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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 4 — Feb. 24, 2014
  • pp: 4388–4403
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Determination of the water vapor continuum absorption by THz-TDS and Molecular Response Theory

Yihong Yang, Mahboubeh Mandehgar, and D. Grischkowsky  »View Author Affiliations


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


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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.

© 2014 Optical Society of America

1. Introduction

The poorly understood continuum absorption is determined empirically and is defined as the difference between the measured total absorption and the absorption of the resonant lines [4

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

]. The latter is usually calculated as the sum of all of the resonant lines based on a lineshape function with the corresponding line intensity and linewidth of individual lines, taken from a spectroscopic database, such as the Millimeter wave Propagation Model (MPM) [5

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

], HITRAN [6

6. 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]

] and JPL [7

7. 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/.

]. The determined continuum absorption depends strongly on the lineshape function, number of lines, line intensities and linewidth chosen for the line-by-line summation method. It has been shown that the van Vleck-Weisskopf (vV-W) lineshape fits the resonant lines near their centers more accurately than the full Lorentz (FL) and Gross lineshapes [8

8. 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]

]. Since then, in most of the literature the vV-W lineshape has used to obtain the continuum absorption within the Millimeter wave [5

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

,9

9. 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]

,10

10. 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]

] and THz regions [11

11. 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]

13

13. 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]

] under various humidity and temperature conditions. Clearly, only the resonance absorption with a strictly defined lineshape function can lead to reliable values of the continuum absorption.

However, two types of vV-W lineshape functions are found in the literature, regarding determinations of the continuum absorption: those with a linear v/vj pre-factor [11

11. 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]

13

13. 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]

], and those with a quadratic (v/vj)2 pre-factor [5

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

,8

8. 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]

10

10. 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]

,14

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

]. In this paper, we will show the quadratic pre-factor agrees with the original vV-W paper [15

15. 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]

] and with Townes and Schawlow [16

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

].

Many recent works have obtained the relative continuum absorption by subtracting the resonance absorption based on the quadratic pre-factor vV-W lineshape function, but with a cutoff frequency of 750 GHz from the line center. We will show by using molecular response theory, that this cut-off is too severe and thereby gives a lower value for the resonant line absorption and a consequent higher value for the continuum absorption.

Most of the experimental studies of the water vapor continuum absorption in the mm wave and THz region have used a Fabry-Perot interferometer (FP) or a Fourier transform spectrometer (FTS) equipped with a multi-pass cell [11

11. 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]

,12

12. 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]

]. An experimental problem for these approaches is significant absorption from an adsorbed layer of water on the reflectors surfaces, which increases with humidity. A new approach based on the variation of the spectrometer optical path-length was proposed to solve this problem [9

9. 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]

,10

10. 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]

]. However, the mismatch of the distribution of electrical field, coupling loss and the water adsorption on the resonator elements could cause systematic error. The most recent work utilizes a Fourier Transform Infrared (FTIR) spectrometer equipped with a long-path cavity of 1-6 m length [13

13. 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]

]. Our THz-TDS long-path setup minimizes the systematic uncertainty from adsorption on chamber elements, having less than 0.4% double pass amplitude loss on 100 nm thick water layers on two mirrors with 45 degree incident angle and essentially no loss with normal incidence on the other eight mirrors [17

17. 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).

].

In this paper, we measured the relative total water vapor absorption, using a 137 m round-trip humidity controlled sample chamber within the 170 m long-path THz-TDS system, that measures the water density from the transit time of the THz pulses [20

20. 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]

]. For our analysis, we use the fundamental molecular response theory (MRT) [21

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

,22

22. 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]

], based on physical principles and measurements, to obtain the resonant line absorption.

MRT resonant absorption consists of a frequency dependent fractional sum of the vV-W absorption and the full Lorentz (FL) absorption, αMRT (ν) = S(ν) αvV-W (ν) + [1- S(ν)] αFL (ν), where S(ν) is the weighting factor, determined by the molecular response time τc = 0.2 ps [21

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

,22

22. 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]

]. Consequently, the MRT resonant absorption is always between the vV-W and FL values of absorption, which provides fundamental limits to the resonant line absorption.

We will show that for the atmosphere at the relatively normal conditions of 20 o C and RH 36.2% (7.0 g/m3), the continuum absorption below 1 THz is easily determined in all of our 4 THz windows of transparency. For the highest frequency window at 850 GHz the total measured absorption is 56 dB/km; the calculated MRT absorption is 40 dB/km, thereby giving the continuum absorption of 16 dB/km. In comparison, under these same conditions, the approximate vV-Wc absorption is calculated to be only 33 dB/km, thereby giving the increased continuum absorption of 23 dB/km.

2. Theory

2.1 van Vleck-Weisskopf (vV-W) lineshape

In the JPL database the absorption coefficient αj(v) of water vapor resonant line can be written as the product of a line intensity Ij with units of (nm2 MHz) and a lineshape function f(v, vj) [4

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

,7

7. 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/.

]: where NH2O is the number density of water vapor in molecules / (cm·nm2), and vj is the resonant line center frequency in MHz.
αj(v)=NH2OIj(v)f(v,vj).
(1)
For both the JPL and the HITRAN databases, the total absorption coefficient is the sum of all the individual water vapor absorption lines, α=jαj. The two types of vV-W lineshape equations are given in different works as:
f1(v,vj)=1π(vvj)2(Δvj(vvj)2+Δvj2+Δvj(v+vj)2+Δvj2).
(2)
f2(v,vj)=1π(vvj)(Δvj(vvj)2+Δvj2+Δvj(v+vj)2+Δvj2).
(3)
where Δvj is the line half-width at half-maximum (HWHM), and vj is line center frequency. The only difference between these two functions is that Eq. (2) has a quadratic, and Eq. (3) has a linear v/vj pre-factor. The amplitude transmissions based on these two types of v-VW line shapes are shown in Appendix A. The quadratic pre-factor vV-W lineshape function is shown in Appendix A to be required for the JPL database, based on the direct conversion of the absorption expression in the original vV-W paper [15

15. 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]

].

The HITRAN equation was used in the calculation and analysis in the following sections, because HITRAN gives the line broadening coefficients, which are used to calculate the corresponding line half-width for all of the individual water vapor lines. All of the conclusions apply to both the JPL and the HITRAN databases, which yield identical results.

2.2 vV-W lineshape functions with cut-off frequency (vV-Wc)

2.3 Connection of the vV-W and FL lineshapes by molecular response theory (MRT)

For the molecular response theory the absorption lineshape function is given by
αjMRT(ν)=S(ν)αjvVW(v)+(1S(ν))αjL(ν).
(4)
for which αjvVW(v)is the lineshape function of the vV-W theory, in Eq. (2), and αjL(v)is the FL lineshape function, and S(v)is the MRT weighting function controlling the transition from the vV-W lineshape at low frequencies to the FL lineshape at higher frequencies. S(ν) is given simply by,
S(ν)=1/[1+(2πντc)2].
(5)
where τcis the collision parameter. S(ν) monotonically changes from one to zero as the frequency increases, and S(ν) = 0.5 for ν1/2 = 1/(2πτc) = 796 GHz for τc = 0.2 ps. Consequently, for2πντc1,αjMRT(ν)αjvVW(ν), and for 2πντc1,αjMRT(ν)αjL(ν). τc is considered to be a measure of the orientation time of molecules during a collision and is expected to be much faster than the duration of a collision. Consistent with the notation of Eq. (2) for the vV-W lineshape, the corresponding full Lorentz (FL) lineshape is given by [8

8. 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]

,15

15. 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]

,21

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

,22

22. 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]

].
fL(v,vj)=1π(vvj)(Δvj(vvj)2+Δvj2Δvj(v+vj)2+Δvj2).
(6)
Note that the FL lineshape has the linear pre-factor and the negative sign for the second term in the brackets. The comparison of the vV-W, FL, MRT and vV-Wc absorption lineshapes on the low and high-frequency wings, of a single resonance line at 1.0 THz and with a peak value of unity is shown in Fig. 1. Surprisingly, because of the linear pre-factor, the FL line is higher than the vV-W line on the low-frequency side, while on the high-frequency side, it is significantly lower as expected [21

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

,22

22. 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]

]. It is important to note that the MRT line, as defined in Eq. (4), will always be between the FL and the vV-W lines. This feature has only the linewidths as a parameter, which are calculated by HITRAN. The value of the MRT line located between the vV-W and FL lines is determined by τc = 0.2 ps [21

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

,22

22. 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]

].

As shown in Fig. 1, the MRT value of the resonant line absorption is between the vV-W and the FL lines. This is not the case for the much lower vV-Wc line, which significantly understates the resonant absorption, and thereby overstates the continuum absorption.

2.4. Empirical continuum absorption function

αc(v,294K)=v2[CW*ρW2+CA*ρAρW].
(8)

In this work, instead of measuring the absolute total absorption αof a humid air sample signal compared with a dry air reference signal, we measured the relative total absorption Δαx between the sample and reference signals with different humidity levels. The designation of Δαx indicates that there will be a cross term due to the quadratic part of the continuum absorption,
Δαx=αSαR=(αMRTS+αcS)(αMRTR+αcR)=ΔαMRT+(αcSαcR)=ΔαMRT+Δαcx.
(9)
where theαS,αMRTS,αcSand αR,αMRTR,αcRdenote the absolute total absorption, the absolute vV-W resonance absorption, and absolute continuum absorption of the sample and reference signals, respectively. The relative resonance line absorption ΔαMRT is linearly proportional to water vapor number density. Based on Eq. (8), the relative continuum absorption including the cross term Δαcx is given by,
Δαcx=αcSαcR=v2[CW*((ρWS)2(ρWR)2)+CA*ρA(ρWSρWR)].
(10)
whereρWS and ρWRare water vapor density of the sample and reference signals respectively, and the density difference is ΔρW=ρWSρWR. Substituting ρWS=ρWR+ΔρWin Eq. (10), we obtain:
Δαcx=v2[CW*(2ρWRΔρW+ΔρW2)+CA*ρAΔρW].
(11)
and the cross term function X is given by

X=v2CW*(2ρWRΔρW).
(12)

The cross term X has to be subtracted from the relative continuum absorptionΔαcx and from the relative total absorptionΔαx. Equations (13a) and (13b) give the absolute continuum absorption Δαc and the absolute total absorptionΔα, which only depend onΔρW .

Δαc=ΔαcxX=v2[CW*ΔρW2+CA*ρAΔρW].
(13a)
Δα=ΔαxX.
(13b)

The value of the water vapor density of the reference THz signalρWR in the additional cross term ρWRΔρW can be obtained from the water vapor partial pressure measured by hygrometers in the sample chamber. The quadratic frequency dependence of the continuum absorption was confirmed in our experiments.

In order to determine the cross-term function X and the continuum absorptionΔαc, we must first determine CW*andCA*. This is done by using Eq. (11) and two measured values of Δαcx for the same window, same reference, but different water vapor densitiesΔρW. Inserting the parameters for each measurement into Eq. (11) gives two linearly independent equations, that can be solved for CW* and CA*. Now, the cross-term function X can be evaluated and then subtracted from Δαcx to obtain the continuum absorptionΔαc.

3. Experimental methods

Fig. 2 Experimental set up with 170 m long-path system.
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).
Figure 2 shows the long-path THz system for the experimental measurement of the continuum absorption described in [20

20. 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]

]. The THz pulses are generated and detected by the standard THz TDS system [18

18. 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]

], which is coupled to the 170 m round trip long-path THz setup by combining an optical train of large flat mirrors and a spherical telescope mirror [3

3. 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]

,4

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

,17

17. 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).

,20

20. 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]

]. In order to obtain the high signal-to-noise ratio of coherent sampling, the final THz pulses propagation distance of 170.46 m from M1 to M10 was adjusted to be precisely an integer multiple(51 in this case) of the laser pulse round-trip of 3.342 m in the mode-locked laser with a repetition rate of 89.6948 MHz,. A humidity controlled sample chamber, transformed from the THz lab hallway, is shown by the red box in Fig. 3 within the long path. This chamber with 137 m total round trip length (from the entrance through the film window, through the chamber and to the exit through the film window) allowed us to increase the chamber humidity up to RH 30% higher than the ambient laboratory atmosphere. Three hygrometers measure the RH and temperature during experiments at both ends of the chamber and on the optical table, shown as the gray rectangle in Fig. 2.

The THz long path system with the humidity controlled chamber allowed the relative measurement of the transit time of the sharp leading edge of the reshaped THz pulses propagated through atmosphere to a precision of 0.1 ps, by using the mode-locked laser as an accurate optical clock. The measured THz pulses and their corresponding Fourier-transformed frequency spectra are shown in Fig. 3, for two groups of measurements taken on two different days, 20 days apart. The measured THz pulses in each group were recorded from the same start position of the time scan, which allowed obtaining the transit time difference between the THz pulses with various RH, as shown in Figs. 3(a) and 3(c). The time values in ps at the beginning of the THz signals are the absolute transit time from the start point.

The frequency spectra in Figs. 3(b) and 3(d) are averages of three THz pulses in each set. The frequency independent part of water vapor refractivity is (n-1) = 61.6 x 10−6 in an atmosphere with RH 58% at 20 °C (density of 10 g/m3) [23

23. 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]

]. The transit time of THz pulses through the 137 m total round-trip path in the RH (density 10 g/m3) controlled chamber is 27.9 ps longer, than for a dry chamber. By comparing the transmitted time difference Δt of the sample and reference pulses with 27.9 ps / 10 g/m3, the relative water vapor density can be calculated to an accuracy of 0.04 g/m3, corresponding to RH 2%, and a 0.1 ps delay change.

In this work, the transit times of THz pulses are not only affected by various RH levels but also by the laser-clock drift and the drift in the long THz optical train. Firstly, the repetition (clock) rate of the Mode-locked laser is 89.6948xx MHz, measured to eight digits by a frequency counter, is quite stable to six digits during measurements. Frequency drift and some jitter occur in the last 2 digits as indicated by xx which illustrates a slow change in the optical clock rate of the order of 100 Hz.

Secondly, the slow change of the length of the long THz optical train is from the heat expansion and cold contraction of the concrete floor and stainless steel (SS) optical table [20

20. 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]

]. The massive concrete floor has very slow response to average temperature changes, on the order of many hours or days, while the temperature response of the SS table is much faster. Moreover, stainless steel and concrete have approximately the same coefficient of thermal expansion 10−5 (ΔL/L)/°C. If the difference temperature ΔT changed by 1 °C, a length difference of 170 m x 10−5 would occur, with the corresponding change in the start time of the THz pulse of 5.7 ps. This time change is approximately equal to the observed day to day and week to week changes as shown in the difference groups of THz signals in Fig. 3.

From the experimental results, the stable transit times for several scans in a series show the stability of the long-path setup and that no significant change in optical train or laser-clock drift occurs. The weak water vapor absorption line center frequencies in the Fourier-transformed frequency spectra of measurements shown in Fig. 2 agree with the HITRAN and the JPL database to an accuracy of 1 GHz [17

17. 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).

], which indicates the stability of the long-path setup within one scan.

4. Results

Fig. 4 (a) Amplitude transmission forΔρW = 7.0 g/m3, which is the spectral ratio between the sample #2 and reference in Fig. 3(d). (b) Measured power attenuation coefficients Δαx (open circles) in dB/km with the smoothed THz windows W1-W4 (solid lines), for the water vapor density differences of ΔρW = 4.1 g/m3 (bottom blue circles), ΔρW = 5.2 g/m3 (middle red circles) and ΔρW = 7.0 g/m3 (top black circles). For comparison the MRT calculation for ΔρW = 4.1 g/m3 is shown as the purple solid bottom line. (3)-(5) indicate the THz windows investigated in [19].
Fig. 5 (a) Illustration of the method to obtain the relative continuum absorptionΔαcxfor the windows with ΔρW = 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 ΔρW = 7.0 g/m3. (b) The calculated cross term X absorption with a quadratic frequency dependence, ΔρW = 7.0 g/m3 (top black line), ΔρW = 5.2 g/m3 (middle red line), and ΔρW = 4.1 g/m3 (bottom blue line). (c) The continuum absorption Δαc from Table 1 and corresponding fitting (solid lines), the linearΔρW 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.
The relative amplitude transmission of sample #2 with respect to the reference of Fig. 3(d) is shown in Fig. 4(a) for the path length of 137 m. This transmission was obtained by dividing the sample amplitude spectrum by the reference spectrum as shown in Fig. 3(d). The corresponding absorption Δαxshown in Figs. 4(b) and 5(a) were obtained by taking the log to the base 10 of the values of transmission per km, multiplied by 20 to obtain the power absorption.

In Fig. 4, four THz transmission windows at 0.41 THz (W1), 0.46 – 0.49 THz (W2), 0.68 THz (W3) and 0.85 THz (W4) are shown clearly within 0.35 – 1 THz. The grey regions cover the no-signal areas, caused by the strong water vapor absorption lines. In Fig. 4(b), in order to minimize the ripple effect, the smoothed measured window curves were obtained by using the Matlab smooth command for 5 points in W1 and W3, 8 points in W4, and none for W2. The ripples on the measurements are caused by small reflections following the main pulse, from surfaces other than the coupled mirrors.

The measured relative total absorption Δαxand the calculated relative resonance absorption for the water vapor density difference of ΔρW = 7.0 g/m3 are shown in Fig. 5(a). The difference between the measured smoothed windows Δαx(red solid line) and the calculated relative resonance absorption (black solid line) is the relative continuum absorption Δαcxdescribed by Eq. (10), which includes the cross term X. Analysis of the measurements of Δαcxin Fig. 5(a), allowed us to determine the corresponding X, shown as the lowest dashed curve. X is shown for all three measurements in Fig. 5(b). We determined the values of relative continuum absorption Δαcxand X at each window, from the difference between the minima of the calculated resonance absorption windows to the minimum of the smoothed windows as shown in the bottom of Fig. 5(a).

Table 1. Determined Values ofΔαcx, X, Δαcin dB/km at Four THz Windows with Different Density

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The differences Δαcxbetween minima of the measurement and the ΔρW = 7.0 g/m3 MRT curve for each window shown in Fig. 5(a) are presented in Table 1, together with the corresponding cross-term X and the desired absolute continuum absorption Δαc. These same parameters are listed in the table for ΔρW = 4.1 g/m3 and ΔρW = 5.2 g/m3. Figures 5(b) and 5(c) show the corresponding values taken from the table, showing excellent agreement with the squared frequency dependence of Eqs. (7)(13). The theoretical curves presented in Figs. 5(b) and 5(c) are obtained from Eqs. (12) and (13a) with CW*=(1.33)2CWand CA*=(1.33×0.84)CA, where CWand CAare given in Table 2.

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

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In Fig. 5(c), the dashed lines for the three curves show that part of the continuum absorption due to the linear dependence onΔρW, the difference between the two curves shows that part of the absorption due to the ΔρW2 quadratic components. It is noteworthy that the fraction shows this ΔρW2dependence, but it is somewhat surprising that the quadratic termΔρW2 is such a relatively small fraction of the total. For example, for 7.0 g/m3 the quadratic term is 33% of the total, and for 5.2 g/m3 the term (highlighted in yellow) is 25% and for 4.1 g/m3 the term is 20%.

In Fig. 5(c), it is informative to compare the ratio of the MRT resonant line absorption to the empirically fit continuum absorption, Rα = αMRTc, for the THz windows of transparency: for W4 at 850 GHz, R = 2.5, For W3 at 680 GHz, R = 3.3, for W2 at 475 GHz, Rα = 6.0, for W1 at 410 GHz Rα = 2.7, for the window at 345 GHz, Rα = 1.7, for the window at 220 GHz, Rα = 0.74, and at 100 GHz, Rα = 0.33. For the windows below 300 GHz, the continuum absorption has become larger than the MRT absorption. This situation has driven much interest in mm wave applications, for which the continuum absorption is the major component.

5. Conclusions

This study experimentally and theoretically investigates the important, but poorly understood water vapor continuum absorption within the 0.35 – 1 THz range, using the long path THz-TDS system. We demonstrated that accurate average relative humidity (RH) changes for the THz path can be obtained by measuring the humidity-dependent different transit times to an accuracy of 0.1 ps of the THz pulses, that have propagated through the 137 m round-trip path within the humidity controlled sample chamber.

We plan future continuum determinations with higher precision, obtained by a much reduced RH of the reference pulse and an increase in the holding time of the sample chamber. Lower reference RH would be possible on a cold dry day in winter, for which the ambient humidity in the laboratory can be less than RH 10%, corresponding to ρw = 1.7 g/m3. A longer holding time in the chamber would allow larger increases in the contained RH. We also plan to increase the spectral amplitudes of the lower frequencies from 95 GHz to 350 GHz, by using different THz transmitters and receivers and larger long-path mirrors, to enable us to measure the important water vapor, THz windows in this range, for which αMRT < αc .

Appendix A: Pre-factor of vV-W lineshape

The calculated resonance amplitude transmissions after 137 m propagation with water vapor density of 6.4 g/m3 based on two types of v-VW lines shapes are shown in Fig. 7.
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.
The linear pre-factor curve using Eq. (3) shows a significantly lower transmission than the quadratic pre-factor curve using Eq. (2) from 0 to 1 THz. Consequently, the continuum absorption obtained by the linear v/vj pre-factor would be smaller than that obtained by the quadratic (v/vj)2 pre-factor.

The quadratic pre-factor vV-W lineshape function will now be shown to be required for the JPL database, based on the direct conversion of the absorption expression in the original vV-W paper [15

15. 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]

] from the classic oscillator to quantum mechanics below 2 THz. In the JPL database the absorption coefficient αj(v) of water vapor resonant line can be written as the product of a line intensity Ij with units of (nm2 MHz) and a lineshape function f(v, vj) [4

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

,7

7. 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/.

]: where NH2O is the number density of water vapor in molecules / (cm·nm2), and vj is the water vapor resonant line center frequency in MHz.
αj(v)=NH2OIj(v)f(v,vj).
(14)
where NH2O is the number density of water vapor in molecules / (cm·nm2), and vj is the water vapor resonant line center frequency in MHz.

The absorption coefficient equation in the HITRAN database has the same format as αj(v˜)=NH2OSj(v˜)f(v˜,v˜j), where NH2O*is the number density of water vapor in molecules / (cm3), Sj is the intensity in a cm−1/(molecule/cm2) and v˜j is the water vapor resonant line center wavenumber in cm−1. Note that Sj can be converted to Ij by Sj=Ij/(c1010) where c is the speed of light in vacuum with units of m/s [6

6. 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]

]. For both the JPL and the HITRAN databases, the total absorption coefficient is the sum of all of individual water vapor absorption lines by using the line-by-line summation method asα=jαj.

The original vV-W paper [15

15. 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]

] shows how the vV-W lineshape functions can be used with the JPL database. Firstly, the classical oscillator theory expression of absorption per unit length is given by Eq. (17) in [15

15. 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]

] and Eq. (13-16) in [16

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

]:
α=Ne2mc(vv0)2[1/2πτ(vv0)2+(1/2πτ)2+1/2πτ(v+v0)2+(1/2πτ)2].
(15)
where τ is the mean time interval between collisions and 1/τ = 2πΔv. In order to convert the classic oscillator expression to the general quantum-mechanical system, the factor e2/mwas replaced by8π2vj|μba2|/3h, (b and a in this quantum-mechanical expression denote the excited and lower states respectively, of the transitionvj), where μab is the corresponding dipole moment matrix element [15

15. 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]

,16

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

,26

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

]. Following Eqs. (13-17) through 13-19 in [16

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

], we have replaced N withΔnj, which is the number density difference between the lower and excited states of transition vj.
αj=Δnj8π2vj|μba|23hc(vvj)2[1/2πτ(vvj)2+(1/2πτ)2+1/2πτ(v+vj)2+(1/2πτ)2].
(16)
The number density njin the lower state of the vj transition is given by
nj=Nfja.
(17)
where N is the total number density andfjais the fractional factor [16

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

],
fja=(2J+1)eEja/kT/j,J(2J+1)eEja/kT.
(18)
The number density difference Δnjis given by
Δnj=nj(1e(EjbEja)/kT).
(19)
whereEjbEja=hvj, and for hvjkTis well approximated by Δnjnj(hvj/kT). Substituting these results in Eq. (15), we obtain
αj=N[8π33ckTvj2|μba|2(2J+1)eEja/kTj,J(2J+1)eEja/kT]1π(vvj)2[1/2πτ(vvj)2+(1/2πτ)2+1/2πτ(v+vj)2+(1/2πτ)2].
(20)
which is in exact agreement with Eq. (13-19) in [16

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

]. Now the absorption coefficient αj shown in Eq. (20) is seen to be a product of the total number density N, the line intensity Ij(in the first bracket) and lineshape function f(v, vj).

We will now show that Ijin Eq. (20) is identical to the line intensity Ij shown as Eq. (1) in the JPL database [7

7. 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/.

] which is given below:
Iba(T)=(8π33hc)νbaSxbaμx2[eEja/kTeEjb/kT]Qrs.
(21)
for vba=vj, Sxbaμx2=(2J+1)μab2according to Eq. (4-28) in [16

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

], and the rotational-spin partition function Qrs=j,J(2J+1)eEja/kT. Using these relationships and the approximation: 1e(EjbEja)/kThvj/kT, forhvjkT, we can rewrite Eq. (21) as
Ij=(8π33ckT)vj2|μba|2(2J+1)eEja/kTj,J(2J+1)eEja/kT.
(22)
which is identical to the line intensity Ijin the first brackets of Eq. (20). And the lineshape function f(v, vj) of Eq. (20) has the quadratic (v/vj)2 pre-factor which is same as the f1(v, vj) of Eq. (2). This quantum-mechanical relationship only holds in the region for hvjkT, which is equivalent to the frequency is much smaller than 6.2 THz, for 300 K [16

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

]. Consequently, the above result for the conversion from classic oscillator to quantum-mechanics is valid below 2 THz and shows that the quadratic pre-factor vV-W lineshape function should be used with the JPL database.

Appendix B: vV-Wc cut-off lineshape

The modified vV-Wc lineshape function with the cut-off [9

9. 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]

,11

11. 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]

,14

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

], is given by
fcutoff(v,vj)=1π(vvj)2(Δvj(vvj)2+Δvj2+Δvj(v+vj)2+Δvj22Δvjvcut2+Δvj2).if|vvj|<vcutfcutoff(v,vj)=0.if|vvj|vcut
(23)
where vcut is the cutoff frequency of 750 GHz in this work. Using the cutoff increases the calculated transmission of water vapor. However, as pointed out by our referee, Eq. (23) has a physical inconsistency, whereby the calculated value becomes negative for frequency differences from resonance, slightly smaller than the cutoff frequency. Consequently, we developed the straight-forward procedures given in Eqs. (24), (25) and (2) to handle the cutoff and to eliminate this inconsistency. For case 1, of Eq. (23) with vj<v, we have
fcutoff(v,vj)=1π(vvj)2(Δvj(vvj)2+Δvj2+Δvj(v+vj)2+Δvj2Δvjvcut2+Δvj2Δvj(2vj+vcut)2+Δvj2).
(24)
for whichfcutoff(v,vj)=0., when vcut(vvj) For case 2, with v<vj, we have
fcutoff(v,vj)=1π(vvj)2(Δvj(vvj)2+Δvj2+Δvj(v+vj)2+Δvj2Δvjvcut2+Δvj21(2vjvcut)2+Δvj2)
(25)
for which fcutoff(v,vj)=0., when vcut(vjv) For case 3, with v<vj<vcut, we havefcutoff(v,vj)=f1(v,vj), given by Eq. (2).

Acknowledgment

This work was partially supported by the National Science Foundation.

References and links

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]

2.

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]

3.

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]

4.

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

5.

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

6.

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]

7.

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/.

8.

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]

9.

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]

10.

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]

11.

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]

12.

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]

13.

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]

14.

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

15.

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]

16.

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

17.

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).

18.

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]

19.

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]

20.

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]

21.

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

22.

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]

23.

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]

24.

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]

25.

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.

26.

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

OCIS Codes
(010.1320) Atmospheric and oceanic optics : Atmospheric transmittance
(300.6495) Spectroscopy : Spectroscopy, teraherz
(010.1030) Atmospheric and oceanic optics : Absorption

ToC Category:
Terahertz Optics

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

Citation
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)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-4-4388


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References

  1. S. Paine, R. Blundell, D. Papa, J. Barrett, S. Radford, “A Fourier transform spectrometer for measurement of atmospheric transmission at submillimeter wavelengths,” Publ. Astron. Soc. Pac. 112(767), 108–118 (2000). [CrossRef]
  2. E. Cianca, T. Rossi, A. Yahalom, Y. Pinhasi, J. Farserotu, C. Sacchi, “EHF for satellite communications: the new broadband frontier,” Proc. IEEE 99(11), 1858–1881 (2011). [CrossRef]
  3. J. S. Melinger, Y. Yang, M. Mandehgar, D. Grischkowsky, “THz detection of small molecule vapors in the atmospheric transmission windows,” Opt. Express 20(6), 6788–6807 (2012). [CrossRef] [PubMed]
  4. Y. Yang, M. Mandehgar, D. Grischkowsky, “Understanding THz pulse transmission in the atmosphere,” IEEE Trans. THz Sci. Technol. 2(4), 406–415 (2012).
  5. H. J. Liebe, “The atmospheric water vapor continuum below 300 GHz,” Int. J. Infrared Millim. Waves 5(2), 207–227 (1984). [CrossRef]
  6. 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, J. Vander Auwera, “The HITRAN 2008 molecular spectroscopic database,” J. Quantum Spectrosc. Radiat. Transfer 110(9–10), 533–572 (2009). [CrossRef]
  7. H. M. Pickett, R. L. Poynter, E. A. Cohen, M. L. Delitsky, J. C. Pearson, 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/ .
  8. 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]
  9. M. A. Koshelev, E. A. Serov, V. V. Parshin, 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]
  10. M. Y. Tretyakov, A. F. Krupnov, M. A. Koshelev, D. S. Makarov, E. A. Serov, 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]
  11. T. Kuhn, A. Bauer, M. Godon, S. Buhler, K. Kunzi, “Water vapor continuum: absorption measurements at 350GHz and model calculations,” J. Quantum Spectrosc. Radiat. Transfer 74(5), 545–562 (2002). [CrossRef]
  12. V. B. Podobedov, D. F. Plusquellic, K. E. Siegrist, G. T. Fraser, Q. Ma, 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]
  13. D. M. Slocum, E. J. Slingerland, R. H. Giles, T. M. Goyette, “Atmospheric absorption of terahertz radiation and water vapor continuum effects,” J. Quantum Spectrosc. Radiat. Transfer 127, 49–63 (2013). [CrossRef]
  14. P. W. Rosenkranz, “Water vapor microwave continuum absorption: a comparison of measurements and models,” Radio Sci. 33(4), 919–928 (1998). [CrossRef]
  15. J. H. Van Vleck, V. F. Weisskopf, “On the shape of collision-broadened lines,” Rev. Mod. Phys. 17(2–3), 227–236 (1945). [CrossRef]
  16. C. H. Townes and A. L. Schawlow, Microwave Spectroscopy (Dover, 1975).
  17. Y. Yang, M. Mandehgar, D. Grischkowsky, “Broad-band THz pulse transmission through the atmosphere,” IEEE Trans. THz Sci. Technol. 1(1), 264–273 (2011).
  18. D. Grischkowsky, S. Keiding, M. van Exter, 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]
  19. Y. Yang, A. Shutler, D. Grischkowsky, “Measurement of the transmission of the atmosphere from 0.2 to 2 THz,” Opt. Express 19(9), 8830–8838 (2011). [CrossRef] [PubMed]
  20. Y. Yang, M. Mandehgar, D. Grischkowsky, “Time domain measurement of the THz refractivity of water vapor,” Opt. Express 20(24), 26208–26218 (2012). [CrossRef] [PubMed]
  21. H. Harde, N. Katzenellenbogen, D. Grischkowsky, “Line-shape transition of collision broadened lines,” Phys. Rev. Lett. 74(8), 1307–1310 (1995). [CrossRef] [PubMed]
  22. H. Harde, R. A. Cheville, D. Grischkowsky, “Terahertz studies of collision broadened rotational lines,” J. Phys. Chem. A 101(20), 3646–3660 (1997). [CrossRef]
  23. D. Grischkowsky, Y. Yang, 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]
  24. M. Mandehgar, Y. Yang, D. Grischkowsky, “Atmosphere characterization for simulation of the two optimal wireless terahertz digital communication links,” Opt. Lett. 38(17), 3437–3440 (2013). [CrossRef] [PubMed]
  25. 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.
  26. J. H. van Vleck, “The absorption of microwaves by oxygen,” Phys. Rev. 71(7), 413–424 (1947). [CrossRef]

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