Enhancement of spectral resolution andaccuracy in asynchronous-optical-sampling
terahertz time-domain spectroscopy for lowpressure gas-phase analysis
Takeshi Yasui,1,2,* Kohji Kawamoto,1 Yi-Da Hsieh,1 Yoshiyuki Sakaguchi,1 Mukesh
Jewariya,2 Hajime Inaba,3 Kaoru Minoshima,3 Francis Hindle,4 and Tsutomu Araki1
1

2

Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531,
Japan
Institute of Technology and Science, The University of Tokushima, 2-1 Minami-Josanjima, Tokushima, Tokushima
770-8506, Japan
3
National Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology, 1-1-1
Umezono, Tsukuba, Ibaraki 305-8563, Japan
4
Laboratoire de Physico-Chimie de l'Atmosphère, Université du Littoral Côte d'Opale, 189A Av. Maurice
Schumann, Dunkerque 59140, France*
yasui@me.tokushima-u.ac.jp

Abstract: The spectral resolution and accuracy of asynchronous-opticalsampling terahertz time-domain spectroscopy (ASOPS-THz-TDS) were
evaluated by examining low-pressure gas-phase samples. Use of dual 56MHz, erbium (Er)-doped, mode-locked femtosecond fiber lasers enhanced
the spectral resolution to as low as 50.5 MHz and the spectral accuracy to as
low as 6.2 × 10−6. The results indicate that ASOPS-THz-TDS has thepotential to achieve high spectral resolution, high spectral accuracy, andwide spectral coverage at the same time. ASOPS-THz-TDS will open a newdoor to gas-phase spectroscopy of multiple chemical species in the field of
atmospheric gas analysis.
©2012 Optical Society of America
OCIS codes: (120.6200) Spectrometers and spectroscopic instrumentation; (300.6320)
Spectroscopy, high-resolution; (300.6495) Spectroscopy, terahertz.

References and links
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1. Introduction
Recently, terahertz (THz) spectroscopy has emerged as a new mode for sensing and material
characterization. One interesting application of THz spectroscopy is in the analysis of
atmospheric molecular gases, because their rotational transitions give them particularly rich
spectral fingerprints in the THz region. Measuring these densely distributed absorption lines
correctly in THz spectroscopy requires high spectral resolution, high spectral accuracy, andbroad spectral coverage. THz time-domain spectroscopy (THz-TDS) with pulsed THz
radiation is a popular spectroscopic technique for obtaining a broadband THz spectrum [1, 2].
In this method, the frequency scale of the THz spectrum is established by mechanical timedelay scanning with a motor-driven translation stage. Therefore, the spectral resolution isdetermined by the reciprocal of the time window of the observed THz temporal waveform,
whereas the spectral accuracy depends on the positioning precision of the translation stage
used for time-delay scanning. However, limited stroke length and poor positioning precisionof usual stepping-motor-driven translation stages are barriers to achieving high spectral
resolution and accuracy in this method. Although the positioning accuracy can be improved
largely by monitoring the stage translation with interferometer, it is still difficult to extend thestroke length largely due to the spot size variation of the laser light and/or the issue of a tradeoff between the scanning range and scanning rate. On the other hand, THz spectroscopy witha tunable, narrow-linewidth, continuous-wave THz wave, namely CW-THz spectroscopy, is apromising spectroscopic technique for achieving high spectral resolution [3, 4]. However, theaccuracy of the frequency scale in this method depends on the performance of an opticalwavemeter employed for measuring the wavelengths of two CW near-infrared lasers used forphotomixing. Although the spectral accuracy can be improved by phase-locking the two CW
lasers to a single optical frequency comb [5], the spectral range of continuous tuning coveredin this method is usually narrower than that in THz-TDS.
One potential method to simultaneously achieve high spectral resolution, high spectral
accuracy, and broad spectral coverage in THz spectroscopy is asynchronous-optical-sampling
THz-TDS (ASOPS-THz-TDS) using two mode-locked lasers with slightly mismatched modelocked frequencies (mode-locked frequency = f1 and f2, offset frequency = ∆f = f2 - f1) for
generation and detection of the pulsed THz radiation [6, 7]. Since ASOPS-THz-TDS helps torealize a time delay much longer than that achievable with a motor-driven translation stage inconventional THz-TDS, it has the potential to achieve high spectral resolution with broad
spectral coverage. For example, when the measurement time window of the pulsed THz
radiation is extended to one pulse period, the spectral resolution can be enhanced to the modelocked frequency f1. In this case, the frequency scale of the spectrum is determined on thebasis of the measurement time scale and a temporal magnification factor of f1/∆f [7].
However, the actual stability of f1 and ∆f may cause fluctuations in the temporal
magnification factor, and hence influence the spectral resolution and accuracy. Although f1
and/or ∆f can be stabilized by referencing to a reference signal synthesized from a microwave
frequency standard, the residual fluctuation will ultimately limit the performance of this#167717 - $15.00 USD(C) 2012 OSA

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technique. Therefore, the actual spectral resolution and accuracy achieved by ASOPS-THzTDS should be evaluated using a standard material, for example, the absorption lines of amolecular gas with a narrow linewidth. Spectral resolution and accuracy in an ASOPS-THzTDS system equipped with ∆f-stabilized, dual 1-GHz Ti:Sapphire lasers (f1 = 1,000,000,000
Hz, f2 = 1,000,002,000 Hz, and ∆f = 2 kHz) were evaluated using molecular gasses at
atmospheric pressure, resulting in the resolution of 1 GHz and accuracy of 5.7 × 105 [8].
Further enhanced performance will be required to increase the ability to identify spectral
fingerprints and expand the selectivity of target gas molecules, for example, analysis ofmultiple chemical species in gas-phase spectroscopy under low pressure [9, 10]. In the work
reported in this paper, we enhanced the spectral resolution and accuracy in ASOPS-THz-TDS
by use of dual 56-MHz, f1-f2-∆f-stabilized, erbium (Er)-doped, mode-locked fiber lasers [11].
2. Experimental setup
Figure 1 shows a schematic diagram of the experimental setup in our fiber-laser-based
ASOPS-THz-TDS system. A pair of self-starting, stretched-pulse, mode-locked, Er-doped
fiber lasers (λc = 1550 nm, ∆t = 50 fs, PAVG = 110 mW, f1 ≈f2 ≈56.1 MHz) [12] was used togenerate and detect the pulsed THz radiation. The 20th-harmonic components of the modelocked frequency (20f1 and 20f2) were extracted from two signals detected with two fast
photodetectors (PDs, bandwidth = 1.2 GHz) through electronic heterodyned processes that
employ two frequency synthesizers (FS1, output freq. = fFS1 = 1,112,480,000 Hz; FS2, output
freq. = fFS2 = 1,112,480,100 Hz) phase-locked to a rubidium frequency standard (Rb-FS,
accuracy = 5 × 10−11 and instability = 2 × 10−11 at 1 s), two double-balanced mixers (DBMs),
and two low-pass filters (LPFs). The resulting beat signals (freq. = 20f1 – fFS1 and 20f2 – fFS2)
were used to generate the final error signals (freq. = 20f1 – fFS1 - fRb and 20f2 – fFS2 - fRb) bymixing with output signals from Rb-FS (output freq. = fRb = 10 MHz). Finally, based on theseerror signal, the cavity length in fiber lasers was adjusted with piezoelectric actuators (quick,fine, and narrow control) and Peltier heaters (slow, coarse, and wide control) throughproportional and integral control systems (PIs) so that 20f1 – fFS1 - fRb = 0 and 20f2 – fFS2 - fRb =0, or 20f1 = fFS1 + fRb and 20f2 = fFS2 + fRb. In this way, the individual mode-locked frequenciesof the two lasers (f1 = 56,124,000 Hz and f2 = 56,124,005 Hz), and thus the frequency offset
between them (∆f = f2 – f1 = 5 Hz), were stabilized by two independent laser control systems.
After wavelength conversion of the two laser beams with second-harmonic-generation
crystals (SHGs), pulsed THz radiation was emitted by a dipole-shaped, low-temperaturegrown, GaAs photoconductive antenna triggered by pump light (PCA1), and was thendetected by another dipole-shaped LT-GaAs-PCA triggered by probe light (PCA2). Portionsof the output light from the two lasers were fed into a sum-frequency-generation crosscorrelator (SFG-XC). The resulting SFG signal was used to generate a time origin signal in
the ASOPS-THz-TDS. The temporal waveform of the pulsed THz radiation was measured
with a digitizer (sampling frequency = 500 kHz) by using the SFG-XC signal as a trigger
signal after amplification with a current preamplifier (AMP, bandwidth = 100 kHz, gain = 5 ×
107 V/A). The time window of the measured temporal waveform was set equal to one pulse
period in order to achieve a spectral resolution equal to the mode-locked frequency. To avoid
pressure broadening of absorption lines, molecular gasses were enclosed in a low-pressure
gas cell (length = 380 mm, diameter = 17 mm) with a pair of Brewster windows made ofpolypropylene plates. The optical path in which the THz beam propagated, except for the gas
cell, was purged with dry nitrogen gas to avoid absorption by atmospheric moisture. Finally,
the absorption spectrum was obtained by using a zero-filling factor of 10, fast Fouriertransformation, and normalization with a reference spectrum obtained under identicalconditions.

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Fig. 1. Experimental setup. FS1 and FS2, frequency synthesizers; Rb-FS, rubidium frequency
standard; DBMs, double-balanced mixers; LPFs, low-pass filters; PD, photodetectors; PIs,
proportional and integral control systems; SFG-XC, sum-frequency-generation crosscorrelator; SHGs, second-harmonic-generation crystals; Ls, lenses; PCA1, photoconductive
antenna for THz generation; PCA2, photoconductive antenna for THz detector; Si-Ls, siliconlenses; AMP, current preamplifier.

3. Results
3.1 Evaluation of spectral resolution using low-pressure water vapor
To evaluate the spectral resolution, we measured the absorption spectrum of the rotationaltransition 110 ←101 at 0.557 THz in water vapor. To decrease the strong absorption of water
vapor, we diluted the water vapor with a foreign gas (dry argon gas). Figure 2(a) shows theabsorption spectrum of the 0.557 THz water line at a total pressure of 1 kPa. In usual, signal
integration of numerous scans is required in ASOPS-THz-TDS due to the fact that a lock-in
amplifier cannot be used. In the present system, signal averaging of 5,000-sweep sequences
under the low scan rate ( = ∆f = 5Hz) resulted in the required time of 1,000 s. If the scan rateis increased by use of a fast current preamplifier or free-space electro-optic sampling
equipped with a fast photodetector, the data acquisition time will be decreased. The spectral
linewidth was determined to be 50.5 MHz when a Lorentzian function was fitted to thespectral shape, indicated by the solid line in Fig. 2(a), which was reasonably consistent withthe mode-locked frequency of 56.1 MHz. The reason for the negative absorption coefficient ismainly due to the system instability of THz spectral amplitude in the acquisition time.
Next, we investigated pressure broadening of the same water line when the total pressure
was increased. Figure 2(b) shows the half-width at half-maximum (HWHM) of the observed
absorption line as a function of the total pressure, which was varied between 1 kPa and 50
kPa. The linear relationship without saturation indicated that the slope gives the pressure
broadening parameter of this mixed gas sample without any influence of the instrumentation
linewidth or the Doppler linewidth. We determined the broadening parameter to be 31.7
MHz/kPa ( = 3.17 MHz/mbar) with a fitting error R of 0.99955, by performing a linear
approximation to y = αx, indicated by the solid line in Fig. 2(b), where y is the HWHM, α is#167717 - $15.00 USD(C) 2012 OSA

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the pressure broadening parameter, and x is the total pressure. Considering the obtained
parameter, the self-broadening coefficient of water ( = 13.8 MHz/mbar), the collisionbroadening coefficient of argon ( = 1.63 MHz/mbar), and the total pressure, the mixture ratioof water vapor to the argon gas was estimated to 10.4% in this experiment. From theseexperiments, we can conclude that our ASOPS-THz-TDS system has the potential to performa spectral resolution comparable to the mode-locked frequency in low-pressure gas-phase
spectroscopy.

Fig. 2. (a) Water absorption spectrum of rotational transition 110-101 at 0.557 THz (totalpressure = 1 kPa) and (b) pressure broadening of 0.557 THz water line as a function of totalpressure.

3.2 Evaluation of spectral accuracy using low-pressure acetonitrile gas
To evaluate the spectral accuracy and demonstrate the capacity to simultaneously probe
multiple absorption lines, we performed gas-phase spectroscopy of acetonitrile (CH3CN). As
CH3CN is a symmetric top molecule, the frequencies of absorption lines caused by its
rotational transition are given byν = 2B ( J + 1) − 2D JK K 2 ( J + 1)

(1)

where B is the rotational constant, J and K are rotational quantum numbers, and DJK is thecentrifugal distortion constant. Since CH3CN has a B value of 9.2 GHz [13], a manifold ofrotational transitions regularly spaced by 2B ( = 18.4 GHz) is expected from the first term in
Eq. (1). Furthermore, from the second term in Eq. (1), each absorption line composing the
manifold has hyperfine structure determined by DJK. Conventionally, the manifold of therotational transitions and the hyperfine structure have been separately measured by using
broadband THz-TDS [2] and a high-resolution CW-THz spectrometer [4]. Here, on the other
hand, we evaluated the possibility that the ASOPS-THz-TDS system allows us to observeboth features solely due to wide dynamic range of the frequency scale.
Figure 3(a) shows an amplitude spectrum of pulsed THz radiation after passing though agas cell filled with CH3CN at 40 Pa, in which the manifold of the regularly spaced rotationaltransitions was clearly found within a frequency range from 0.3 to 0.9 THz in Fig. 3(a). To
observe the detailed structure of the manifold, we calculated the absorption spectrum around0.65 THz, as shown in Fig. 3(b). The six observed absorption lines had a mutual frequency
spacing of 18.4 GHz, in good agreement with the value reported in the literature [2]. We
expanded the range to observe hyperfine structure of the J = 35 to J = 34 transition around0.64 THz and assigned lines K = 3 to 10, as shown in Fig. 3(c). To determine the center
frequencies of these absorption lines, we performed multi-peak fitting analysis using a
Lorentzian function, indicated by the black solid line in Fig. 3(c). Table 1 summarizes theresults for the absorption lines, showing a comparison between experimental values andvalues reported in JPL database [14], and the frequency discrepancy between them. The mean

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and standard deviation of the discrepancy for the eight assigned absorption lines were 4 MHz
and 3 MHz, respectively. When spectral accuracy is defined as the ratio of the frequency
discrepancy to the value reported in the literature, the mean spectral accuracy was 6.2 × 10−6in this experiment.
Accuracy of the absorption strength is also important to make the reliable quantitative
analysis in gas-phase spectroscopy under low pressure. To evaluate the quality of the obtained
spectrum, one should compare the obtained spectrum with that calculated from spectral
database. However, HITRAN database is not possible as this database presently only has
CH3CN at wavenumbers from 890 - 946 cm−1 [15]. Although JPL database gives integrated
intensities of each absorption line in this molecule [14], it is impossible to make thecalculation of the complete spectrum, as there are no values for the broadening coefficients.
Here, we made a simple comparison of our spectrum with the integrated intensities in JPL
database, indicated as red lines in Fig. 3(c). The relative variation between neighboring lines
is reasonably well reproduced and is limited by the signal-to-noise ratio of the measurements
and the accuracy of the line strength calculations included in the database.

Fig. 3. (a) Amplitude spectrum of pulsed THz radiation after passing though a gas cell filledwith CH3CN at 40 Pa, (b) absorption spectrum of CH3CN between 0.6 and 0.7 THz, and (c)expanded absorption spectrum around 0.65 THz.

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Table 1. Comparison of CH3CN absorption line positions as reported in the literature[14] and obtained using ASOPS-THz-TDS in this work.
J

K

35-34

10
9
8
7
6
5
4
3
2
1
0

Literature value
Experimental value
(THz)
(THz)
0.642 049 478 7
0.642 046
0.642 280 721 6
0.642 281
0.642 487 872 7
0.642 483
0.642 670 849 7
0.642 673
0.642 829 579 3
0.642 825
0.642 963 997 8
0.642 974
0.643 074 051 00.643 075
0.643 159 694 2
0.643 156
0.643 220 892 8
Not assigned
0.643 257 622 0
Not assigned
0.643 269 866 7
Not assigned(Mean) ± (standard deviation)

Discrepancy
(MHz)
4
0
5
3
5
10
1
4
4±3

4. Discussions
We first discuss the bandwidth limitation of the present ASOPS-THz-TDS system. The
spectral bandwidth observed in Fig. 3(a) was smaller than that of the previous ASOPS-THzTDS system equipped with dual 1-GHz lasers (typically, 6 THz) [8]. We consider that thedifference of spectral bandwidth between them is caused by that of the time resolution
between them, rather than the pulse duration, bandwidth of the photoconductive antenna, or
timing jitter between dual lasers. From the calculation of the bandwidth limitation [16] using
the specifications of our system (electric bandwidth of current preamplifier = 100 kHz, f1 =56,124,000 Hz, and ∆f = 5 Hz), a time resolution of the present system is estimated to be 0.89
ps. This resolution leads to the available bandwidth of 1.2 THz, which is reasonably
consistent with the spectral bandwidth in Fig. 3(a). To extend the spectral bandwidth, it isrequired to increase electric bandwidth and/or ∆f while keeping the good stability of thetemporal magnification factor of f1/∆f.
It will be also interesting to compare our f1-f2-∆f-stabilized, 56-MHz ASOPS-THz-TDS
system with the previous ∆f-stabilized, 1-GHz ASOPS-THz-TDS system from the viewpointof the spectral resolution. One important factor to limit the actual resolution in ASOPS-THzTDS is the accumulated timing jitter per time increment at the end of the sample interval [16].
This is because such the timing jitter fluctuates the size of the time-delay window and hence
the spectral resolution. We estimated from the accumulated timing jitter of 300 fs [11] and thepulse period of 17.8 ns in our system that the contribution of the timing jitter to the spectral
resolution was 0.9 kHz. On the other hand, the jitter contribution in the previous system wasestimated to be 0.2 MHz to the spectral resolution [8]. Although the jitter contribution to thespectral resolution in our system is much smaller than that in the previous system, bothcontributions are negligible to the actual spectral resolution. Therefore, we can conclude thatsimultaneous stabilization of f1, f2, and ∆f in our system does not make much sense at thepresent time. However, if the spectral resolution in ASOPS-THz-TDS can go down below 1
MHz, one may have to consider the jitter contribution caused by unstabilized f1 and f2. Further
work is in progress to enhance the spectral resolution of ASOPS-THz-TDS.
Finally, we discussed the spectral accuracy in ASOPS-THz-TDS. The accuracy in oursystem was 10-times better than that obtained with the previous ASOPS-THz-TDS system[8]. One reason for the improved accuracy is that the frequency resolution is greatly enhanced
by use of a lower mode-locked frequency rather than simultaneous stabilization of f1, f2, and∆f as discussed above. Also, the accuracy of the temporal magnification factor (f1/∆f) will

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limit the useful accuracy to around 10−6. Another factor to limit the spectral accuracy isexistence of fluctuated background in the spectrum as observed in Fig. 2(a) although thebackground should be zero line to obtain the good fitting result to the experimental data.
Fitting error caused by the fluctuated background also influences the spectral accuracy. The
present results are therefore within the experimental uncertainty when compared with thetabulated values.
5. Conclusion
ASOPS-THz-TDS system, equipped with dual 56-MHz fiber lasers, achieved a spectral
resolution of 50.5 MHz and a frequency accuracy of 6.2 × 10−6 over a spectral range of 0-2
THz. The achieved resolution and accuracy were respectively 20-times and 10-times better
than those obtained with the previous ASOPS-THz-TDS system equipped with dual 1-GHz
Ti:Sapphire lasers [8]. The results clearly indicate the superior performance of this system forgas-phase spectroscopy of multiple chemical species under low pressure. Finally, it should beemphasized that the frequency scale of THz spectrum established in our ASOPS-THz-TDS is
traceable to Rb-ST within 6.2 × 10−6 by stabilizing f1 and ∆f. An assured traceability of thefrequency scale to the frequency standard is a big advantage of this method over conventionalTHz spectroscopic methods without any traceability system, and hence opens the door forestablishment of frequency metrology in THz spectroscopy.
Acknowledgments
This work was supported by Collaborative Research Based on Industrial Demand from theJapan Science and Technology Agency, and Grants-in-Aid for Scientific Research 21360039
and 23656265 from the Ministry of Education, Culture, Sports, Science, and Technology ofJapan. We also gratefully acknowledge financial support from the Renovation Center ofInstruments for Science Education and Technology at Osaka University. We are grateful to
Dr. Hiromichi Hoshina of RIKEN for fruitful discussions.

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