Determination of the water vapor continuum absorption by THz-TDS and Molecular Response Theory

Yihong Yang; Mahboubeh Mandehgar; D. Grischkowsky

doi:10.1364/OE.22.004388

Determination of the water vapor continuum absorption by THz-TDS and Molecular Response Theory

Yihong Yang, Mahboubeh Mandehgar, and D. Grischkowsky

Optics Express
Vol. 22,
Issue 4,
pp. 4388-4403
(2014)
•https://doi.org/10.1364/OE.22.004388

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Yihong Yang, Mahboubeh Mandehgar, and D. Grischkowsky, "Determination of the water vapor continuum absorption by THz-TDS and Molecular Response Theory," Opt. Express 22, 4388-4403 (2014)

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Related Topics
Table of Contents Category
- Terahertz and X-ray Optics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Atmospheric transmittance (010.1320)
- Absorption (010.1030)
- Spectroscopy, teraherz (300.6495)

About this Article
History
- Original Manuscript: November 21, 2013
- Revised Manuscript: February 10, 2014
- Manuscript Accepted: February 11, 2014
- Published: February 19, 2014

Accessible

Open Access

Abstract

Determination of the water vapor continuum absorption from 0.35 to 1 THz is reported. The THz pulses propagate though a 137 m long humidity-controlled chamber and are measured by THz time-domain spectroscopy (THz-TDS). The average relative humidity along the entire THz path is precisely obtained by measuring the difference between transit times of the sample and reference THz pulses to an accuracy of 0.1 ps. Using the measured total absorption and the calculated resonance line absorption with the Molecular Response Theory lineshape, based on physical principles and measurements, an accurate continuum absorption is obtained within four THz absorption windows, that agrees well with the empirical theory. The absorption is significantly smaller than that obtained using the van Vleck-Weisskopf lineshape with a 750 GHz cut-off.

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Publication

S. Paine, R. Blundell, D. Papa, J. Barrett, and S. Radford, “A Fourier transform spectrometer for measurement of atmospheric transmission at submillimeter wavelengths,” Publ. Astron. Soc. Pac. 112(767), 108–118 (2000).
[Crossref]
E. Cianca, T. Rossi, A. Yahalom, Y. Pinhasi, J. Farserotu, and C. Sacchi, “EHF for satellite communications: the new broadband frontier,” Proc. IEEE 99(11), 1858–1881 (2011).
[Crossref]
J. S. Melinger, Y. Yang, M. Mandehgar, and D. Grischkowsky, “THz detection of small molecule vapors in the atmospheric transmission windows,” Opt. Express 20(6), 6788–6807 (2012).
[Crossref] [PubMed]
Y. Yang, M. Mandehgar, and D. Grischkowsky, “Understanding THz pulse transmission in the atmosphere,” IEEE Trans. THz Sci. Technol. 2(4), 406–415 (2012).
H. J. Liebe, “The atmospheric water vapor continuum below 300 GHz,” Int. J. Infrared Millim. Waves 5(2), 207–227 (1984).
[Crossref]
L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. F. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J.-P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nikitin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Šimečková, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, “The HITRAN 2008 molecular spectroscopic database,” J. Quantum Spectrosc. Radiat. Transfer 110(9–10), 533–572 (2009).
[Crossref]
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[Crossref]
M. A. Koshelev, E. A. Serov, V. V. Parshin, and M. Yu. Tretyakov, “Millimeter wave continuum absorption in moist nitrogen at temperature 261-328K,” J. Quantum Spectrosc. Radiat. Transfer 112(17), 2704–2712 (2011).
[Crossref]
M. Y. Tretyakov, A. F. Krupnov, M. A. Koshelev, D. S. Makarov, E. A. Serov, and V. V. Parshin, “Resonator spectrometer for precise broadband investigations of atmospheric absorption in discrete lines and water vapor related continuum in millimeter wave range,” Rev. Sci. Instrum. 80(9), 093106 (2009).
[Crossref] [PubMed]
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[Crossref]
V. B. Podobedov, D. F. Plusquellic, K. E. Siegrist, G. T. Fraser, Q. Ma, and R. H. Tipping, “New measurements of the water vapor continuum in the region from 0.3 to 2.7 THz,” J. Quantum Spectrosc. Radiat. Transfer 109(3), 458–467 (2008).
[Crossref]
D. M. Slocum, E. J. Slingerland, R. H. Giles, and T. M. Goyette, “Atmospheric absorption of terahertz radiation and water vapor continuum effects,” J. Quantum Spectrosc. Radiat. Transfer 127, 49–63 (2013).
[Crossref]
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[Crossref]
J. H. Van Vleck and V. F. Weisskopf, “On the shape of collision-broadened lines,” Rev. Mod. Phys. 17(2–3), 227–236 (1945).
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C. H. Townes and A. L. Schawlow, Microwave Spectroscopy (Dover, 1975).
Y. Yang, M. Mandehgar, and D. Grischkowsky, “Broad-band THz pulse transmission through the atmosphere,” IEEE Trans. THz Sci. Technol. 1(1), 264–273 (2011).
D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990).
[Crossref]
Y. Yang, A. Shutler, and D. Grischkowsky, “Measurement of the transmission of the atmosphere from 0.2 to 2 THz,” Opt. Express 19(9), 8830–8838 (2011).
[Crossref] [PubMed]
Y. Yang, M. Mandehgar, and D. Grischkowsky, “Time domain measurement of the THz refractivity of water vapor,” Opt. Express 20(24), 26208–26218 (2012).
[Crossref] [PubMed]
H. Harde, N. Katzenellenbogen, and D. Grischkowsky, “Line-shape transition of collision broadened lines,” Phys. Rev. Lett. 74(8), 1307–1310 (1995).
[Crossref] [PubMed]
H. Harde, R. A. Cheville, and D. Grischkowsky, “Terahertz studies of collision broadened rotational lines,” J. Phys. Chem. A 101(20), 3646–3660 (1997).
[Crossref]
D. Grischkowsky, Y. Yang, and M. Mandehgar, “Zero-frequency refractivity of water vapor, comparison of Debye and van-Vleck Weisskopf theory,” Opt. Express 21(16), 18899–18908 (2013).
[Crossref] [PubMed]
M. Mandehgar, Y. Yang, and D. Grischkowsky, “Atmosphere characterization for simulation of the two optimal wireless terahertz digital communication links,” Opt. Lett. 38(17), 3437–3440 (2013).
[Crossref] [PubMed]
D. E. Burch and D. A. Gryvnak, “Continuum absorption by water vapor in the infrared and millimeter regions,” in Atmospheric Water Vapor, A. Deepak, ed. (Academic, 1980), pp. 47–76.
J. H. van Vleck, “The absorption of microwaves by oxygen,” Phys. Rev. 71(7), 413–424 (1947).
[Crossref]

2013 (3)

D. M. Slocum, E. J. Slingerland, R. H. Giles, and T. M. Goyette, “Atmospheric absorption of terahertz radiation and water vapor continuum effects,” J. Quantum Spectrosc. Radiat. Transfer 127, 49–63 (2013).
[Crossref]

D. Grischkowsky, Y. Yang, and M. Mandehgar, “Zero-frequency refractivity of water vapor, comparison of Debye and van-Vleck Weisskopf theory,” Opt. Express 21(16), 18899–18908 (2013).
[Crossref] [PubMed]

M. Mandehgar, Y. Yang, and D. Grischkowsky, “Atmosphere characterization for simulation of the two optimal wireless terahertz digital communication links,” Opt. Lett. 38(17), 3437–3440 (2013).
[Crossref] [PubMed]

2012 (3)

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Time domain measurement of the THz refractivity of water vapor,” Opt. Express 20(24), 26208–26218 (2012).
[Crossref] [PubMed]

J. S. Melinger, Y. Yang, M. Mandehgar, and D. Grischkowsky, “THz detection of small molecule vapors in the atmospheric transmission windows,” Opt. Express 20(6), 6788–6807 (2012).
[Crossref] [PubMed]

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Understanding THz pulse transmission in the atmosphere,” IEEE Trans. THz Sci. Technol. 2(4), 406–415 (2012).

2011 (4)

E. Cianca, T. Rossi, A. Yahalom, Y. Pinhasi, J. Farserotu, and C. Sacchi, “EHF for satellite communications: the new broadband frontier,” Proc. IEEE 99(11), 1858–1881 (2011).
[Crossref]

M. A. Koshelev, E. A. Serov, V. V. Parshin, and M. Yu. Tretyakov, “Millimeter wave continuum absorption in moist nitrogen at temperature 261-328K,” J. Quantum Spectrosc. Radiat. Transfer 112(17), 2704–2712 (2011).
[Crossref]

Y. Yang, A. Shutler, and D. Grischkowsky, “Measurement of the transmission of the atmosphere from 0.2 to 2 THz,” Opt. Express 19(9), 8830–8838 (2011).
[Crossref] [PubMed]

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Broad-band THz pulse transmission through the atmosphere,” IEEE Trans. THz Sci. Technol. 1(1), 264–273 (2011).

2009 (2)

M. Y. Tretyakov, A. F. Krupnov, M. A. Koshelev, D. S. Makarov, E. A. Serov, and V. V. Parshin, “Resonator spectrometer for precise broadband investigations of atmospheric absorption in discrete lines and water vapor related continuum in millimeter wave range,” Rev. Sci. Instrum. 80(9), 093106 (2009).
[Crossref] [PubMed]

L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. F. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J.-P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nikitin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Šimečková, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, “The HITRAN 2008 molecular spectroscopic database,” J. Quantum Spectrosc. Radiat. Transfer 110(9–10), 533–572 (2009).
[Crossref]

2008 (1)

V. B. Podobedov, D. F. Plusquellic, K. E. Siegrist, G. T. Fraser, Q. Ma, and R. H. Tipping, “New measurements of the water vapor continuum in the region from 0.3 to 2.7 THz,” J. Quantum Spectrosc. Radiat. Transfer 109(3), 458–467 (2008).
[Crossref]

2002 (1)

T. Kuhn, A. Bauer, M. Godon, S. Buhler, and K. Kunzi, “Water vapor continuum: absorption measurements at 350GHz and model calculations,” J. Quantum Spectrosc. Radiat. Transfer 74(5), 545–562 (2002).
[Crossref]

2000 (1)

S. Paine, R. Blundell, D. Papa, J. Barrett, and S. Radford, “A Fourier transform spectrometer for measurement of atmospheric transmission at submillimeter wavelengths,” Publ. Astron. Soc. Pac. 112(767), 108–118 (2000).
[Crossref]

1998 (2)

H. M. Pickett, R. L. Poynter, E. A. Cohen, M. L. Delitsky, J. C. Pearson, and H. S. P. Muller, “Sub-millimeter, millimeter, and microwave spectral line catalog,” J. Quantum Spectrosc. Radiat. Transfer 60(5), 883–890 (1998); Access to specific catalog entries may be found at http://spec.jpl.nasa.gov/ .

P. W. Rosenkranz, “Water vapor microwave continuum absorption: a comparison of measurements and models,” Radio Sci. 33(4), 919–928 (1998).
[Crossref]

1997 (1)

H. Harde, R. A. Cheville, and D. Grischkowsky, “Terahertz studies of collision broadened rotational lines,” J. Phys. Chem. A 101(20), 3646–3660 (1997).
[Crossref]

1995 (1)

H. Harde, N. Katzenellenbogen, and D. Grischkowsky, “Line-shape transition of collision broadened lines,” Phys. Rev. Lett. 74(8), 1307–1310 (1995).
[Crossref] [PubMed]

1990 (1)

D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990).
[Crossref]

1986 (1)

R. J. Hill, “Water vapor-absorption lineshape comparison using the 22-GHz line: the Van Vleck-Weisskopf shape affirmed,” Radio Sci. 21(3), 447–451 (1986).
[Crossref]

1984 (1)

H. J. Liebe, “The atmospheric water vapor continuum below 300 GHz,” Int. J. Infrared Millim. Waves 5(2), 207–227 (1984).
[Crossref]

1947 (1)

J. H. van Vleck, “The absorption of microwaves by oxygen,” Phys. Rev. 71(7), 413–424 (1947).
[Crossref]

1945 (1)

J. H. Van Vleck and V. F. Weisskopf, “On the shape of collision-broadened lines,” Rev. Mod. Phys. 17(2–3), 227–236 (1945).
[Crossref]

Barbe, A.

Barrett, J.

Bauer, A.

Benner, D. C.

Bernath, P. F.

Birk, M.

Blundell, R.

Boudon, V.

Brown, L. R.

Buhler, S.

Campargue, A.

Champion, J.-P.

Chance, K.

Cheville, R. A.

H. Harde, R. A. Cheville, and D. Grischkowsky, “Terahertz studies of collision broadened rotational lines,” J. Phys. Chem. A 101(20), 3646–3660 (1997).
[Crossref]

Cianca, E.

E. Cianca, T. Rossi, A. Yahalom, Y. Pinhasi, J. Farserotu, and C. Sacchi, “EHF for satellite communications: the new broadband frontier,” Proc. IEEE 99(11), 1858–1881 (2011).
[Crossref]

Cohen, E. A.

Coudert, L. H.

Dana, V.

Delitsky, M. L.

Devi, V. M.

Fally, S.

Farserotu, J.

E. Cianca, T. Rossi, A. Yahalom, Y. Pinhasi, J. Farserotu, and C. Sacchi, “EHF for satellite communications: the new broadband frontier,” Proc. IEEE 99(11), 1858–1881 (2011).
[Crossref]

Fattinger, C.

Flaud, J.-M.

Fraser, G. T.

Gamache, R. R.

Giles, R. H.

Godon, M.

Goldman, A.

Gordon, I. E.

Goyette, T. M.

Grischkowsky, D.

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Time domain measurement of the THz refractivity of water vapor,” Opt. Express 20(24), 26208–26218 (2012).
[Crossref] [PubMed]

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Understanding THz pulse transmission in the atmosphere,” IEEE Trans. THz Sci. Technol. 2(4), 406–415 (2012).

Y. Yang, A. Shutler, and D. Grischkowsky, “Measurement of the transmission of the atmosphere from 0.2 to 2 THz,” Opt. Express 19(9), 8830–8838 (2011).
[Crossref] [PubMed]

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Broad-band THz pulse transmission through the atmosphere,” IEEE Trans. THz Sci. Technol. 1(1), 264–273 (2011).

H. Harde, R. A. Cheville, and D. Grischkowsky, “Terahertz studies of collision broadened rotational lines,” J. Phys. Chem. A 101(20), 3646–3660 (1997).
[Crossref]

H. Harde, N. Katzenellenbogen, and D. Grischkowsky, “Line-shape transition of collision broadened lines,” Phys. Rev. Lett. 74(8), 1307–1310 (1995).
[Crossref] [PubMed]

Harde, H.

H. Harde, R. A. Cheville, and D. Grischkowsky, “Terahertz studies of collision broadened rotational lines,” J. Phys. Chem. A 101(20), 3646–3660 (1997).
[Crossref]

H. Harde, N. Katzenellenbogen, and D. Grischkowsky, “Line-shape transition of collision broadened lines,” Phys. Rev. Lett. 74(8), 1307–1310 (1995).
[Crossref] [PubMed]

Hill, R. J.

R. J. Hill, “Water vapor-absorption lineshape comparison using the 22-GHz line: the Van Vleck-Weisskopf shape affirmed,” Radio Sci. 21(3), 447–451 (1986).
[Crossref]

Jacquemart, D.

Katzenellenbogen, N.

H. Harde, N. Katzenellenbogen, and D. Grischkowsky, “Line-shape transition of collision broadened lines,” Phys. Rev. Lett. 74(8), 1307–1310 (1995).
[Crossref] [PubMed]

Keiding, S.

Kleiner, I.

Koshelev, M. A.

Krupnov, A. F.

Kuhn, T.

Kunzi, K.

Lacome, N.

Lafferty, W. J.

Liebe, H. J.

H. J. Liebe, “The atmospheric water vapor continuum below 300 GHz,” Int. J. Infrared Millim. Waves 5(2), 207–227 (1984).
[Crossref]

Ma, Q.

Makarov, D. S.

Mandehgar, M.

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Time domain measurement of the THz refractivity of water vapor,” Opt. Express 20(24), 26208–26218 (2012).
[Crossref] [PubMed]

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Understanding THz pulse transmission in the atmosphere,” IEEE Trans. THz Sci. Technol. 2(4), 406–415 (2012).

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Broad-band THz pulse transmission through the atmosphere,” IEEE Trans. THz Sci. Technol. 1(1), 264–273 (2011).

Mandin, J.-Y.

Massie, S. T.

Melinger, J. S.

Mikhailenko, S. N.

Miller, C. E.

Moazzen-Ahmadi, N.

Muller, H. S. P.

Naumenko, O. V.

Nikitin, A. V.

Orphal, J.

Paine, S.

Papa, D.

Parshin, V. V.

Pearson, J. C.

Perevalov, V. I.

Perrin, A.

Pickett, H. M.

Pinhasi, Y.

E. Cianca, T. Rossi, A. Yahalom, Y. Pinhasi, J. Farserotu, and C. Sacchi, “EHF for satellite communications: the new broadband frontier,” Proc. IEEE 99(11), 1858–1881 (2011).
[Crossref]

Plusquellic, D. F.

Podobedov, V. B.

Poynter, R. L.

Predoi-Cross, A.

Radford, S.

Rinsland, C. P.

Rosenkranz, P. W.

P. W. Rosenkranz, “Water vapor microwave continuum absorption: a comparison of measurements and models,” Radio Sci. 33(4), 919–928 (1998).
[Crossref]

Rossi, T.

E. Cianca, T. Rossi, A. Yahalom, Y. Pinhasi, J. Farserotu, and C. Sacchi, “EHF for satellite communications: the new broadband frontier,” Proc. IEEE 99(11), 1858–1881 (2011).
[Crossref]

Rotger, M.

Rothman, L. S.

Sacchi, C.

E. Cianca, T. Rossi, A. Yahalom, Y. Pinhasi, J. Farserotu, and C. Sacchi, “EHF for satellite communications: the new broadband frontier,” Proc. IEEE 99(11), 1858–1881 (2011).
[Crossref]

Serov, E. A.

Shutler, A.

Y. Yang, A. Shutler, and D. Grischkowsky, “Measurement of the transmission of the atmosphere from 0.2 to 2 THz,” Opt. Express 19(9), 8830–8838 (2011).
[Crossref] [PubMed]

Siegrist, K. E.

Šimecková, M.

Slingerland, E. J.

Slocum, D. M.

Smith, M. A. H.

Sung, K.

Tashkun, S. A.

Tennyson, J.

Tipping, R. H.

Toth, R. A.

Tretyakov, M. Y.

Tretyakov, M. Yu.

van Exter, M.

van Vleck, J. H.

J. H. van Vleck, “The absorption of microwaves by oxygen,” Phys. Rev. 71(7), 413–424 (1947).
[Crossref]

J. H. Van Vleck and V. F. Weisskopf, “On the shape of collision-broadened lines,” Rev. Mod. Phys. 17(2–3), 227–236 (1945).
[Crossref]

Vandaele, A. C.

Vander Auwera, J.

Weisskopf, V. F.

J. H. Van Vleck and V. F. Weisskopf, “On the shape of collision-broadened lines,” Rev. Mod. Phys. 17(2–3), 227–236 (1945).
[Crossref]

Yahalom, A.

E. Cianca, T. Rossi, A. Yahalom, Y. Pinhasi, J. Farserotu, and C. Sacchi, “EHF for satellite communications: the new broadband frontier,” Proc. IEEE 99(11), 1858–1881 (2011).
[Crossref]

Yang, Y.

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Time domain measurement of the THz refractivity of water vapor,” Opt. Express 20(24), 26208–26218 (2012).
[Crossref] [PubMed]

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Understanding THz pulse transmission in the atmosphere,” IEEE Trans. THz Sci. Technol. 2(4), 406–415 (2012).

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Broad-band THz pulse transmission through the atmosphere,” IEEE Trans. THz Sci. Technol. 1(1), 264–273 (2011).

Y. Yang, A. Shutler, and D. Grischkowsky, “Measurement of the transmission of the atmosphere from 0.2 to 2 THz,” Opt. Express 19(9), 8830–8838 (2011).
[Crossref] [PubMed]

IEEE Trans. THz Sci. Technol. (2)

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Understanding THz pulse transmission in the atmosphere,” IEEE Trans. THz Sci. Technol. 2(4), 406–415 (2012).

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Broad-band THz pulse transmission through the atmosphere,” IEEE Trans. THz Sci. Technol. 1(1), 264–273 (2011).

Int. J. Infrared Millim. Waves (1)

H. J. Liebe, “The atmospheric water vapor continuum below 300 GHz,” Int. J. Infrared Millim. Waves 5(2), 207–227 (1984).
[Crossref]

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

J. Phys. Chem. A (1)

H. Harde, R. A. Cheville, and D. Grischkowsky, “Terahertz studies of collision broadened rotational lines,” J. Phys. Chem. A 101(20), 3646–3660 (1997).
[Crossref]

J. Quantum Spectrosc. Radiat. Transfer (6)

Opt. Express (4)

Y. Yang, A. Shutler, and D. Grischkowsky, “Measurement of the transmission of the atmosphere from 0.2 to 2 THz,” Opt. Express 19(9), 8830–8838 (2011).
[Crossref] [PubMed]

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Time domain measurement of the THz refractivity of water vapor,” Opt. Express 20(24), 26208–26218 (2012).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. (1)

J. H. van Vleck, “The absorption of microwaves by oxygen,” Phys. Rev. 71(7), 413–424 (1947).
[Crossref]

Phys. Rev. Lett. (1)

H. Harde, N. Katzenellenbogen, and D. Grischkowsky, “Line-shape transition of collision broadened lines,” Phys. Rev. Lett. 74(8), 1307–1310 (1995).
[Crossref] [PubMed]

Proc. IEEE (1)

E. Cianca, T. Rossi, A. Yahalom, Y. Pinhasi, J. Farserotu, and C. Sacchi, “EHF for satellite communications: the new broadband frontier,” Proc. IEEE 99(11), 1858–1881 (2011).
[Crossref]

Publ. Astron. Soc. Pac. (1)

Radio Sci. (2)

R. J. Hill, “Water vapor-absorption lineshape comparison using the 22-GHz line: the Van Vleck-Weisskopf shape affirmed,” Radio Sci. 21(3), 447–451 (1986).
[Crossref]

P. W. Rosenkranz, “Water vapor microwave continuum absorption: a comparison of measurements and models,” Radio Sci. 33(4), 919–928 (1998).
[Crossref]

Rev. Mod. Phys. (1)

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Fig. 1

Absorption line comparison for a single resonance line normalized to unity with center frequency at 1.0 THz. vV-W (dashed line), FL (dotted line), MRT (red line between vV-W and FL lines), and the Eqs. (2), (24), (25) vV-Wc (dash-dot line) showing the abrupt cut-off at 1.75 THz (750 GHz from line center). All lineshapes have (HWHM) linewidth of 3.15 GHz . For MRT, τ_c = 0.2 ps.

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Fig. 2

Experimental set up with 170 m long-path system.

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Fig. 3

The measured transmitted THz pulses and the corresponding amplitude frequency spectra for humidity levels on different days. (a) Reference pulse (top trace) and sample pulse (bottom trace). (b) Amplitude spectra corresponding to (a). (c) Reference pulse (top trace) and two sample pulses (lower traces). (d) Amplitude spectra corresponding to (c).

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Fig. 4

(a) Amplitude transmission for $Δ ρ_{W}$ = 7.0 g/m³, which is the spectral ratio between the sample #2 and reference in Fig. 3(d). (b) Measured power attenuation coefficients $Δ α_{x}$ (open circles) in dB/km with the smoothed THz windows W1-W4 (solid lines), for the water vapor density differences of $Δ ρ_{W}$ = 4.1 g/m³ (bottom blue circles), $Δ ρ_{W}$ = 5.2 g/m³ (middle red circles) and $Δ ρ_{W}$ = 7.0 g/m³ (top black circles). For comparison the MRT calculation for $Δ ρ_{W}$ = 4.1 g/m³ is shown as the purple solid bottom line. (3)-(5) indicate the THz windows investigated in [19].

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Fig. 5

(a) Illustration of the method to obtain the relative continuum absorption $Δ α_{c x}$ for the windows with $Δ ρ_{W}$ = 7.0 g/m³. The measured total absorption (blue circles), smoothed measured THz window (red solid line), the resonance absorption with MRT lineshape (black line). The quadratic fitting for X (black dash line) with yellow highlight for $Δ ρ_{W}$ = 7.0 g/m³. (b) The calculated cross term X absorption with a quadratic frequency dependence, $Δ ρ_{W}$ = 7.0 g/m³ (top black line), $Δ ρ_{W}$ = 5.2 g/m³ (middle red line), and $Δ ρ_{W}$ = 4.1 g/m³ (bottom blue line). (c) The continuum absorption $Δ α_{c}$ from Table 1 and corresponding fitting (solid lines), the linear $Δ ρ_{W}$ component (dash lines), and the historical curve in [24,25] for 7 g/m³ (dash dot line). The MRT calculation of Fig. 5(a) is shown as the lower red curve and is also shown as the 5X magnified red curve. The comparison between the empirical theory and historical curve below 400 GHz are also shown with a 5X magnification.

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Fig. 6

The measured absolute total absorption $Δ α$ (red dots) and the resonance absorption with MRT lineshape (black line) for $Δ ρ_{W}$ = 7.0 g/m³.

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Fig. 7

(a) The calculated amplitude transmissions of the two different pre-factor vV-W lineshapes after 137 m propagation at RH 37% and 20 °C which is equivalent to density of 6.4 g/m³, using the quadratic term of Eq. (2) (upper black line) and using the linear term of Eq. (3) (lower red line). (b) Corresponding power attenuation in dB/km.

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Tables (2)

Table 1 Determined Values of $Δ α_{c x}$ , X, $Δ α_{c}$ in dB/km at Four THz Windows with Different Density

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Table 2 Laboratory Determinations of Water Vapor Self and Foreign Continuum Parameters in Millimeter Wave and THz Range. C_W and C_A Parameters Are in Units of dB/km/(GHz hPa)²

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Equations (26)

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α_{j} (v) = N_{H 2 O} \cdot I_{j} (v) \cdot f (v, v_{j}) .

f_{1} (v, v_{j}) = \frac{1}{π} {(\frac{v}{v_{j}})}^{2} \cdot (\frac{Δ v_{j}}{{(v - v_{j})}^{2} + Δ v_{j}^{2}} + \frac{Δ v_{j}}{{(v + v_{j})}^{2} + Δ v_{j}^{2}}) .

f_{2} (v, v_{j}) = \frac{1}{π} (\frac{v}{v_{j}}) \cdot (\frac{Δ v_{j}}{{(v - v_{j})}^{2} + Δ v_{j}^{2}} + \frac{Δ v_{j}}{{(v + v_{j})}^{2} + Δ v_{j}^{2}}) .

α_{j}^{M R T} (ν) = S (ν) α_{j}^{v V - W} (v) + (1 - S (ν)) α_{j}^{L} (ν) .

S (ν) = 1 / [1 + {(2 π ν τ_{c})}^{2}] .

f_{L} (v, v_{j}) = \frac{1}{π} (\frac{v}{v_{j}}) \cdot (\frac{Δ v_{j}}{{(v - v_{j})}^{2} + Δ v_{j}^{2}} - \frac{Δ v_{j}}{{(v + v_{j})}^{2} + Δ v_{j}^{2}}) .

α_{c} (v, T) = v^{2} \cdot (C_{W}^{0} \cdot θ^{n_{s} + 3} \cdot P_{W}^{2} + C_{A}^{0} \cdot θ^{n_{f} + 3} \cdot P_{A} \cdot P_{W}) .

α_{c} (v, 294 K) = v^{2} [C_{W}^{*} \cdot ρ_{W}^{2} + C_{A}^{*} \cdot ρ_{A} \cdot ρ_{W}] .

Δ α_{x} = α^{S} - α^{R} = (α_{M R T}^{S} + α_{c}^{S}) - (α_{M R T}^{R} + α_{c}^{R}) = Δ α_{M R T} + (α_{c}^{S} - α_{c}^{R}) = Δ α_{M R T} + Δ α_{c x} .

Δ α_{c x} = α_{c}^{S} - α_{c}^{R} = v^{2} [C_{W}^{*} \cdot ({(ρ_{W}^{S})}^{2} - {(ρ_{W}^{R})}^{2}) + C_{A}^{*} \cdot ρ_{A} \cdot (ρ_{W}^{S} - ρ_{W}^{R})] .

Δ α_{c x} = v^{2} [C_{W}^{*} \cdot (2 ρ_{W}^{R} Δ ρ_{W} + Δ ρ_{W}^{2}) + C_{A}^{*} \cdot ρ_{A} \cdot Δ ρ_{W}] .

X = v^{2} C_{W}^{*} (2 ρ_{W}^{R} Δ ρ_{W}) .

Δ α_{c} = Δ α_{c x} - X = v^{2} [C_{W}^{*} \cdot Δ ρ_{W}^{2} + C_{A}^{*} \cdot ρ_{A} \cdot Δ ρ_{W}] .

Δ α = Δ α_{x} - X .

α_{j} (v) = N_{H 2 O} \cdot I_{j} (v) \cdot f (v, v_{j}) .

α = \frac{N e^{2}}{m c} {(\frac{v}{v_{0}})}^{2} [\frac{1 / 2 π τ}{{(v - v_{0})}^{2} + {(1 / 2 π τ)}^{2}} + \frac{1 / 2 π τ}{{(v + v_{0})}^{2} + {(1 / 2 π τ)}^{2}}] .

α_{j} = Δ n_{j} \frac{8 π^{2} v_{j} {| μ_{b a} |}^{2}}{3 h c} {(\frac{v}{v_{j}})}^{2} [\frac{1 / 2 π τ}{{(v - v_{j})}^{2} + {(1 / 2 π τ)}^{2}} + \frac{1 / 2 π τ}{{(v + v_{j})}^{2} + {(1 / 2 π τ)}^{2}}] .

n_{j} = N f_{j a} .

f_{j a} = (2 J + 1) e^{- E_{j a} / k T} / \sum_{j, J} (2 J + 1) e^{- E_{j a} / k T} .

Δ n_{j} = n_{j} (1 - e^{- (E_{j b} - E_{j a}) / k T}) .

α_{j} = N [\frac{8 π^{3}}{3 c k T} \cdot \frac{v_{j}^{2} {| μ_{b a} |}^{2} (2 J + 1) e^{- E_{j a} / k T}}{\sum_{j, J} (2 J + 1) e^{- E_{j a} / k T}}] \cdot \frac{1}{π} {(\frac{v}{v_{j}})}^{2} [\frac{1 / 2 π τ}{{(v - v_{j})}^{2} + {(1 / 2 π τ)}^{2}} + \frac{1 / 2 π τ}{{(v + v_{j})}^{2} + {(1 / 2 π τ)}^{2}}] .

I_{b a} (T) = (\frac{8 π^{3}}{3 h c}) \cdot \frac{ν_{b a} {}^{x}S_{b a} μ_{x}^{2} [e^{- E_{j a} / k T} - e^{- E_{j b} / k T}]}{Q_{r s}} .

I_{j} = (\frac{8 π^{3}}{3 c k T}) \cdot \frac{v_{j}^{2} {| μ_{b a} |}^{2} (2 J + 1) e^{- E_{j a} / k T}}{\sum_{j, J} (2 J + 1) e^{- E_{j a} / k T}} .

\begin{array}{l} f_{c u t o f f} (v, v_{j}) = \frac{1}{π} {(\frac{v}{v_{j}})}^{2} \cdot (\frac{Δ v_{j}}{{(v - v_{j})}^{2} + Δ v_{j}^{2}} + \frac{Δ v_{j}}{{(v + v_{j})}^{2} + Δ v_{j}^{2}} - \frac{2 Δ v_{j}}{v_{c u t}^{2} + Δ v_{j}^{2}}) . i f | v - v_{j} | < v_{c u t} \\ f_{c u t o f f} (v, v_{j}) = 0. i f | v - v_{j} | \geq v_{c u t} \end{array}

f_{c u t o f f} (v, v_{j}) = \frac{1}{π} {(\frac{v}{v_{j}})}^{2} \cdot (\frac{Δ v_{j}}{{(v - v_{j})}^{2} + Δ v_{j}^{2}} + \frac{Δ v_{j}}{{(v + v_{j})}^{2} + Δ v_{j}^{2}} - \frac{Δ v_{j}}{v_{c u t}^{2} + Δ v_{j}^{2}} - \frac{Δ v_{j}}{{(2 v_{j} + v_{c u t})}^{2} + Δ v_{j}^{2}}) .

f_{c u t o f f} (v, v_{j}) = \frac{1}{π} {(\frac{v}{v_{j}})}^{2} \cdot (\frac{Δ v_{j}}{{(v - v_{j})}^{2} + Δ v_{j}^{2}} + \frac{Δ v_{j}}{{(v + v_{j})}^{2} + Δ v_{j}^{2}} - \frac{Δ v_{j}}{v_{c u t}^{2} + Δ v_{j}^{2}} - \frac{1}{{(2 v_{j} - v_{c u t})}^{2} + Δ v_{j}^{2}})

Windows	∆ρ_w(4.1 g/m³)			∆ρ_w(5.2 g/m³)			∆ρ_w(7.0 g/m³)
All values (dB/km)	∆α_cx	X	∆α_c	∆α_cx	X	∆α_c	∆α_cx	X	∆α_c
W1	2.8	0.9	1.9	3.7	1.2	2.5	5.3	1.5	3.8
W2	3.1	1.1	2.0	4.2	1.4	2.8	6.8	1.9	4.9
W3	8.1	2.4	5.7	11.0	3.2	7.8	15.8	4.2	11.6
W4	12.5	3.8	8.7	16.5	4.9	11.6	22.5	6.5	16.0

Reference	C_W (x10⁻⁷)	C_A (x10⁻⁹)	n_s	n_f	Experimental conditions	Database	v-VW Pre-factor	Cutoff (GHz)
This Work	0.95	1.69	NA	NA	0.35-1 THz 294 K	HITRAN	(v/v_j)²	None
Slocum [13]	0.45	4.12	NA	NA	0.3-1.5 THz 296 K	HITRAN	v/v_j	None
Podobedov [12]	0.48*	2.55*	5.50	1.80	0.3-2.7 THz 293-333 K	HITRAN	v/v_j	750
Koshelev [9]	0.94*	3.11*	5.24	0.91	107-143 GHz 261-328 K	R98 [14]	(v/v_j)²	750

Windows	∆ρ_w(4.1 g/m³)			∆ρ_w(5.2 g/m³)			∆ρ_w(7.0 g/m³)
All values (dB/km)	∆α_cx	X	∆α_c	∆α_cx	X	∆α_c	∆α_cx	X	∆α_c
W1	2.8	0.9	1.9	3.7	1.2	2.5	5.3	1.5	3.8
W2	3.1	1.1	2.0	4.2	1.4	2.8	6.8	1.9	4.9
W3	8.1	2.4	5.7	11.0	3.2	7.8	15.8	4.2	11.6
W4	12.5	3.8	8.7	16.5	4.9	11.6	22.5	6.5	16.0

Reference	C_W (x10⁻⁷)	C_A (x10⁻⁹)	n_s	n_f	Experimental conditions	Database	v-VW Pre-factor	Cutoff (GHz)
This Work	0.95	1.69	NA	NA	0.35-1 THz 294 K	HITRAN	(v/v_j)²	None
Slocum [13]	0.45	4.12	NA	NA	0.3-1.5 THz 296 K	HITRAN	v/v_j	None
Podobedov [12]	0.48*	2.55*	5.50	1.80	0.3-2.7 THz 293-333 K	HITRAN	v/v_j	750
Koshelev [9]	0.94*	3.11*	5.24	0.91	107-143 GHz 261-328 K	R98 [14]	(v/v_j)²	750