitskiy, I. Goryachev, A. Tcypkin, Y. V. Grachev, Y. G. Toropova, and V. Tuchin, “Glycerol dehydration of native and diabetic animal tissues studied by thz-tds and nmr methods,” Biomed. Opt. Express 9, 1198–1215 (2018).
[Crossref] [PubMed]

A. V. Balakin, S. V. Garnov, V. A. Makarov, N. A. Kuzechkin, P. A. Obraztsov, P. M. Solyankin, A. P. Shkurinov, and Y. Zhu, “”terhune-like” transformation of the terahertz polarization ellipse “mutually induced” by three-wave joint propagation in liquid,” Opt. Lett. 43, 4406–4409 (2018).
[Crossref] [PubMed]

2017 (5)

P. Bowlan, J. Bowlan, S. A. Trugman, R. V. Aguilar, J. Qi, X. Liu, J. Furdyna, M. Dobrowolska, A. J. Taylor, D. A. Yarotski, and R. P. Prasankumar, “Probing and controlling terahertz-driven structural dynamics with surface sensitivity,” Optica 4, 383–387 (2017).
[Crossref]

C. Vicario, M. Shalaby, and C. P. Hauri, “Subcycle extreme nonlinearities in gap induced by an ultrastrong terahertz field,” Phys. Rev. Lett. 118, 083901 (2017).
[Crossref] [PubMed]

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

X. C. Zhang, A. Shkurinov, and Y. Zhang, “Extreme terahertz science,” Nature Photon. 11, 16–18 (2017).
[Crossref]

J. Dong, A. Locquet, M. Melis, and D. Citrin, “Global mapping of stratigraphy of an old-master painting using sparsity-based terahertz reflectometry,” Sci. Rep. 7, 15098 (2017).
[Crossref] [PubMed]

2016 (4)

T. Nagatsuma, G. Ducournau, and C. C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nature Photon. 10, 371–379 (2016).
[Crossref]

S. Baierl, M. Hohenleutner, T. Kampfrath, A. Zvezdin, A. Kimel, R. Huber, and R. Mikhaylovskiy, “Nonlinear spin control by terahertz-driven anisotropy fields,” Nature Photon. 10, 715–718 (2016).
[Crossref]

S. Baierl, J. H. Mentink, M. Hohenleutner, L. Braun, T.-M. Do, C. Lange, A. Sell, M. Fiebig, G. Woltersdorf, T. Kampfrath, and R. Huber, “Terahertz-driven nonlinear spin response of antiferromagnetic nickel oxide,” Phys. Rev. Lett. 117, 197201 (2016).
[Crossref] [PubMed]

K. J. Kaltenecker, A. Tuniz, S. C. Fleming, A. Argyros, B. T. Kuhlmey, M. Walther, and B. M. Fischer, “Ultrabroadband perfect imaging in terahertz wire media using single-cycle pulses,” Optica 3, 458–464 (2016).
[Crossref]

2015 (5)

K. Dolgaleva, D. V. Materikina, R. W. Boyd, and S. A. Kozlov, “Prediction of an extremely large nonlinear refractive index for crystals at terahertz frequencies,” Phys. Rev. A 92, 023809 (2015).
[Crossref]

M. Shalaby and C. P. Hauri, “Demonstration of a low-frequency three-dimensional terahertz bullet with extreme brightness,” Nat. Commun. 6, 5976 (2015).
[Crossref] [PubMed]

C. Lombosi, G. Polonyi, M. Mechler, Z. Ollmann, J. Hebling, and J. A. Fulop, “Nonlinear distortion of intense THz beams,” New J. Phys. 17, 083041 (2015).
[Crossref]

S. Li, G. Kumar, and T. E. Murphy, “Terahertz nonlinear conduction and absorption saturation in silicon waveguides,” Optica 2, 553–557 (2015).
[Crossref]

X. Zheng, R. Chen, G. Shi, J. Zhang, Z. Xu, X. Cheng, and T. Jiang, “Characterization of nonlinear properties of black phosphorus nanoplatelets with femtosecond pulsed z-scan measurements,” Opt. Lett. 40, 3480–3483 (2015).
[Crossref] [PubMed]

2012 (2)

G. Sharma, I. Al-Naib, H. Hafez, R. Morandotti, D. Cooke, and T. Ozaki, “Carrier density dependence of the nonlinear absorption of intense thz radiation in gaas,” Opt. Express 20, 18016–18024 (2012).
[Crossref] [PubMed]

D. Turchinovich, J. M. Hvam, and M. C. Hoffmann, “Self-phase modulation of a single-cycle terahertz pulse by nonlinear free-carrier response in a semiconductor,” Phys. Rev. B 85, 201304 (2012).
[Crossref]

2010 (1)

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Observation of nonequilibrium carrier distribution in ge, si, and gaas by terahertz pump–terahertz probe measurements,” Phys. Rev. B 81, 035201 (2010).
[Crossref]

2009 (1)

2006 (1)

P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Nonlinear terahertz response of n-type gaas,” Phys. Rev. Lett. 96, 187402 (2006).
[Crossref]

2000 (1)

M. Yin, H. Li, S. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single z-scan method,” Appl. Phys. B 70, 587–591 (2000).
[Crossref]

1995 (1)

L. Thrane, R. H. Jacobsen, P. U. Jepsen, and S. Keiding, “Thz reflection spectroscopy of liquid water,” Chem. Phys. Lett. 240, 330–333 (1995).
[Crossref]

1994 (1)

1990 (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[Crossref]

1989 (1)

A. Watanabe, H. Saito, Y. Ishida, M. Nakamoto, and T. Yajima, “A new nozzle producing ultrathin liquid sheets for femtosecond pulse dye lasers,” Opt. Commun. 71, 301–304 (1989).
[Crossref]

1979 (1)

P. Ho and R. Alfano, “Optical kerr effect in liquids,” Phys. Rev. A 20, 2170 (1979).
[Crossref]

1977 (1)

W. L. Smith, P. Liu, and N. Bloembergen, “Superbroadening in h 2 o and d 2 o by self-focused picosecond pulses from a yalg: Nd laser,” Phys. Rev. A 15, 2396–2403 (1977).
[Crossref]

1973 (1)

1971 (1)

K. Yang, P. Richards, and Y. Shen, “Generation of far-infrared radiation by picosecond light pulses in linbo3,” Appl. Phys. Lett. 19, 320–323 (1971).
[Crossref]

1969 (1)

M. Paillette, “Recherches expérimentales sur les effets kerr induits par une onde lumineuse,” Ann. Phys.-Paris,  14, 671–712 (1969).
[Crossref]

1967 (2)

P. Schatzberg, “Molecular diameter of water from solubility and diffusion measurements,” J. Phys. Chem. 71, 4569–4570 (1967).
[Crossref]

G. Kell, “Precise representation of volume properties of water at one atmosphere,” JCED 12, 66–69 (1967).

Aguilar, R. V.

Alfano, R.

P. Ho and R. Alfano, “Optical kerr effect in liquids,” Phys. Rev. A 20, 2170 (1979).
[Crossref]

Al-Naib, I.

Argyros, A.

Baierl, S.

S. Baierl, M. Hohenleutner, T. Kampfrath, A. Zvezdin, A. Kimel, R. Huber, and R. Mikhaylovskiy, “Nonlinear spin control by terahertz-driven anisotropy fields,” Nature Photon. 10, 715–718 (2016).
[Crossref]

S. Baierl, J. H. Mentink, M. Hohenleutner, L. Braun, T.-M. Do, C. Lange, A. Sell, M. Fiebig, G. Woltersdorf, T. Kampfrath, and R. Huber, “Terahertz-driven nonlinear spin response of antiferromagnetic nickel oxide,” Phys. Rev. Lett. 117, 197201 (2016).
[Crossref] [PubMed]

Balakin, A. V.

Beleites, B.

A. Woldegeorgis, T. Kurihara, B. Beleites, J. Bossert, R. Grosse, G. G. Paulus, F. Ronneberger, and A. Gopal, “Thz induced nonlinear effects in materials at intensities above 26 gw/cm 2,” J. Infrared Millim. Terahertz Waves 39, 667–680 (2018).
[Crossref]

Bespalov, V.

A. Tcypkin, S. Putilin, M. Kulya, M. Melnik, A. Drozdov, V. Bespalov, X.-C. Zhang, R. Boyd, and S. Kozlov, “Experimental estimate of the nonlinear refractive index of crystalline znse in the terahertz spectral range,” Bull. Russ. Acad. Sci.: Phys. 82, 1547–1549 (2018).
[Crossref]

Bespalov, V. G.

Y. V. Grachev, X. Liu, S. E. Putilin, A. N. Tsypkin, V. G. Bespalov, S. A. Kozlov, and X.-C. Zhang, “Wireless data transmission method using pulsed thz sliced spectral supercontinuum,” IEEE Photonics Technol. Lett. 30, 103–106 (2018).
[Crossref]

Bloembergen, N.

W. L. Smith, P. Liu, and N. Bloembergen, “Superbroadening in h 2 o and d 2 o by self-focused picosecond pulses from a yalg: Nd laser,” Phys. Rev. A 15, 2396–2403 (1977).
[Crossref]

Bossert, J.

A. Woldegeorgis, T. Kurihara, B. Beleites, J. Bossert, R. Grosse, G. G. Paulus, F. Ronneberger, and A. Gopal, “Thz induced nonlinear effects in materials at intensities above 26 gw/cm 2,” J. Infrared Millim. Terahertz Waves 39, 667–680 (2018).
[Crossref]

Bowlan, J.

Bowlan, P.

Boyd, R.

A. Tcypkin, S. Putilin, M. Kulya, M. Melnik, A. Drozdov, V. Bespalov, X.-C. Zhang, R. Boyd, and S. Kozlov, “Experimental estimate of the nonlinear refractive index of crystalline znse in the terahertz spectral range,” Bull. Russ. Acad. Sci.: Phys. 82, 1547–1549 (2018).
[Crossref]

Boyd, R. W.

K. Dolgaleva, D. V. Materikina, R. W. Boyd, and S. A. Kozlov, “Prediction of an extremely large nonlinear refractive index for crystals at terahertz frequencies,” Phys. Rev. A 92, 023809 (2015).
[Crossref]

R. W. Boyd, Nonlinear optics (Elsevier, 2003).

Braun, L.

S. Baierl, J. H. Mentink, M. Hohenleutner, L. Braun, T.-M. Do, C. Lange, A. Sell, M. Fiebig, G. Woltersdorf, T. Kampfrath, and R. Huber, “Terahertz-driven nonlinear spin response of antiferromagnetic nickel oxide,” Phys. Rev. Lett. 117, 197201 (2016).
[Crossref] [PubMed]

Chen, R.

Cheng, X.

Cheung, Y.

Citrin, D.

J. Dong, A. Locquet, M. Melis, and D. Citrin, “Global mapping of stratigraphy of an old-master painting using sparsity-based terahertz reflectometry,” Sci. Rep. 7, 15098 (2017).
[Crossref] [PubMed]

Cooke, D.

Dai, J.

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

Do, T.-M.

S. Baierl, J. H. Mentink, M. Hohenleutner, L. Braun, T.-M. Do, C. Lange, A. Sell, M. Fiebig, G. Woltersdorf, T. Kampfrath, and R. Huber, “Terahertz-driven nonlinear spin response of antiferromagnetic nickel oxide,” Phys. Rev. Lett. 117, 197201 (2016).
[Crossref] [PubMed]

Dobrowolska, M.

Dolgaleva, K.

K. Dolgaleva, D. V. Materikina, R. W. Boyd, and S. A. Kozlov, “Prediction of an extremely large nonlinear refractive index for crystals at terahertz frequencies,” Phys. Rev. A 92, 023809 (2015).
[Crossref]

Dong, J.

J. Dong, A. Locquet, M. Melis, and D. Citrin, “Global mapping of stratigraphy of an old-master painting using sparsity-based terahertz reflectometry,” Sci. Rep. 7, 15098 (2017).
[Crossref] [PubMed]

Drozdov, A.

A. Tcypkin, S. Putilin, M. Kulya, M. Melnik, A. Drozdov, V. Bespalov, X.-C. Zhang, R. Boyd, and S. Kozlov, “Experimental estimate of the nonlinear refractive index of crystalline znse in the terahertz spectral range,” Bull. Russ. Acad. Sci.: Phys. 82, 1547–1549 (2018).
[Crossref]

Ducournau, G.

T. Nagatsuma, G. Ducournau, and C. C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nature Photon. 10, 371–379 (2016).
[Crossref]

E, Yiwen

Yiwen E, Q. Jin, A. Tcypkin, and X.-C. Zhang, “Terahertz wave generation from liquid water films via laser-induced breakdown,” Appl. Phys. Lett. 113, 181103 (2018).
[Crossref]

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

Elsaesser, T.

P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Nonlinear terahertz response of n-type gaas,” Phys. Rev. Lett. 96, 187402 (2006).
[Crossref]

Fiebig, M.

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M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
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Zhang, X.

G. Kaur, P. Han, and X. Zhang, “Terahertz induced nonlinear effects in doped silicon observed by open-aperture z-scan,” in “Infrared Millimeter and Terahertz Waves (IRMMW-THz), 2010 35th International Conference on,” (IEEE, 2010), pp. 1–2.

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Q. Jin, Yiwen E, K. Williams, J. Dai, and X.-C. Zhang, “Observation of broadband terahertz wave generation from liquid water,” Appl. Phys. Lett. 111, 071103 (2017).
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Yiwen E, Q. Jin, A. Tcypkin, and X.-C. Zhang, “Terahertz wave generation from liquid water films via laser-induced breakdown,” Appl. Phys. Lett. 113, 181103 (2018).
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K. Yang, P. Richards, and Y. Shen, “Generation of far-infrared radiation by picosecond light pulses in linbo3,” Appl. Phys. Lett. 19, 320–323 (1971).
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Biomed. Opt. Express (1)

Bull. Russ. Acad. Sci.: Phys. (1)

A. Tcypkin, S. Putilin, M. Kulya, M. Melnik, A. Drozdov, V. Bespalov, X.-C. Zhang, R. Boyd, and S. Kozlov, “Experimental estimate of the nonlinear refractive index of crystalline znse in the terahertz spectral range,” Bull. Russ. Acad. Sci.: Phys. 82, 1547–1549 (2018).
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[Crossref]

IEEE Photonics Technol. Lett. (1)

Y. V. Grachev, X. Liu, S. E. Putilin, A. N. Tsypkin, V. G. Bespalov, S. A. Kozlov, and X.-C. Zhang, “Wireless data transmission method using pulsed thz sliced spectral supercontinuum,” IEEE Photonics Technol. Lett. 30, 103–106 (2018).
[Crossref]

J. Infrared Millim. Terahertz Waves (1)

A. Woldegeorgis, T. Kurihara, B. Beleites, J. Bossert, R. Grosse, G. G. Paulus, F. Ronneberger, and A. Gopal, “Thz induced nonlinear effects in materials at intensities above 26 gw/cm 2,” J. Infrared Millim. Terahertz Waves 39, 667–680 (2018).
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S. Baierl, M. Hohenleutner, T. Kampfrath, A. Zvezdin, A. Kimel, R. Huber, and R. Mikhaylovskiy, “Nonlinear spin control by terahertz-driven anisotropy fields,” Nature Photon. 10, 715–718 (2016).
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Opt. Commun. (1)

A. Watanabe, H. Saito, Y. Ishida, M. Nakamoto, and T. Yajima, “A new nozzle producing ultrathin liquid sheets for femtosecond pulse dye lasers,” Opt. Commun. 71, 301–304 (1989).
[Crossref]

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Optica (3)

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S. Lin, S. Yu, and D. Talbayev, “Measurement of quadratic terahertz optical nonlinearities using second-harmonic lock-in detection,” Phys. Rev. Appl. 10, 044007 (2018).
[Crossref]

Phys. Rev. B (2)

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Observation of nonequilibrium carrier distribution in ge, si, and gaas by terahertz pump–terahertz probe measurements,” Phys. Rev. B 81, 035201 (2010).
[Crossref]

D. Turchinovich, J. M. Hvam, and M. C. Hoffmann, “Self-phase modulation of a single-cycle terahertz pulse by nonlinear free-carrier response in a semiconductor,” Phys. Rev. B 85, 201304 (2012).
[Crossref]

Phys. Rev. Lett. (3)

S. Baierl, J. H. Mentink, M. Hohenleutner, L. Braun, T.-M. Do, C. Lange, A. Sell, M. Fiebig, G. Woltersdorf, T. Kampfrath, and R. Huber, “Terahertz-driven nonlinear spin response of antiferromagnetic nickel oxide,” Phys. Rev. Lett. 117, 197201 (2016).
[Crossref] [PubMed]

C. Vicario, M. Shalaby, and C. P. Hauri, “Subcycle extreme nonlinearities in gap induced by an ultrastrong terahertz field,” Phys. Rev. Lett. 118, 083901 (2017).
[Crossref] [PubMed]

P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Nonlinear terahertz response of n-type gaas,” Phys. Rev. Lett. 96, 187402 (2006).
[Crossref]

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J. Dong, A. Locquet, M. Melis, and D. Citrin, “Global mapping of stratigraphy of an old-master painting using sparsity-based terahertz reflectometry,” Sci. Rep. 7, 15098 (2017).
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Other (2)

G. Kaur, P. Han, and X. Zhang, “Terahertz induced nonlinear effects in doped silicon observed by open-aperture z-scan,” in “Infrared Millimeter and Terahertz Waves (IRMMW-THz), 2010 35th International Conference on,” (IEEE, 2010), pp. 1–2.

R. W. Boyd, Nonlinear optics (Elsevier, 2003).

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Figures (3)

Fig. 1
Fig. 1 (a) The experimental setup for measuring the nonlinear refractive index (n2) of a liquid jet in the THz spectral range. Two parabolic mirrors (PM1 and PM2) with a focal length of 12.5 mm form the caustics area where the water jet (jet) is scanned along the z axis. The synchronization is performed using the mechanical modulator (M) located between the lens and the Golay cell (GC). The aperture (A) is moved from open to closed position to change the geometry of Z-scan from open to closed aperture. Insert - Geometrical position of the jet moved along the z axis relative to the THz radiation. The temporal waveform (b) and its spectrum (c) of the THz pulse generated by the TERA-AX system.
Fig. 2
Fig. 2 Z-scan curves for a 0.1 mm thick water jet measured with open (a) and closed (b) aperture for different THz radiation energy values of 4 nJ, 40 nJ and 400 nJ. Δ T = 0.013 is the differential of the Z-scan curve measured with the closed aperture of radius 1.5 mm.
Fig. 3
Fig. 3 Comparison of the experimental results of the closed aperture measurement of Z-scan method for the pulsed broadband THz radiation for the water jet 0.1 mm thick with an analytical Z-scan curve for monochromatic radiation with the wavelength of 0.4 mm. The analytical curve was calculated using Eq. (2).

Equations (5)

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n 2 = Δ T 0.406 I in × 2 λ 2 π L α ( 1 S ) 0.25
T ( z ) = + P T ( Δ Φ 0 ( t ) ) d t S + P i ( t ) d t
P T ( Δ Φ 0 ( t ) ) = c 0 N 0 π 0 r a a | E a ( r , t ) | 2 r d r
E a ( r , t ) = E ( z , r = 0 , t ) exp ( α L / 2 ) × m = 0 + [ i Δ ϕ 0 ( z , t ) ] m m ! w m 0 w m exp ( r 2 w m 2 i k r 2 2 R m + i Q m )
n ¯ 2 , ν = n ¯ 2 , ν ( 1 ) + n ¯ 2 , ν ( 2 ) = 3 a 1 2 m 2 ω 4 α T 2 32 n 0 π 2 q 2 N 2 k B 2 [ n 0 , ν 2 1 ] 3 9 32 π N n 0 ω [ n 0 , ν 2 1 ] 2

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