Abstract

We report the measurement of the essentially frequency independent refractivity of water vapor from 0.1 to 1 THz, independent of the simultaneous strong THz pulse broadening and absorption. The humidity dependent transit time of THz pulses through a 170 m long round trip path was measured to a precision of 0.1 ps, using a mode-locked laser as an optical clock.

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References

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  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]
  2. 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]
  3. 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]
  4. 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]
  5. C. C. Bradley and H. A. Gebbie, “Refractive index of nitrogen, water vapor, and their mixtures at submillimeter wavelengths,” Appl. Opt.10(4), 755–758 (1971).
    [CrossRef] [PubMed]
  6. H. Matsumoto, “The refractive index of moist air in the 3-µm region,” Metrologia18(2), 49–52 (1982).
    [CrossRef]
  7. R. J. Hill and R. S. Lawrence, “Refractive index of water vapor in the infrared windows,” Infrared Phys.26(6), 371–376 (1986).
    [CrossRef]
  8. R. Schödel, A. Walkov, and A. Abou-Zeid, “High-accuracy determination of water vapor refractivity by length interferometry,” Opt. Lett.31(13), 1979–1981 (2006).
    [CrossRef] [PubMed]
  9. D. Grischkowsky, S. Keiding, M. Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B: Opt. Phys.7(10), 2006–2015 (1990).
    [CrossRef]
  10. Y. Yang, A. Shutler, and D. Grischkowsky, “Measurement of the transmission of the atmosphere from 0.2 to 2 THz,” Opt. Express19(9), 8830–8838 (2011).
    [CrossRef] [PubMed]
  11. Y. Yang, M. Mandehgar, and D. Grischkowsky, “Broad-band THz pulse transmission through the atmosphere,” IEEE Trans. THz Sci. Technol.1, 264–273 (2011).
  12. Y. Yang, M. Mandehgar, and D. Grischkowsky, “Understanding THz pulse transmission in the atmosphere,” IEEE Trans. THz Sci. Technol.2, 406–415 (2012).
  13. I. Wilke, A. M. MacLeod, W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, “Single-shot electron-beam bunch length measurements,” Phys. Rev. Lett.88(12), 124801 (2002).
    [CrossRef] [PubMed]
  14. A. M. Weiner, Ultrafast Optics, (John Wiley and Sons, Inc. 2009).
  15. 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. Quant. Spectrosc. Radiat. Transfer60(5), 883–890 (1998).
    [CrossRef]
  16. P. Debye, Polar Molecules, 89–90 (Dover Publ. Co., 1957).
  17. B. R. Bean, and E. J. Dutton, Radio Meteorology (National Bureau of Standards, Monograph #92, March 1966), Chap. 1
  18. 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]
  19. C. H. Townes and A. L. Schawlow, Microwave Spectroscopy (Dover Publ. Co., 1975).
  20. M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett.56(17), 1694–1696 (1990).
    [CrossRef]
  21. A. Deepak, T. D. Wilkerson, and L. H. Ruhnke, eds., Atmospheric Water Vapor, (Academic Press, 1980). This book is the Proceedings of the International Workshop on Atmospheric Water Vapor, Vail, Colorado, September 11–13, 1979.
  22. D. E. Burch and D. A. Gryvnak, “Continuum absorption by water vapor in the infrared and millimeter regions,” Proceedings of the International Workshop on Atmospheric Water Vapor, [21] 47–76 (1979).
  23. Y. Scribano and C. Leforestier, “Contribution of water dimer absorption to the millimeter and far infrared atmospheric water continuum,” J. Chem. Phys.126(23), 234301 (2007).
    [CrossRef] [PubMed]

2012 (1)

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

2011 (2)

Y. Yang, A. Shutler, and D. Grischkowsky, “Measurement of the transmission of the atmosphere from 0.2 to 2 THz,” Opt. Express19(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, 264–273 (2011).

2007 (1)

Y. Scribano and C. Leforestier, “Contribution of water dimer absorption to the millimeter and far infrared atmospheric water continuum,” J. Chem. Phys.126(23), 234301 (2007).
[CrossRef] [PubMed]

2006 (1)

2002 (1)

I. Wilke, A. M. MacLeod, W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, “Single-shot electron-beam bunch length measurements,” Phys. Rev. Lett.88(12), 124801 (2002).
[CrossRef] [PubMed]

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,” J. Quant. Spectrosc. Radiat. Transfer60(5), 883–890 (1998).
[CrossRef]

1990 (2)

M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett.56(17), 1694–1696 (1990).
[CrossRef]

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

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]

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]

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]

Abou-Zeid, A.

Berden, G.

I. Wilke, A. M. MacLeod, W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, “Single-shot electron-beam bunch length measurements,” Phys. Rev. Lett.88(12), 124801 (2002).
[CrossRef] [PubMed]

Bradley, C. C.

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,” J. Quant. Spectrosc. Radiat. Transfer60(5), 883–890 (1998).
[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,” J. Quant. Spectrosc. Radiat. Transfer60(5), 883–890 (1998).
[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]

Exter, M.

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

Fattinger, C.

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

Gebbie, H. A.

Gillespie, W. A.

I. Wilke, A. M. MacLeod, W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, “Single-shot electron-beam bunch length measurements,” Phys. Rev. Lett.88(12), 124801 (2002).
[CrossRef] [PubMed]

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, A. Shutler, and D. Grischkowsky, “Measurement of the transmission of the atmosphere from 0.2 to 2 THz,” Opt. Express19(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, 264–273 (2011).

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

M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett.56(17), 1694–1696 (1990).
[CrossRef]

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]

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]

Keiding, S.

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

Knippels, G. M. H.

I. Wilke, A. M. MacLeod, W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, “Single-shot electron-beam bunch length measurements,” Phys. Rev. Lett.88(12), 124801 (2002).
[CrossRef] [PubMed]

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]

Leforestier, C.

Y. Scribano and C. Leforestier, “Contribution of water dimer absorption to the millimeter and far infrared atmospheric water continuum,” J. Chem. Phys.126(23), 234301 (2007).
[CrossRef] [PubMed]

MacLeod, A. M.

I. Wilke, A. M. MacLeod, W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, “Single-shot electron-beam bunch length measurements,” Phys. Rev. Lett.88(12), 124801 (2002).
[CrossRef] [PubMed]

Manabe, 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]

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, “Broad-band THz pulse transmission through the atmosphere,” IEEE Trans. THz Sci. Technol.1, 264–273 (2011).

Matsumoto, H.

H. Matsumoto, “The refractive index of moist air in the 3-µm region,” Metrologia18(2), 49–52 (1982).
[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,” J. Quant. Spectrosc. Radiat. Transfer60(5), 883–890 (1998).
[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]

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,” J. Quant. Spectrosc. Radiat. Transfer60(5), 883–890 (1998).
[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,” J. Quant. Spectrosc. Radiat. Transfer60(5), 883–890 (1998).
[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,” J. Quant. Spectrosc. Radiat. Transfer60(5), 883–890 (1998).
[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]

Schödel, R.

Scribano, Y.

Y. Scribano and C. Leforestier, “Contribution of water dimer absorption to the millimeter and far infrared atmospheric water continuum,” J. Chem. Phys.126(23), 234301 (2007).
[CrossRef] [PubMed]

Shutler, A.

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]

van der Meer, A. F. G.

I. Wilke, A. M. MacLeod, W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, “Single-shot electron-beam bunch length measurements,” Phys. Rev. Lett.88(12), 124801 (2002).
[CrossRef] [PubMed]

van Exter, M.

M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett.56(17), 1694–1696 (1990).
[CrossRef]

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).
[CrossRef]

Walkov, A.

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]

Wilke, I.

I. Wilke, A. M. MacLeod, W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, “Single-shot electron-beam bunch length measurements,” Phys. Rev. Lett.88(12), 124801 (2002).
[CrossRef] [PubMed]

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, “Broad-band THz pulse transmission through the atmosphere,” IEEE Trans. THz Sci. Technol.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. Express19(9), 8830–8838 (2011).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett.56(17), 1694–1696 (1990).
[CrossRef]

IEEE Trans. THz Sci. Technol. (2)

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

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

Infrared Phys. (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]

Int. J. Infrared Millim. Waves (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]

J. Chem. Phys. (1)

Y. Scribano and C. Leforestier, “Contribution of water dimer absorption to the millimeter and far infrared atmospheric water continuum,” J. Chem. Phys.126(23), 234301 (2007).
[CrossRef] [PubMed]

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

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

J. Quant. Spectrosc. Radiat. Transfer (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,” J. Quant. Spectrosc. Radiat. Transfer60(5), 883–890 (1998).
[CrossRef]

Metrologia (1)

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

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

I. Wilke, A. M. MacLeod, W. A. Gillespie, G. Berden, G. M. H. Knippels, and A. F. G. van der Meer, “Single-shot electron-beam bunch length measurements,” Phys. Rev. Lett.88(12), 124801 (2002).
[CrossRef] [PubMed]

Proc. Phys. Soc. B (3)

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]

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]

Rev. Mod. Phys. (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]

Other (6)

C. H. Townes and A. L. Schawlow, Microwave Spectroscopy (Dover Publ. Co., 1975).

P. Debye, Polar Molecules, 89–90 (Dover Publ. Co., 1957).

B. R. Bean, and E. J. Dutton, Radio Meteorology (National Bureau of Standards, Monograph #92, March 1966), Chap. 1

A. M. Weiner, Ultrafast Optics, (John Wiley and Sons, Inc. 2009).

A. Deepak, T. D. Wilkerson, and L. H. Ruhnke, eds., Atmospheric Water Vapor, (Academic Press, 1980). This book is the Proceedings of the International Workshop on Atmospheric Water Vapor, Vail, Colorado, September 11–13, 1979.

D. E. Burch and D. A. Gryvnak, “Continuum absorption by water vapor in the infrared and millimeter regions,” Proceedings of the International Workshop on Atmospheric Water Vapor, [21] 47–76 (1979).

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Figures (4)

Fig. 1
Fig. 1

Top (x-z plane) view of the long-path set-up with the sample chamber outlined (red online). Insets: Side (y-z plane) views of all mirrors. Solid lines show the optical path and the outgoing THz beam (in insets), dased lines show the incoming THz beam. Arrows indicate the THz beam direction, colors distinguish overlapping beams in the side view. The indicated angles are θ1 = 5.4°, θ2 = 19°, θ3 = 80°, θ4 = 2.4°, and φ = −1.25°. Three measured transmitted THz pulses (top) RH 22% (4.0 g/m3), (middle) RH 43% (7.9 g/m3), (bottom) RH 58% (10.6 g/m3) at 21 °C show the frequency-independent water vapor delays with respect to the top pulse of Δt = 11.5 ps and Δt = 19.5 ps and, where Δt = (no – 1)L/c. The dashed lines mark the corresponding first minimums at 18.15 ps, 29.63 ps, and 37.63 ps.

Fig. 2
Fig. 2

Amplitude spectra of the transmitted pulses of Fig. 1.

Fig. 3
Fig. 3

(a) The measured pulse time-shift vs RH at 21 °C for four independent measurements, performed many weeks apart. (b) Replot of the data and extended lines of (a), with the time delay at zero RH subtracted from the data series. The overlap of all data was fit a straight line with a standard deviation of 1.40; and a slope: 5.84 ps/ RH 10%. For conversion to other units RH 54% at 21 °C is equivalent to 10.1 mm Hg and a water vapor density of 10 g/m3.

Fig. 4
Fig. 4

Total refractivity of water vapor at 20 °C and 10 g/m3. (a). The calculated refractivity of all the water vapor lines (Fig. 3(b) [12]), added to the measured frequency-independent refractivity (yellow highlight) of (70 x 10−6)/[1 + (f/f1/2)2] for f1/2 = 2 THz. (b) The calculated refractivity of all the water vapor lines [12], added to the adjusted frequency-independent refractivity (yellow highlight) of (61 x 10−6)/[1 + (f/f1/2)2] for f1/2 = 2 THz. The measurements of [13] are indicated by the three open circles at 61 x 10−6 on the dashed lines at 9.2, 24 and 72 GHz, respectively. The measurements of [5] are indicated by the two open circles at 63 and 80 x 10−6 on the dashed lines at 0.890 and 0.965 THz. It should be noted that without the frequency-independent term (n(0) – 1)/[1 + (f/f1/2)2 ], the curves drop to the zero base line, and become identical to Fig. 3(b) [12].

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

n ˜ D (ω)1= ( 2πN μ 2 3kT ) / ( 1+iωτ )
n ˜ D (ω)1= n 0 (0)1 1+iωτ
n ˜ D ( ω )1= n 0 ( 0 )1 1+ ( ωτ ) 2 i [ n 0 ( 0 )1 ]ωτ 1+ ( ωτ ) 2
n 0 (0)1= 2πN μ 2 3kT
α D ( ω )=2( ω c ) [ n 0 ( 0 )1 ]ωτ 1+ ( ωτ ) 2
α D ( limit )=2 n 0 ( 0 )1 ( cτ )
n H 2 O ( ω )1= n 0 ( 0 )1 1+ ( ωτ ) 2 +[ n( ω )1 ]

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