Abstract

We report on spontaneous parametric down-conversion (SPDC) in periodically poled lithium niobate (PPLN) using 660 nm pump wavelength and the type 0 phase-matching condition to the terahertz and even sub-terahertz frequency range. Detection of the frequency-shifted signal photons is achieved by using highly efficient and narrowband volume Bragg gratings and an uncooled sCMOS camera. The acquired frequency-angular spectrum shows backward and forward generation of terahertz and sub-terahertz photons by SPDC, as well as up-conversion and higher order quasi phase-matching (QPM). The frequency-angular spectrum is theoretically calculated using a Monte-Carlo integration scheme showing a high agreement with the measurement. This work is one important step toward quantum sensing and imaging in the terahertz and sub-terahertz frequency range.

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

Full Article  |  PDF Article
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Opt. Express 15(14) 8770-8780 (2007)

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    [Crossref]

2018 (4)

C. Liewald, S. Mastel, J. Hesler, A. J. Huber, R. Hillenbrand, and F. Keilmann, “All-electronic terahertz nanoscopy,” Optica,  5(2), 159–163 (2018).
[Crossref]

T. Pfeiffer, S. Weber, J. Klier, S. Bachtler, D. Molter, J. Jonuscheit, and G. von Freymann, “Terahertz thickness determination with interferometric vibration correction for industrial applications,” Opt. Express,  26(10), 12558–12568 (2018).
[Crossref] [PubMed]

V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. L. Schwefel, “Towards terahertz detection and calibration through spontaneous parametric down-conversion in the terahertz idler-frequency range generated by a 795 nm diode laser system,” APL Photonics,  3(5), 051704 (2018).
[Crossref]

J. Schneeloch, S. H. Knarr, D. F. Bogorin, M. L. Levangie, C. C. Tison, R. Frank, G. A. Howland, M. L. Fanto, and P. M. Alsing, “Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion,” arXiv preprint arXiv: 1807.10885 (2018).

2017 (1)

S. Krimi, G. Torosyan, and R. Beigang, “Advanced GPU-based terahertz approach for in-line multilayer thickness measurements,” IEEE J. Sel. Top. Quantum,  23(4), 1–12 (2017).
[Crossref]

2016 (2)

J. Schneeloch and J. C. Howell, “Introduction to the transverse spatial correlations in spontaneous parametric down-conversion through the biphoton birth zone,” J. Opt.,  18(5), 053501 (2016).
[Crossref]

V. V. Kornienko, S. A. Savinov, Y. A. Mityagin, and G. K. Kitaeva, “Terahertz continuous wave nonlinear-optical detection without phase-locking between a source and the detector,” Opt. Lett., 41(17), 4075–4078 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (2)

G. K. Kitaeva, P. V. Yakunin, V. V. Kornienko, and A. N. Penin, “Absolute brightness measurements in the terahertz frequency range using vacuum and thermal fluctuations as references,” Appl. Phys. B,  116(4), 929–937 (2014).
[Crossref]

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, “Quantum imaging with undetected photons,” Nature,  512(7515), 409–412 (2014).
[Crossref] [PubMed]

2013 (1)

V. V. Kornienko, G. K. Kitaeva, I. I. Naumova, A. N. Tuchak, A. N. Penin, and P. V. Yakunin, “Evaluating the spectral sensitivity of the nonlinear-optical terahertz wave radiation detecors via spontaneous parametric down-conversion spectra,” Opt. Spectrosc.,  116(4), 520–528 (2013).
[Crossref]

2012 (1)

2011 (4)

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging-Modern techniques and applications,” Laser Photonics Rev.,  5(1), 124–166 (2011).
[Crossref]

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys.,  83(2), 543–586 (2011).
[Crossref]

F. Ellrich, T. Weinland, D. Molter, J. Jonuscheit, and R. Beigang, “Compact fiber-coupled terahertz spectroscopy system pumped at 800 nm wavelength,” Rev. Sci. Instrum.,  82(5), 053102 (2011).
[Crossref] [PubMed]

G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” J. Infrared Millim. Terahertz Waves,  32(10), 1144–1156 (2011).
[Crossref]

2010 (3)

O. Gayer, Z. Sacks, E. Galun, and A. Arie, Erratum to: “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO 3,” Appl. Phys. B,  101(1), 343–348 (2010).
[Crossref]

F. Z. Meng, M. D. Thomson, D. Molter, T. Löfler, J. Jonuscheit, R. Beigang, J. Bartschke, T. Bauer, M. Nittmann, and H. G. Roskos, “Coherent electro-optical detection of terahertz radiation from an optical parametric oscillator,” Opt. Express,  18(11), 11316–11326 (2010).
[Crossref] [PubMed]

R. Sowade, I. Breunig, C. Tulea, and K. Buse, “Nonlinear coefficient and temperature dependence of the refractive index of lithium niobate crystals in the terahertz regime,” Appl. Phys. B,  99(1–2), 63–66 (2010).
[Crossref]

2009 (2)

2008 (3)

B. Sartorius, H. Roehle, H. Künzel, J. Böttcher, M. Schlak, D. Stanze, H. Venghaus, and M. Schell, “All-fiber terahertz time-domain spectrometer operating at 1.5 μm telecom wavelengths,” Opt. Express,  16(13), 9565–9570 (2008).
[Crossref] [PubMed]

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices,” Nano Lett.,  8(11), 3766–3770 (2008).
[Crossref] [PubMed]

K. L. Vodopyanov, “Optical THz-wave generation with periodically-inverted GaAs,” Laser Photonics Rev.,  2(1–2), 11–25 (2008).
[Crossref]

2007 (2)

J. A. L’huillier, G. Torosyan, M. Theuer, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 1: theory,” Appl. Phys. B,  86(2), 185–196 (2007).
[Crossref]

J. A. L’huillier, G. Torosyan, M. Theuer, C. Rau, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 2: experiments,” Appl. Phys. B,  86(2), 197–208 (2007).
[Crossref]

2006 (1)

2004 (1)

J. Hebling, A- G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tiltes pulse fronts,” Appl. Phys. B,  78(5), 593–599 (2004).
[Crossref]

2003 (1)

2002 (1)

K. Kawase, J. Shikata, and H. Ito, “Terahertz wave parametric source,” J. Phys. D,  35(3), R1–R14 (2002).
[Crossref]

1995 (1)

1990 (1)

Ahr, F.

Aizpurua, J.

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices,” Nano Lett.,  8(11), 3766–3770 (2008).
[Crossref] [PubMed]

Almási, G.

J. Hebling, A- G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tiltes pulse fronts,” Appl. Phys. B,  78(5), 593–599 (2004).
[Crossref]

Alsing, P. M.

J. Schneeloch, S. H. Knarr, D. F. Bogorin, M. L. Levangie, C. C. Tison, R. Frank, G. A. Howland, M. L. Fanto, and P. M. Alsing, “Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion,” arXiv preprint arXiv: 1807.10885 (2018).

Arie, A.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, Erratum to: “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO 3,” Appl. Phys. B,  101(1), 343–348 (2010).
[Crossref]

Avetisyan, Y.

J. A. L’huillier, G. Torosyan, M. Theuer, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 1: theory,” Appl. Phys. B,  86(2), 185–196 (2007).
[Crossref]

J. A. L’huillier, G. Torosyan, M. Theuer, C. Rau, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 2: experiments,” Appl. Phys. B,  86(2), 197–208 (2007).
[Crossref]

Bachtler, S.

Ballon, G.

Bartal, B.

J. Hebling, A- G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tiltes pulse fronts,” Appl. Phys. B,  78(5), 593–599 (2004).
[Crossref]

Bartschke, J.

Bauer, T.

Beigang, R.

S. Krimi, G. Torosyan, and R. Beigang, “Advanced GPU-based terahertz approach for in-line multilayer thickness measurements,” IEEE J. Sel. Top. Quantum,  23(4), 1–12 (2017).
[Crossref]

D. Molter, G. Torosyan, G. Ballon, L. Drigo, R. Beigang, and J. Léotin, “Step-scan time-domain terahertz magneto-spectroscopy,” Opt. Express,  20(6), 5993–6002 (2012).
[Crossref] [PubMed]

F. Ellrich, T. Weinland, D. Molter, J. Jonuscheit, and R. Beigang, “Compact fiber-coupled terahertz spectroscopy system pumped at 800 nm wavelength,” Rev. Sci. Instrum.,  82(5), 053102 (2011).
[Crossref] [PubMed]

F. Z. Meng, M. D. Thomson, D. Molter, T. Löfler, J. Jonuscheit, R. Beigang, J. Bartschke, T. Bauer, M. Nittmann, and H. G. Roskos, “Coherent electro-optical detection of terahertz radiation from an optical parametric oscillator,” Opt. Express,  18(11), 11316–11326 (2010).
[Crossref] [PubMed]

D. Molter, M. Theuer, and R. Beigang, “Nanosecond terahertz optical parametric oscillator with a novel quasi phase-matching scheme in lithium niobate,” Opt. Express,  17(8), 6623–6628 (2009).
[Crossref] [PubMed]

J. A. L’huillier, G. Torosyan, M. Theuer, C. Rau, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 2: experiments,” Appl. Phys. B,  86(2), 197–208 (2007).
[Crossref]

J. A. L’huillier, G. Torosyan, M. Theuer, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 1: theory,” Appl. Phys. B,  86(2), 185–196 (2007).
[Crossref]

Bogorin, D. F.

J. Schneeloch, S. H. Knarr, D. F. Bogorin, M. L. Levangie, C. C. Tison, R. Frank, G. A. Howland, M. L. Fanto, and P. M. Alsing, “Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion,” arXiv preprint arXiv: 1807.10885 (2018).

Bonn, M.

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys.,  83(2), 543–586 (2011).
[Crossref]

Borish, V.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, “Quantum imaging with undetected photons,” Nature,  512(7515), 409–412 (2014).
[Crossref] [PubMed]

Böttcher, J.

Breunig, I.

R. Sowade, I. Breunig, C. Tulea, and K. Buse, “Nonlinear coefficient and temperature dependence of the refractive index of lithium niobate crystals in the terahertz regime,” Appl. Phys. B,  99(1–2), 63–66 (2010).
[Crossref]

R. Sowade, I. Breunig, I. C. Mayorga, J. Kiessling, C. Tulea, V. Dierolf, and K. Buse, “Continuous-wave optical parametric terahertz source,” Opt. Express,  17(25), 22303–22310 (2009).
[Crossref]

Buse, K.

R. Sowade, I. Breunig, C. Tulea, and K. Buse, “Nonlinear coefficient and temperature dependence of the refractive index of lithium niobate crystals in the terahertz regime,” Appl. Phys. B,  99(1–2), 63–66 (2010).
[Crossref]

R. Sowade, I. Breunig, I. C. Mayorga, J. Kiessling, C. Tulea, V. Dierolf, and K. Buse, “Continuous-wave optical parametric terahertz source,” Opt. Express,  17(25), 22303–22310 (2009).
[Crossref]

Cole, G. D.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, “Quantum imaging with undetected photons,” Nature,  512(7515), 409–412 (2014).
[Crossref] [PubMed]

Cooke, D. G.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging-Modern techniques and applications,” Laser Photonics Rev.,  5(1), 124–166 (2011).
[Crossref]

Dierolf, V.

Drigo, L.

Dunn, M. H.

Edwards, T. J.

Ellrich, F.

F. Ellrich, T. Weinland, D. Molter, J. Jonuscheit, and R. Beigang, “Compact fiber-coupled terahertz spectroscopy system pumped at 800 nm wavelength,” Rev. Sci. Instrum.,  82(5), 053102 (2011).
[Crossref] [PubMed]

Fanto, M. L.

J. Schneeloch, S. H. Knarr, D. F. Bogorin, M. L. Levangie, C. C. Tison, R. Frank, G. A. Howland, M. L. Fanto, and P. M. Alsing, “Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion,” arXiv preprint arXiv: 1807.10885 (2018).

Fattinger, C.

Frank, R.

J. Schneeloch, S. H. Knarr, D. F. Bogorin, M. L. Levangie, C. C. Tison, R. Frank, G. A. Howland, M. L. Fanto, and P. M. Alsing, “Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion,” arXiv preprint arXiv: 1807.10885 (2018).

Galun, E.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, Erratum to: “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO 3,” Appl. Phys. B,  101(1), 343–348 (2010).
[Crossref]

Gayer, O.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, Erratum to: “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO 3,” Appl. Phys. B,  101(1), 343–348 (2010).
[Crossref]

Grischkowsky, D.

Hebling, J.

J. Hebling, A- G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tiltes pulse fronts,” Appl. Phys. B,  78(5), 593–599 (2004).
[Crossref]

Heinz, T. F.

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys.,  83(2), 543–586 (2011).
[Crossref]

Hendry, E.

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys.,  83(2), 543–586 (2011).
[Crossref]

Hesler, J.

Hillenbrand, R.

C. Liewald, S. Mastel, J. Hesler, A. J. Huber, R. Hillenbrand, and F. Keilmann, “All-electronic terahertz nanoscopy,” Optica,  5(2), 159–163 (2018).
[Crossref]

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices,” Nano Lett.,  8(11), 3766–3770 (2008).
[Crossref] [PubMed]

Howell, J. C.

J. Schneeloch and J. C. Howell, “Introduction to the transverse spatial correlations in spontaneous parametric down-conversion through the biphoton birth zone,” J. Opt.,  18(5), 053501 (2016).
[Crossref]

Howland, G. A.

J. Schneeloch, S. H. Knarr, D. F. Bogorin, M. L. Levangie, C. C. Tison, R. Frank, G. A. Howland, M. L. Fanto, and P. M. Alsing, “Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion,” arXiv preprint arXiv: 1807.10885 (2018).

Hu, B. B.

Huang, W. R.

Huber, A. J.

C. Liewald, S. Mastel, J. Hesler, A. J. Huber, R. Hillenbrand, and F. Keilmann, “All-electronic terahertz nanoscopy,” Optica,  5(2), 159–163 (2018).
[Crossref]

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices,” Nano Lett.,  8(11), 3766–3770 (2008).
[Crossref] [PubMed]

Inoue, H.

Ito, H.

K. Kawase, J. Shikata, and H. Ito, “Terahertz wave parametric source,” J. Phys. D,  35(3), R1–R14 (2002).
[Crossref]

Jepsen, P. U.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging-Modern techniques and applications,” Laser Photonics Rev.,  5(1), 124–166 (2011).
[Crossref]

Jonuscheit, J.

Kärtner, F. X.

Kawase, K.

Keiding, S.

Keilmann, F.

C. Liewald, S. Mastel, J. Hesler, A. J. Huber, R. Hillenbrand, and F. Keilmann, “All-electronic terahertz nanoscopy,” Optica,  5(2), 159–163 (2018).
[Crossref]

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices,” Nano Lett.,  8(11), 3766–3770 (2008).
[Crossref] [PubMed]

Kiessling, J.

Kitaeva, G. K.

V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. L. Schwefel, “Towards terahertz detection and calibration through spontaneous parametric down-conversion in the terahertz idler-frequency range generated by a 795 nm diode laser system,” APL Photonics,  3(5), 051704 (2018).
[Crossref]

V. V. Kornienko, S. A. Savinov, Y. A. Mityagin, and G. K. Kitaeva, “Terahertz continuous wave nonlinear-optical detection without phase-locking between a source and the detector,” Opt. Lett., 41(17), 4075–4078 (2016).
[Crossref] [PubMed]

G. K. Kitaeva, P. V. Yakunin, V. V. Kornienko, and A. N. Penin, “Absolute brightness measurements in the terahertz frequency range using vacuum and thermal fluctuations as references,” Appl. Phys. B,  116(4), 929–937 (2014).
[Crossref]

V. V. Kornienko, G. K. Kitaeva, I. I. Naumova, A. N. Tuchak, A. N. Penin, and P. V. Yakunin, “Evaluating the spectral sensitivity of the nonlinear-optical terahertz wave radiation detecors via spontaneous parametric down-conversion spectra,” Opt. Spectrosc.,  116(4), 520–528 (2013).
[Crossref]

G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” J. Infrared Millim. Terahertz Waves,  32(10), 1144–1156 (2011).
[Crossref]

Klier, J.

Knarr, S. H.

J. Schneeloch, S. H. Knarr, D. F. Bogorin, M. L. Levangie, C. C. Tison, R. Frank, G. A. Howland, M. L. Fanto, and P. M. Alsing, “Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion,” arXiv preprint arXiv: 1807.10885 (2018).

Koch, M.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging-Modern techniques and applications,” Laser Photonics Rev.,  5(1), 124–166 (2011).
[Crossref]

Kornienko, V. V.

V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. L. Schwefel, “Towards terahertz detection and calibration through spontaneous parametric down-conversion in the terahertz idler-frequency range generated by a 795 nm diode laser system,” APL Photonics,  3(5), 051704 (2018).
[Crossref]

V. V. Kornienko, S. A. Savinov, Y. A. Mityagin, and G. K. Kitaeva, “Terahertz continuous wave nonlinear-optical detection without phase-locking between a source and the detector,” Opt. Lett., 41(17), 4075–4078 (2016).
[Crossref] [PubMed]

G. K. Kitaeva, P. V. Yakunin, V. V. Kornienko, and A. N. Penin, “Absolute brightness measurements in the terahertz frequency range using vacuum and thermal fluctuations as references,” Appl. Phys. B,  116(4), 929–937 (2014).
[Crossref]

V. V. Kornienko, G. K. Kitaeva, I. I. Naumova, A. N. Tuchak, A. N. Penin, and P. V. Yakunin, “Evaluating the spectral sensitivity of the nonlinear-optical terahertz wave radiation detecors via spontaneous parametric down-conversion spectra,” Opt. Spectrosc.,  116(4), 520–528 (2013).
[Crossref]

Kovalev, S. P.

G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” J. Infrared Millim. Terahertz Waves,  32(10), 1144–1156 (2011).
[Crossref]

Krimi, S.

S. Krimi, G. Torosyan, and R. Beigang, “Advanced GPU-based terahertz approach for in-line multilayer thickness measurements,” IEEE J. Sel. Top. Quantum,  23(4), 1–12 (2017).
[Crossref]

Kuhl, J.

J. Hebling, A- G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tiltes pulse fronts,” Appl. Phys. B,  78(5), 593–599 (2004).
[Crossref]

Künzel, H.

L’huillier, J. A.

J. A. L’huillier, G. Torosyan, M. Theuer, C. Rau, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 2: experiments,” Appl. Phys. B,  86(2), 197–208 (2007).
[Crossref]

J. A. L’huillier, G. Torosyan, M. Theuer, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 1: theory,” Appl. Phys. B,  86(2), 185–196 (2007).
[Crossref]

Lapkiewicz, R.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, “Quantum imaging with undetected photons,” Nature,  512(7515), 409–412 (2014).
[Crossref] [PubMed]

Lemos, G. B.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, “Quantum imaging with undetected photons,” Nature,  512(7515), 409–412 (2014).
[Crossref] [PubMed]

Léotin, J.

Leuchs, G.

V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. L. Schwefel, “Towards terahertz detection and calibration through spontaneous parametric down-conversion in the terahertz idler-frequency range generated by a 795 nm diode laser system,” APL Photonics,  3(5), 051704 (2018).
[Crossref]

Levangie, M. L.

J. Schneeloch, S. H. Knarr, D. F. Bogorin, M. L. Levangie, C. C. Tison, R. Frank, G. A. Howland, M. L. Fanto, and P. M. Alsing, “Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion,” arXiv preprint arXiv: 1807.10885 (2018).

Liewald, C.

Löfler, T.

Mastel, S.

Mayorga, I. C.

Meng, F. Z.

Mityagin, Y. A.

Molter, D.

Naumova, I. I.

V. V. Kornienko, G. K. Kitaeva, I. I. Naumova, A. N. Tuchak, A. N. Penin, and P. V. Yakunin, “Evaluating the spectral sensitivity of the nonlinear-optical terahertz wave radiation detecors via spontaneous parametric down-conversion spectra,” Opt. Spectrosc.,  116(4), 520–528 (2013).
[Crossref]

Nittmann, M.

Nuss, M. C.

Ogawa, Y.

Penin, A. N.

G. K. Kitaeva, P. V. Yakunin, V. V. Kornienko, and A. N. Penin, “Absolute brightness measurements in the terahertz frequency range using vacuum and thermal fluctuations as references,” Appl. Phys. B,  116(4), 929–937 (2014).
[Crossref]

V. V. Kornienko, G. K. Kitaeva, I. I. Naumova, A. N. Tuchak, A. N. Penin, and P. V. Yakunin, “Evaluating the spectral sensitivity of the nonlinear-optical terahertz wave radiation detecors via spontaneous parametric down-conversion spectra,” Opt. Spectrosc.,  116(4), 520–528 (2013).
[Crossref]

G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” J. Infrared Millim. Terahertz Waves,  32(10), 1144–1156 (2011).
[Crossref]

Pfeiffer, T.

Rae, C. F.

Ramelow, S.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, “Quantum imaging with undetected photons,” Nature,  512(7515), 409–412 (2014).
[Crossref] [PubMed]

Rau, C.

J. A. L’huillier, G. Torosyan, M. Theuer, C. Rau, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 2: experiments,” Appl. Phys. B,  86(2), 197–208 (2007).
[Crossref]

Roehle, H.

Roskos, H. G.

Sacks, Z.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, Erratum to: “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO 3,” Appl. Phys. B,  101(1), 343–348 (2010).
[Crossref]

Sartorius, B.

Savinov, S. A.

Schell, M.

Schlak, M.

Schneeloch, J.

J. Schneeloch, S. H. Knarr, D. F. Bogorin, M. L. Levangie, C. C. Tison, R. Frank, G. A. Howland, M. L. Fanto, and P. M. Alsing, “Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion,” arXiv preprint arXiv: 1807.10885 (2018).

J. Schneeloch and J. C. Howell, “Introduction to the transverse spatial correlations in spontaneous parametric down-conversion through the biphoton birth zone,” J. Opt.,  18(5), 053501 (2016).
[Crossref]

Schwefel, H. G. L.

V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. L. Schwefel, “Towards terahertz detection and calibration through spontaneous parametric down-conversion in the terahertz idler-frequency range generated by a 795 nm diode laser system,” APL Photonics,  3(5), 051704 (2018).
[Crossref]

Sedlmeir, F.

V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. L. Schwefel, “Towards terahertz detection and calibration through spontaneous parametric down-conversion in the terahertz idler-frequency range generated by a 795 nm diode laser system,” APL Photonics,  3(5), 051704 (2018).
[Crossref]

Shan, J.

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys.,  83(2), 543–586 (2011).
[Crossref]

Shikata, J.

K. Kawase, J. Shikata, and H. Ito, “Terahertz wave parametric source,” J. Phys. D,  35(3), R1–R14 (2002).
[Crossref]

Sowade, R.

R. Sowade, I. Breunig, C. Tulea, and K. Buse, “Nonlinear coefficient and temperature dependence of the refractive index of lithium niobate crystals in the terahertz regime,” Appl. Phys. B,  99(1–2), 63–66 (2010).
[Crossref]

R. Sowade, I. Breunig, I. C. Mayorga, J. Kiessling, C. Tulea, V. Dierolf, and K. Buse, “Continuous-wave optical parametric terahertz source,” Opt. Express,  17(25), 22303–22310 (2009).
[Crossref]

Spurr, M. B.

Stanze, D.

Stepanov, A- G.

J. Hebling, A- G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tiltes pulse fronts,” Appl. Phys. B,  78(5), 593–599 (2004).
[Crossref]

Theuer, M.

D. Molter, M. Theuer, and R. Beigang, “Nanosecond terahertz optical parametric oscillator with a novel quasi phase-matching scheme in lithium niobate,” Opt. Express,  17(8), 6623–6628 (2009).
[Crossref] [PubMed]

J. A. L’huillier, G. Torosyan, M. Theuer, C. Rau, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 2: experiments,” Appl. Phys. B,  86(2), 197–208 (2007).
[Crossref]

J. A. L’huillier, G. Torosyan, M. Theuer, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 1: theory,” Appl. Phys. B,  86(2), 185–196 (2007).
[Crossref]

Thomson, M. D.

Tison, C. C.

J. Schneeloch, S. H. Knarr, D. F. Bogorin, M. L. Levangie, C. C. Tison, R. Frank, G. A. Howland, M. L. Fanto, and P. M. Alsing, “Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion,” arXiv preprint arXiv: 1807.10885 (2018).

Torosyan, G.

S. Krimi, G. Torosyan, and R. Beigang, “Advanced GPU-based terahertz approach for in-line multilayer thickness measurements,” IEEE J. Sel. Top. Quantum,  23(4), 1–12 (2017).
[Crossref]

D. Molter, G. Torosyan, G. Ballon, L. Drigo, R. Beigang, and J. Léotin, “Step-scan time-domain terahertz magneto-spectroscopy,” Opt. Express,  20(6), 5993–6002 (2012).
[Crossref] [PubMed]

J. A. L’huillier, G. Torosyan, M. Theuer, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 1: theory,” Appl. Phys. B,  86(2), 185–196 (2007).
[Crossref]

J. A. L’huillier, G. Torosyan, M. Theuer, C. Rau, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 2: experiments,” Appl. Phys. B,  86(2), 197–208 (2007).
[Crossref]

Tuchak, A. N.

V. V. Kornienko, G. K. Kitaeva, I. I. Naumova, A. N. Tuchak, A. N. Penin, and P. V. Yakunin, “Evaluating the spectral sensitivity of the nonlinear-optical terahertz wave radiation detecors via spontaneous parametric down-conversion spectra,” Opt. Spectrosc.,  116(4), 520–528 (2013).
[Crossref]

G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” J. Infrared Millim. Terahertz Waves,  32(10), 1144–1156 (2011).
[Crossref]

Tulea, C.

R. Sowade, I. Breunig, C. Tulea, and K. Buse, “Nonlinear coefficient and temperature dependence of the refractive index of lithium niobate crystals in the terahertz regime,” Appl. Phys. B,  99(1–2), 63–66 (2010).
[Crossref]

R. Sowade, I. Breunig, I. C. Mayorga, J. Kiessling, C. Tulea, V. Dierolf, and K. Buse, “Continuous-wave optical parametric terahertz source,” Opt. Express,  17(25), 22303–22310 (2009).
[Crossref]

Ulbricht, R.

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys.,  83(2), 543–586 (2011).
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van Exter, M.

Venghaus, H.

Vodopyanov, K. L.

K. L. Vodopyanov, “Optical THz-wave generation with periodically-inverted GaAs,” Laser Photonics Rev.,  2(1–2), 11–25 (2008).
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von Freymann, G.

Walsh, D.

Watanabe, Y.

Weber, S.

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Weinland, T.

F. Ellrich, T. Weinland, D. Molter, J. Jonuscheit, and R. Beigang, “Compact fiber-coupled terahertz spectroscopy system pumped at 800 nm wavelength,” Rev. Sci. Instrum.,  82(5), 053102 (2011).
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Wittborn, J.

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices,” Nano Lett.,  8(11), 3766–3770 (2008).
[Crossref] [PubMed]

Wu, X.

Yakunin, P. V.

G. K. Kitaeva, P. V. Yakunin, V. V. Kornienko, and A. N. Penin, “Absolute brightness measurements in the terahertz frequency range using vacuum and thermal fluctuations as references,” Appl. Phys. B,  116(4), 929–937 (2014).
[Crossref]

V. V. Kornienko, G. K. Kitaeva, I. I. Naumova, A. N. Tuchak, A. N. Penin, and P. V. Yakunin, “Evaluating the spectral sensitivity of the nonlinear-optical terahertz wave radiation detecors via spontaneous parametric down-conversion spectra,” Opt. Spectrosc.,  116(4), 520–528 (2013).
[Crossref]

G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” J. Infrared Millim. Terahertz Waves,  32(10), 1144–1156 (2011).
[Crossref]

Zeilinger, A.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, “Quantum imaging with undetected photons,” Nature,  512(7515), 409–412 (2014).
[Crossref] [PubMed]

Zhou, C.

APL Photonics (1)

V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. L. Schwefel, “Towards terahertz detection and calibration through spontaneous parametric down-conversion in the terahertz idler-frequency range generated by a 795 nm diode laser system,” APL Photonics,  3(5), 051704 (2018).
[Crossref]

Appl. Phys. B (6)

J. A. L’huillier, G. Torosyan, M. Theuer, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 1: theory,” Appl. Phys. B,  86(2), 185–196 (2007).
[Crossref]

J. A. L’huillier, G. Torosyan, M. Theuer, C. Rau, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate - part 2: experiments,” Appl. Phys. B,  86(2), 197–208 (2007).
[Crossref]

G. K. Kitaeva, P. V. Yakunin, V. V. Kornienko, and A. N. Penin, “Absolute brightness measurements in the terahertz frequency range using vacuum and thermal fluctuations as references,” Appl. Phys. B,  116(4), 929–937 (2014).
[Crossref]

O. Gayer, Z. Sacks, E. Galun, and A. Arie, Erratum to: “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO 3,” Appl. Phys. B,  101(1), 343–348 (2010).
[Crossref]

J. Hebling, A- G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tiltes pulse fronts,” Appl. Phys. B,  78(5), 593–599 (2004).
[Crossref]

R. Sowade, I. Breunig, C. Tulea, and K. Buse, “Nonlinear coefficient and temperature dependence of the refractive index of lithium niobate crystals in the terahertz regime,” Appl. Phys. B,  99(1–2), 63–66 (2010).
[Crossref]

arXiv preprint arXiv (1)

J. Schneeloch, S. H. Knarr, D. F. Bogorin, M. L. Levangie, C. C. Tison, R. Frank, G. A. Howland, M. L. Fanto, and P. M. Alsing, “Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion,” arXiv preprint arXiv: 1807.10885 (2018).

IEEE J. Sel. Top. Quantum (1)

S. Krimi, G. Torosyan, and R. Beigang, “Advanced GPU-based terahertz approach for in-line multilayer thickness measurements,” IEEE J. Sel. Top. Quantum,  23(4), 1–12 (2017).
[Crossref]

J. Infrared Millim. Terahertz Waves (1)

G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” J. Infrared Millim. Terahertz Waves,  32(10), 1144–1156 (2011).
[Crossref]

J. Opt. (1)

J. Schneeloch and J. C. Howell, “Introduction to the transverse spatial correlations in spontaneous parametric down-conversion through the biphoton birth zone,” J. Opt.,  18(5), 053501 (2016).
[Crossref]

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

J. Phys. D (1)

K. Kawase, J. Shikata, and H. Ito, “Terahertz wave parametric source,” J. Phys. D,  35(3), R1–R14 (2002).
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Laser Photonics Rev. (2)

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging-Modern techniques and applications,” Laser Photonics Rev.,  5(1), 124–166 (2011).
[Crossref]

K. L. Vodopyanov, “Optical THz-wave generation with periodically-inverted GaAs,” Laser Photonics Rev.,  2(1–2), 11–25 (2008).
[Crossref]

Nano Lett. (1)

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices,” Nano Lett.,  8(11), 3766–3770 (2008).
[Crossref] [PubMed]

Nature (1)

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, “Quantum imaging with undetected photons,” Nature,  512(7515), 409–412 (2014).
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Opt. Express (9)

T. J. Edwards, D. Walsh, M. B. Spurr, C. F. Rae, and M. H. Dunn, “Compact source of continuously and widely-tunable terahertz radiation,” Opt. Express,  14(4), 1582–1589 (2006).
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D. Molter, M. Theuer, and R. Beigang, “Nanosecond terahertz optical parametric oscillator with a novel quasi phase-matching scheme in lithium niobate,” Opt. Express,  17(8), 6623–6628 (2009).
[Crossref] [PubMed]

R. Sowade, I. Breunig, I. C. Mayorga, J. Kiessling, C. Tulea, V. Dierolf, and K. Buse, “Continuous-wave optical parametric terahertz source,” Opt. Express,  17(25), 22303–22310 (2009).
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F. Z. Meng, M. D. Thomson, D. Molter, T. Löfler, J. Jonuscheit, R. Beigang, J. Bartschke, T. Bauer, M. Nittmann, and H. G. Roskos, “Coherent electro-optical detection of terahertz radiation from an optical parametric oscillator,” Opt. Express,  18(11), 11316–11326 (2010).
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D. Molter, G. Torosyan, G. Ballon, L. Drigo, R. Beigang, and J. Léotin, “Step-scan time-domain terahertz magneto-spectroscopy,” Opt. Express,  20(6), 5993–6002 (2012).
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T. Pfeiffer, S. Weber, J. Klier, S. Bachtler, D. Molter, J. Jonuscheit, and G. von Freymann, “Terahertz thickness determination with interferometric vibration correction for industrial applications,” Opt. Express,  26(10), 12558–12568 (2018).
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X. Wu, C. Zhou, W. R. Huang, F. Ahr, and F. X. Kärtner, “Temperature dependent refractive index and absorption coefficient of congruent lithium niobate crystals in the terahertz range,” Opt. Express,  23(23), 29729–29737 (2015).
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Opt. Spectrosc. (1)

V. V. Kornienko, G. K. Kitaeva, I. I. Naumova, A. N. Tuchak, A. N. Penin, and P. V. Yakunin, “Evaluating the spectral sensitivity of the nonlinear-optical terahertz wave radiation detecors via spontaneous parametric down-conversion spectra,” Opt. Spectrosc.,  116(4), 520–528 (2013).
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Rev. Mod. Phys. (1)

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys.,  83(2), 543–586 (2011).
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Rev. Sci. Instrum. (1)

F. Ellrich, T. Weinland, D. Molter, J. Jonuscheit, and R. Beigang, “Compact fiber-coupled terahertz spectroscopy system pumped at 800 nm wavelength,” Rev. Sci. Instrum.,  82(5), 053102 (2011).
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S. Weinberg, The Quantum Theory of Fields, Vol. I: Foundations (Cambridge University Press, 1995).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Phase-matching schemes. The periodic poling of the nonlinear crystal leads to a k-vector component kΛ, which can have two directions. This yields phase-matched terahertz generation in forward and backward direction. Pump (p), signal (s) and idler (THz) wave vectors have to be considered as non-collinear in down- (sd) and up-conversion (su).
Fig. 2
Fig. 2 Schematic experimental setup. RBP: reflective bandpass filter. λ/2: zero-order half-wave plate. f: lens. PPLN: periodically poled MgO-doped LiNbO3-crystal. VBG: volume Bragg grating. SF: spatial filter. TG: transmission grating. M: mirror. PF: polarization filter. Additional mirrors used for beam folding as well as beam blocks used in the real setup are not shown. Length of optical paths are not to scale.
Fig. 3
Fig. 3 a) Laser output spectrum with the RBP. The pump signal has a FWHM of about 0.1 nm. b) Filter characteristics of the used volume Bragg gratings. All these filters provide at least an optical density of 4 at the design (pump) wavelength. The spectral width of the filters is well suited for experiments in the (idler) frequency range down to 0.3 THz.
Fig. 4
Fig. 4 Frequency-angular spectrum of a PPLN crystal with Λ = 170 μm (crystal length = 1 cm) pumped at 659.58 nm. An additional slit is placed in the beam path. The scattering angle is the one outside of the crystal. This single unworked image is recorded with an illumination time of 500 ms.
Fig. 5
Fig. 5 Frequency-angular spectrum of a PPLN crystal with Λ = 80 μm and crystal length of 1 mm pumped at 659.58 nm. An additional slit is placed in the beam path. This raw image is recorded with an illumination time of 5000 ms to get an intensity distribution comparable to the 10 mm long crystal with 500 ms illumination time (shown in Fig. 4).
Fig. 6
Fig. 6 Pump power dependence of the photon count rate per pixel in the collinear forward direction. The linear dependence is a clear indication that our experiments are performed in the low-gain regime. The insets show the considered region.
Fig. 7
Fig. 7 Simulated frequency-angular spectrum for the setup used for Fig. 4. The color scale corresponds to the one in Fig. 4 minus the average dark count rate. Shape and count rates agree well with the experimentally observed spectrum.

Equations (20)

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ω p = ω s + ω THz k p = k s + k THz k Λ + Δ k
ω p + ω THz = ω s k p + k THz = k s k Λ + Δ k
H I = 3 ! 3 ϵ 0 d 3 r χ eff ( 2 ) ( r ) E p ( r , t ) E s ( r , t ) E THz ( r , t ) = d 3 r H I ,
( k p k s k THz ) = 2 π | M | 2 δ ( ω p ω s ω THz ) δ 3 ( k p k s k THz ) d 3 k s d 3 k THz .
| M | 2 = | k s , k THz | H I | k p | 2 = | 2 χ e f f ( 2 ) ( 2 π ) 3 / 2 ϵ 0 ω p 2 n p 2 ω s 2 n s 2 ω T H z 2 n T H z 2 | 2 .
P = 1 | 1 u THz 1 u s | 1 1 u s 1 u THz ( n s ω s c ) 2 Ω s ,
1 u j = d k j d ω j ,    j = p , s , THz .
Γ = 2 π | M | 2 P
ρ = Γ L u p = 1 8 π 2 ( χ eff ( 2 ) ) 2 ϵ 0 ω p ω s ω T H z n p 2 n s 2 n T H z 2 | 1 u T H z 1 u s | 1 1 u s 1 u T H z ( n s ω s c ) 2 Ω s L u p .
1 + N th = 1 + 1 exp ( ω THz / k B T ) 1
R s = η ρ ( 1 + N th ) P p ω p ,
| ψ = i d t H I ( t ) | 0 ,
Γ ( θ s , λ s ) = 1 T I Ω ( θ s ) d φ s ψ | a s a s | ψ k s | 2 sin  ( θ s )
= Z m   odd Ω ( θ s ) d φ s d 3 k THz | A ( k p , k s , k THz ) | 2 | k s | 2 sin   ( θ s ) ,
A ( k p , k s , k THz ) = ω s ω THz n s 2 n THz 2 ( 1 2 Δ k z L ) exp  ( 1 4 ( Δ k x 2 + Δ k y 2 ) w 0 2 ) ( 1 2 Δ ω T I ) ,
Z = ϵ 0 c 3 4 ( 2 π ) 3 u p ( χ eff ( 2 ) ) 2 w 0 2 L 3 P p ,
R d ( θ s , λ s ) = η S D T ( 1 + N th ) Γ ( θ s , λ s ) .
R u ( θ s , λ s ) = η S D T N th Γ ( θ s , λ s ) .
R s = 5.2 10 6 1 Ws × P p ,
d eff = 78   pm V .

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