Abstract

We show that the zero-frequency, refractivity of water vapor calculated by the van-Vleck Weisskopf theory via a summation over all the water lines from 22.2 GHz to 30 THz can explain all of the previous measurements from 0.5 MHz to microwave, mm-waves and THz frequencies. This result removes a long standing discrepancy in comparisons of measurements and theory, and is in excellent agreement with experiments.

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    [CrossRef]
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  22. S. A. Clough, Y. Beers, G. P. Klein, and L. S. Rothman, “Dipole moment of water from Stark measurements of H2O, HDO, and D2O,” J. Chem. Phys.59(5), 2254–2259 (1973).
    [CrossRef]
  23. T. R. Dyke and J. S. Muenter, “Electric dipole moments of low J states of H2O and D2O,” J. Chem. Phys.59(6), 3125–3127 (1973).
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    [CrossRef]
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  26. Private communication from referee of [12].
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    [CrossRef]
  28. L. Thrane, R. H. Jacobsen, P. Uhd Jepsen, and S. R. Keiding, “THz reflection spectroscopy of liquid water,” Chem. Phys. Lett.240(4), 330–333 (1995).
    [CrossRef]
  29. J. T. Kindt and C. A. Schmuttenmaer, “Far-infrared dielectric properties of polar liquids probed by femtosecond terahertz pulse spectroscopy,” J. Phys. Chem.100(24), 10373–10379 (1996).
    [CrossRef]
  30. C. Ro̸nne, L. Thrane, P.-O. Åstrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys.107(14), 5319–5331 (1997).
    [CrossRef]

2012 (2)

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Time domain measurement of the THz refractivity of water vapor,” Opt. Express20(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, 406–415 (2012).

2009 (1)

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

2006 (1)

1998 (1)

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,” JQSRT60(5), 883–890 (1998).Access to specific catalog entries may be found at http://spec.jpl.nasa.gov/ .
[CrossRef]

1997 (1)

C. Ro̸nne, L. Thrane, P.-O. Åstrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys.107(14), 5319–5331 (1997).
[CrossRef]

1996 (1)

J. T. Kindt and C. A. Schmuttenmaer, “Far-infrared dielectric properties of polar liquids probed by femtosecond terahertz pulse spectroscopy,” J. Phys. Chem.100(24), 10373–10379 (1996).
[CrossRef]

1995 (1)

L. Thrane, R. H. Jacobsen, P. Uhd Jepsen, and S. R. Keiding, “THz reflection spectroscopy of liquid water,” Chem. Phys. Lett.240(4), 330–333 (1995).
[CrossRef]

1991 (2)

H. J. Liebe, G. A. Hufford, and T. Manabe, “A model for the complex permittivity of water at frequencies below 1 THz,” Int. J. Infrared Millim. Waves12(7), 659–675 (1991).
[CrossRef]

S. L. Shostak, W. L. Ebenstein, and J. S. Muenter, “The dipole moment of water. I. Dipole moments and hyperfine properties of H2O and HDO in the ground and excited vibrational states,” J. Chem. Phys.94(9), 5875–5882 (1991).
[CrossRef]

1986 (1)

R. J. Hill and R. S. Lawrence, “Refractive index of water vapor in the infrared windows,” Infrared Phys.26(6), 371–376 (1986).
[CrossRef]

1985 (1)

T. Manabe, Y. Furuhama, T. Ihara, S. Saito, H. Tanaka, and A. Ono, “Measurements of attenuation and refractive dispersion due to atmospheric water vapor at 80 and 240 GHz,” Int. J. Infrared Millim. Waves6(4), 313–322 (1985).
[CrossRef]

1982 (1)

H. Matsumoto, “The refractive index of moist air in the 3-µm region,” Metrologia18(2), 49–52 (1982).
[CrossRef]

1973 (2)

S. A. Clough, Y. Beers, G. P. Klein, and L. S. Rothman, “Dipole moment of water from Stark measurements of H2O, HDO, and D2O,” J. Chem. Phys.59(5), 2254–2259 (1973).
[CrossRef]

T. R. Dyke and J. S. Muenter, “Electric dipole moments of low J states of H2O and D2O,” J. Chem. Phys.59(6), 3125–3127 (1973).
[CrossRef]

1972 (1)

Y. Beers and G. P. Klein, “The Stark splitting of millimeter wave transitions of water,” J. Res. Natl. Bur. Stand., Sect. A76a, 521–528 (1972).

1971 (1)

1955 (1)

K. D. Froome, “The refractive indices of water vapour, air, oxygen, nitrogen and argon at 72 kMc/s,” Proc. Phys. Soc. B68(11), 833–835 (1955).
[CrossRef]

1953 (1)

L. Essen, “The refractive indices of water vapour, air, oxygen, nitrogen, hydrogen, deuterium and helium,” Proc. Phys. Soc. B66(3), 189–193 (1953).
[CrossRef]

1952 (1)

G. Birnbaum and S. K. Chatterjee, “The dielectric constant of water vapor in the microwave region,” J. Appl. Phys.23(2), 220–223 (1952).
[CrossRef]

1951 (1)

L. Essen and K. D. Froome, “The refractive indices and dielectric constants of air and its principal constituents at 24,000 Mc/s,” Proc. Phys. Soc. B64(10), 862–875 (1951).
[CrossRef]

1948 (2)

C. M. Crain, “The dielectric constant of several gases at a wave-length of 3.2 centimeters,” Phys. Rev.74(6), 691–693 (1948).
[CrossRef]

S. Golden, T. Wentink, R. Hillger, and M. Strandberg, “Stark spectrum of H2O,” Phys. Rev.73(1), 92–93 (1948).
[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]

1935 (1)

J. D. Stranathan, “Dielectric constant of water vapor,” Phys. Rev.48(6), 538–544 (1935).
[CrossRef]

Abou-Zeid, A.

Åstrand, P.-O.

C. Ro̸nne, L. Thrane, P.-O. Åstrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys.107(14), 5319–5331 (1997).
[CrossRef]

Barbe, A.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Beers, Y.

S. A. Clough, Y. Beers, G. P. Klein, and L. S. Rothman, “Dipole moment of water from Stark measurements of H2O, HDO, and D2O,” J. Chem. Phys.59(5), 2254–2259 (1973).
[CrossRef]

Y. Beers and G. P. Klein, “The Stark splitting of millimeter wave transitions of water,” J. Res. Natl. Bur. Stand., Sect. A76a, 521–528 (1972).

Benner, D. C.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Bernath, P. F.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Birk, M.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Birnbaum, G.

G. Birnbaum and S. K. Chatterjee, “The dielectric constant of water vapor in the microwave region,” J. Appl. Phys.23(2), 220–223 (1952).
[CrossRef]

Boudon, V.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Bradley, C. C.

Brown, L. R.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Campargue, A.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Champion, J.-P.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Chance, K.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Chatterjee, S. K.

G. Birnbaum and S. K. Chatterjee, “The dielectric constant of water vapor in the microwave region,” J. Appl. Phys.23(2), 220–223 (1952).
[CrossRef]

Clough, S. A.

S. A. Clough, Y. Beers, G. P. Klein, and L. S. Rothman, “Dipole moment of water from Stark measurements of H2O, HDO, and D2O,” J. Chem. Phys.59(5), 2254–2259 (1973).
[CrossRef]

Cohen, E. A.

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,” JQSRT60(5), 883–890 (1998).Access to specific catalog entries may be found at http://spec.jpl.nasa.gov/ .
[CrossRef]

Coudert, L. H.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Crain, C. M.

C. M. Crain, “The dielectric constant of several gases at a wave-length of 3.2 centimeters,” Phys. Rev.74(6), 691–693 (1948).
[CrossRef]

Dana, V.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Delitsky, M. L.

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,” JQSRT60(5), 883–890 (1998).Access to specific catalog entries may be found at http://spec.jpl.nasa.gov/ .
[CrossRef]

Devi, V. M.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Dyke, T. R.

T. R. Dyke and J. S. Muenter, “Electric dipole moments of low J states of H2O and D2O,” J. Chem. Phys.59(6), 3125–3127 (1973).
[CrossRef]

Ebenstein, W. L.

S. L. Shostak, W. L. Ebenstein, and J. S. Muenter, “The dipole moment of water. I. Dipole moments and hyperfine properties of H2O and HDO in the ground and excited vibrational states,” J. Chem. Phys.94(9), 5875–5882 (1991).
[CrossRef]

Essen, L.

L. Essen, “The refractive indices of water vapour, air, oxygen, nitrogen, hydrogen, deuterium and helium,” Proc. Phys. Soc. B66(3), 189–193 (1953).
[CrossRef]

L. Essen and K. D. Froome, “The refractive indices and dielectric constants of air and its principal constituents at 24,000 Mc/s,” Proc. Phys. Soc. B64(10), 862–875 (1951).
[CrossRef]

Fally, S.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Flaud, J.-M.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Froome, K. D.

K. D. Froome, “The refractive indices of water vapour, air, oxygen, nitrogen and argon at 72 kMc/s,” Proc. Phys. Soc. B68(11), 833–835 (1955).
[CrossRef]

L. Essen and K. D. Froome, “The refractive indices and dielectric constants of air and its principal constituents at 24,000 Mc/s,” Proc. Phys. Soc. B64(10), 862–875 (1951).
[CrossRef]

Furuhama, Y.

T. Manabe, Y. Furuhama, T. Ihara, S. Saito, H. Tanaka, and A. Ono, “Measurements of attenuation and refractive dispersion due to atmospheric water vapor at 80 and 240 GHz,” Int. J. Infrared Millim. Waves6(4), 313–322 (1985).
[CrossRef]

Gamache, R. R.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
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Gebbie, H. A.

Golden, S.

S. Golden, T. Wentink, R. Hillger, and M. Strandberg, “Stark spectrum of H2O,” Phys. Rev.73(1), 92–93 (1948).
[CrossRef]

Goldman, A.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Gordon, I. E.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Grischkowsky, D.

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

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Time domain measurement of the THz refractivity of water vapor,” Opt. Express20(24), 26208–26218 (2012).
[CrossRef] [PubMed]

Hill, R. J.

R. J. Hill and R. S. Lawrence, “Refractive index of water vapor in the infrared windows,” Infrared Phys.26(6), 371–376 (1986).
[CrossRef]

Hillger, R.

S. Golden, T. Wentink, R. Hillger, and M. Strandberg, “Stark spectrum of H2O,” Phys. Rev.73(1), 92–93 (1948).
[CrossRef]

Hufford, G. A.

H. J. Liebe, G. A. Hufford, and T. Manabe, “A model for the complex permittivity of water at frequencies below 1 THz,” Int. J. Infrared Millim. Waves12(7), 659–675 (1991).
[CrossRef]

Ihara, T.

T. Manabe, Y. Furuhama, T. Ihara, S. Saito, H. Tanaka, and A. Ono, “Measurements of attenuation and refractive dispersion due to atmospheric water vapor at 80 and 240 GHz,” Int. J. Infrared Millim. Waves6(4), 313–322 (1985).
[CrossRef]

Jacobsen, R. H.

L. Thrane, R. H. Jacobsen, P. Uhd Jepsen, and S. R. Keiding, “THz reflection spectroscopy of liquid water,” Chem. Phys. Lett.240(4), 330–333 (1995).
[CrossRef]

Jacquemart, D.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Keiding, S. R.

C. Ro̸nne, L. Thrane, P.-O. Åstrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys.107(14), 5319–5331 (1997).
[CrossRef]

L. Thrane, R. H. Jacobsen, P. Uhd Jepsen, and S. R. Keiding, “THz reflection spectroscopy of liquid water,” Chem. Phys. Lett.240(4), 330–333 (1995).
[CrossRef]

Kindt, J. T.

J. T. Kindt and C. A. Schmuttenmaer, “Far-infrared dielectric properties of polar liquids probed by femtosecond terahertz pulse spectroscopy,” J. Phys. Chem.100(24), 10373–10379 (1996).
[CrossRef]

Klein, G. P.

S. A. Clough, Y. Beers, G. P. Klein, and L. S. Rothman, “Dipole moment of water from Stark measurements of H2O, HDO, and D2O,” J. Chem. Phys.59(5), 2254–2259 (1973).
[CrossRef]

Y. Beers and G. P. Klein, “The Stark splitting of millimeter wave transitions of water,” J. Res. Natl. Bur. Stand., Sect. A76a, 521–528 (1972).

Kleiner, I.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Lacome, N.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Lafferty, W. J.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Lawrence, R. S.

R. J. Hill and R. S. Lawrence, “Refractive index of water vapor in the infrared windows,” Infrared Phys.26(6), 371–376 (1986).
[CrossRef]

Liebe, H. J.

H. J. Liebe, G. A. Hufford, and T. Manabe, “A model for the complex permittivity of water at frequencies below 1 THz,” Int. J. Infrared Millim. Waves12(7), 659–675 (1991).
[CrossRef]

Manabe, T.

H. J. Liebe, G. A. Hufford, and T. Manabe, “A model for the complex permittivity of water at frequencies below 1 THz,” Int. J. Infrared Millim. Waves12(7), 659–675 (1991).
[CrossRef]

T. Manabe, Y. Furuhama, T. Ihara, S. Saito, H. Tanaka, and A. Ono, “Measurements of attenuation and refractive dispersion due to atmospheric water vapor at 80 and 240 GHz,” Int. J. Infrared Millim. Waves6(4), 313–322 (1985).
[CrossRef]

Mandehgar, M.

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

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Time domain measurement of the THz refractivity of water vapor,” Opt. Express20(24), 26208–26218 (2012).
[CrossRef] [PubMed]

Mandin, J.-Y.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Massie, S. T.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Matsumoto, H.

H. Matsumoto, “The refractive index of moist air in the 3-µm region,” Metrologia18(2), 49–52 (1982).
[CrossRef]

Mikhailenko, S. N.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Mikkelsen, K. V.

C. Ro̸nne, L. Thrane, P.-O. Åstrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys.107(14), 5319–5331 (1997).
[CrossRef]

Miller, C. E.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Moazzen-Ahmadi, N.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Muenter, J. S.

S. L. Shostak, W. L. Ebenstein, and J. S. Muenter, “The dipole moment of water. I. Dipole moments and hyperfine properties of H2O and HDO in the ground and excited vibrational states,” J. Chem. Phys.94(9), 5875–5882 (1991).
[CrossRef]

T. R. Dyke and J. S. Muenter, “Electric dipole moments of low J states of H2O and D2O,” J. Chem. Phys.59(6), 3125–3127 (1973).
[CrossRef]

Muller, H. S. P.

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,” JQSRT60(5), 883–890 (1998).Access to specific catalog entries may be found at http://spec.jpl.nasa.gov/ .
[CrossRef]

Naumenko, O. V.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Nikitin, A. V.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Ono, A.

T. Manabe, Y. Furuhama, T. Ihara, S. Saito, H. Tanaka, and A. Ono, “Measurements of attenuation and refractive dispersion due to atmospheric water vapor at 80 and 240 GHz,” Int. J. Infrared Millim. Waves6(4), 313–322 (1985).
[CrossRef]

Orphal, J.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Pearson, J. C.

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,” JQSRT60(5), 883–890 (1998).Access to specific catalog entries may be found at http://spec.jpl.nasa.gov/ .
[CrossRef]

Perevalov, V. I.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Perrin, A.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Pickett, H. M.

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,” JQSRT60(5), 883–890 (1998).Access to specific catalog entries may be found at http://spec.jpl.nasa.gov/ .
[CrossRef]

Poynter, R. L.

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,” JQSRT60(5), 883–890 (1998).Access to specific catalog entries may be found at http://spec.jpl.nasa.gov/ .
[CrossRef]

Predoi-Cross, A.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Rinsland, C. P.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Ro?nne, C.

C. Ro̸nne, L. Thrane, P.-O. Åstrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys.107(14), 5319–5331 (1997).
[CrossRef]

Rotger, M.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Rothman, L. S.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

S. A. Clough, Y. Beers, G. P. Klein, and L. S. Rothman, “Dipole moment of water from Stark measurements of H2O, HDO, and D2O,” J. Chem. Phys.59(5), 2254–2259 (1973).
[CrossRef]

Saito, S.

T. Manabe, Y. Furuhama, T. Ihara, S. Saito, H. Tanaka, and A. Ono, “Measurements of attenuation and refractive dispersion due to atmospheric water vapor at 80 and 240 GHz,” Int. J. Infrared Millim. Waves6(4), 313–322 (1985).
[CrossRef]

Schmuttenmaer, C. A.

J. T. Kindt and C. A. Schmuttenmaer, “Far-infrared dielectric properties of polar liquids probed by femtosecond terahertz pulse spectroscopy,” J. Phys. Chem.100(24), 10373–10379 (1996).
[CrossRef]

Schödel, R.

Shostak, S. L.

S. L. Shostak, W. L. Ebenstein, and J. S. Muenter, “The dipole moment of water. I. Dipole moments and hyperfine properties of H2O and HDO in the ground and excited vibrational states,” J. Chem. Phys.94(9), 5875–5882 (1991).
[CrossRef]

Šimecková, M.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Smith, M. A. H.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Stranathan, J. D.

J. D. Stranathan, “Dielectric constant of water vapor,” Phys. Rev.48(6), 538–544 (1935).
[CrossRef]

Strandberg, M.

S. Golden, T. Wentink, R. Hillger, and M. Strandberg, “Stark spectrum of H2O,” Phys. Rev.73(1), 92–93 (1948).
[CrossRef]

Sung, K.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Tanaka, H.

T. Manabe, Y. Furuhama, T. Ihara, S. Saito, H. Tanaka, and A. Ono, “Measurements of attenuation and refractive dispersion due to atmospheric water vapor at 80 and 240 GHz,” Int. J. Infrared Millim. Waves6(4), 313–322 (1985).
[CrossRef]

Tashkun, S. A.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Tennyson, J.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Thrane, L.

C. Ro̸nne, L. Thrane, P.-O. Åstrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys.107(14), 5319–5331 (1997).
[CrossRef]

L. Thrane, R. H. Jacobsen, P. Uhd Jepsen, and S. R. Keiding, “THz reflection spectroscopy of liquid water,” Chem. Phys. Lett.240(4), 330–333 (1995).
[CrossRef]

Toth, R. A.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Uhd Jepsen, P.

L. Thrane, R. H. Jacobsen, P. Uhd Jepsen, and S. R. Keiding, “THz reflection spectroscopy of liquid water,” Chem. Phys. Lett.240(4), 330–333 (1995).
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Van Vleck, J. H.

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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Vandaele, A. C.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Vander Auwera, J.

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. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009).
[CrossRef]

Walkov, A.

Wallqvist, A.

C. Ro̸nne, L. Thrane, P.-O. Åstrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys.107(14), 5319–5331 (1997).
[CrossRef]

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]

Wentink, T.

S. Golden, T. Wentink, R. Hillger, and M. Strandberg, “Stark spectrum of H2O,” Phys. Rev.73(1), 92–93 (1948).
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Yang, Y.

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

Y. Yang, M. Mandehgar, and D. Grischkowsky, “Time domain measurement of the THz refractivity of water vapor,” Opt. Express20(24), 26208–26218 (2012).
[CrossRef] [PubMed]

Appl. Opt. (1)

Chem. Phys. Lett. (1)

L. Thrane, R. H. Jacobsen, P. Uhd Jepsen, and S. R. Keiding, “THz reflection spectroscopy of liquid water,” Chem. Phys. Lett.240(4), 330–333 (1995).
[CrossRef]

IEEE Trans. THz Sci. Technol. (1)

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

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Int. J. Infrared Millim. Waves (2)

T. Manabe, Y. Furuhama, T. Ihara, S. Saito, H. Tanaka, and A. Ono, “Measurements of attenuation and refractive dispersion due to atmospheric water vapor at 80 and 240 GHz,” Int. J. Infrared Millim. Waves6(4), 313–322 (1985).
[CrossRef]

H. J. Liebe, G. A. Hufford, and T. Manabe, “A model for the complex permittivity of water at frequencies below 1 THz,” Int. J. Infrared Millim. Waves12(7), 659–675 (1991).
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J. Appl. Phys. (1)

G. Birnbaum and S. K. Chatterjee, “The dielectric constant of water vapor in the microwave region,” J. Appl. Phys.23(2), 220–223 (1952).
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J. Chem. Phys. (4)

S. A. Clough, Y. Beers, G. P. Klein, and L. S. Rothman, “Dipole moment of water from Stark measurements of H2O, HDO, and D2O,” J. Chem. Phys.59(5), 2254–2259 (1973).
[CrossRef]

T. R. Dyke and J. S. Muenter, “Electric dipole moments of low J states of H2O and D2O,” J. Chem. Phys.59(6), 3125–3127 (1973).
[CrossRef]

S. L. Shostak, W. L. Ebenstein, and J. S. Muenter, “The dipole moment of water. I. Dipole moments and hyperfine properties of H2O and HDO in the ground and excited vibrational states,” J. Chem. Phys.94(9), 5875–5882 (1991).
[CrossRef]

C. Ro̸nne, L. Thrane, P.-O. Åstrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys.107(14), 5319–5331 (1997).
[CrossRef]

J. Phys. Chem. (1)

J. T. Kindt and C. A. Schmuttenmaer, “Far-infrared dielectric properties of polar liquids probed by femtosecond terahertz pulse spectroscopy,” J. Phys. Chem.100(24), 10373–10379 (1996).
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Figures (2)

Fig. 1
Fig. 1

The normalized frequency dependence (f/f1/2) for the Debye refractivity (upper curve at zero) and absorption (lower curve at zero). These curves describe the frequency dependence shown in brackets in Eqs. (7a) and (7b).

Fig. 2
Fig. 2

Refractivity of water vapor at 20 °C and 10 g/m3, as calculated by the complete van-Vleck Weisskopf theory including the zero-frequency response, and the additional small term б(n(0)-1)v-VW = 3.02 x10−6 which describes the atomic and electric polarization of the water vapor, which is independent of the electric dipole moment. The measurements of [46] of 61x10−6 at 9.2, 24 and 72 GHz are indicated by the 3 open circles, respectively. The measurements of [8] are 63 and 80x10−6 for 890 and 965 GHz, respectively. The straight line at 61.06 x10−6 marks the complete calculated value of (n(0) −1).

Equations (27)

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(n(0)1) vVW =cD j 2 A j π ω j 2 .
( n ˜ (ω)1) D = ( 2πND μ 2 3kT ) / ( 1+iωτ ) .
(n(0)1) D = 2πND μ 2 3kT .
( n ˜ (ω)1) D = (n(0)1) D 1+iωτ .
( n ˜ (ω)1) D = (n( 0 )1) D 1+ ( ωτ ) 2 i (n( 0 )1) D ωτ 1+ ( ωτ ) 2 .
α D (ω)=( 2ω c ) (n( 0 )1) D ωτ 1+ (ωτ) 2 .
(n(f)1) D = ( n(0)1 ) D [ 1 1+ (f/ f 1/2 ) 2 ].
α D (f)= 4π f 1/2 c (n( 0 )1) D [ (f/ f 1/2 ) 2 1+ (f/ f 1/2 ) 2 ].
α(ω)=D j A j π ( ω ω j ) 2 [ Δ ω j (ω ω j ) 2 + ( Δ ω j /2 ) 2 + Δ ω j (ω+ ω j ) 2 + ( Δ ω j /2 ) 2 ].
Δk(ω)=D j 2 A j π ω j ( ω ω j ω j 2 ω 2 ) [ 1 Δ ω j 2 8 ω j ( ω ω j ) ( ω j +ω ( ω j ω) 2 + ( Δ ω j /2 ) 2 ω j ω ( ω j +ω) 2 + ( Δ ω j /2 ) 2 ) ].
D= 10 18 πN,
(n(ω)1) vVW =Δk λ 0 /2π=Δk(c/ω).
A j =( 8 π 3 3hc ) ν ba S x ba μ x 2 [ e E a / kT e E b / kT ] Q rs .
Q rs =    j ( 2J + 1 ) e Ea / kT .
A j =( 8 π 3 3hc ) ν ba S x ba μ x 2 ( 1 e ( E b E a ) / kT ) e E a / kT Q rs .
A j =( 8 π 3 3hc ) ν ba S x ba μ x 2 ( h ν ba / kT ) e E a / kT Q rs ,
A j =( 2π 3c ) ω ba S x ba μ x 2 ( ω ba / kT ) e E a / kT Q rs .
A j = C j ω j 2 .
(n( 0 )1) vVW =cD j 2 π C j .
C j =( 2π 3c ) S x ba μ x 2 e E a / kT Q rs kT .
(n( 0 )1) vVW =cπN( 2 π ) j ( 2π / 3c )( 2J+1 ) μ ab 2 e E a / kT Q rs kT .
(n( 0 )1) vVW =N( 4π 3kT ) j (2J+1) μ ab 2 e E a / kT Q rs .
f a = ( 2J+1 ) e E a / kT Q rs .
(n( 0 )1) vVW =N( 4π 3kT ) j f a μ ab 2 .
[ (n( 0 )1) vVW ] Limit =N( 2π 3kT ) j μ ab 2 .
j μ ab 2 = μ 2 .
[ (n( 0 )1) vVW ] Limit = 2πND μ 2 3kT .

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