Terahertz Frequency-Domain Spectroscopyof Low-Pressure Acetonitrile Gas bya Photomixing Terahertz Synthesizer
Referenced to Dual Optical Frequency
Combs
Yi-Da Hsieh, Hiroto Kimura, Kenta
Hayashi, Takeo Minamikawa, Yasuhiro
Mizutani, Hirotsugu Yamamoto, Tetsuo
Iwata, Hajime Inaba, et al.
Journal of Infrared, Millimeter, andTerahertz Waves
ISSN 1866-6892
Volume 37
Number 9
J Infrared Milli Terahz Waves (2016)
37:903-915
DOI 10.1007/s10762-016-0277-6

1 23

Your article is protected by copyright and allrights are held exclusively by Springer Science+Business Media New York. This e-offprint isfor personal use only and shall not be selfarchived in electronic repositories. If you wish
to self-archive your article, please use theaccepted manuscript version for posting on
your own website. You may further deposit
the accepted manuscript version in any
repository, provided it is only made publicly
available 12 months after official publicationor later and provided acknowledgement isgiven to the original source of publication
and a link is inserted to the published article
on Springer's website. The link must be
accompanied by the following text: "The final
publication is available at link.springer.com”.

1 23

Author's personal copy
J Infrared Milli Terahz Waves (2016) 37:903–915
DOI 10.1007/s10762-016-0277-6

Terahertz Frequency-Domain Spectroscopyof Low-Pressure Acetonitrile Gas by a Photomixing
Terahertz Synthesizer Referenced to Dual Optical
Frequency Combs
Yi-Da Hsieh 1,2 & Hiroto Kimura 3 & Kenta Hayashi 3 &Takeo Minamikawa 1,2 & Yasuhiro Mizutani 2,4 &Hirotsugu Yamamoto 2,5 & Tetsuo Iwata 1,2 & Hajime Inaba 2,6 &Kaoru Minoshima 2,7 & Francis Hindle 8 & Takeshi Yasui 1,2

Received: 7 January 2016 / Accepted: 19 April 2016 /Published online: 2 May 2016
# Springer Science+Business Media New York 2016

Abstract A terahertz (THz) frequency synthesizer based on photomixing of two near-infraredlasers with a sub-THz to THz frequency offset is a powerful tool for spectroscopy of polar gas
molecules due to its broad spectral coverage; however, its frequency accuracy and resolution are
relatively low. To tune the output frequency continuously and widely while maintaining its
traceability to a frequency standard, we developed a photomixing THz synthesizer phase-locked
to dual optical frequency combs (OFCs). While the phase-locking to dual OFCs ensured continuous* Takeshi Yasui
yasui.takeshi@tokushima-u.ac.jp

1

Graduate School of Science and Technology, Tokushima University, 2-1, Minami-Josanjima,
Tokushima 770-8506, Japan

2

JST, ERATO, MINOSHIMA Intelligent Optical Synthesizer Project, 2-1, Minami-Josanjima,
Tokushima 770-8506, Japan

3

Graduate School of Advanced Technology and Science, Tokushima University, 2-1,
Minami-Josanjima, Tokushima 770-8506, Japan

4

Graduate School of Engineering, Osaka University, 2-1, Yamadaoka, Suita, Osaka 565-0871, Japan

5

Center for Optical Research and Education, Utsunomiya University, 7-1-2, Yoto, Utsunomiya,Tochigi 321-858, Japan

6

National Metrology Institute of Japan, National Institute of Advanced Industrial Science andTechnology, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8563, Japan

7

Graduate School of Informatics and Engineering, The University of Electro-Communications, 1-5-1,
Chofugaoka, Chofu, Tokyo 182-8585, Japan

8

Laboratoire de Physico-Chimie de l’Atmosphère, Université du Littoral Côte d’Opale, 189A Av.
Maurice Schumann, 59140 Dunkerque, FranceAuthor's personal copy
904

J Infrared Milli Terahz Waves (2016) 37:903–915

tuning within a spectral range of 120 GHz, in addition to the traceability to the frequency standard,
use of a broadband uni-traveling carrier photodiode for photomixing enabled the generation of CWTHz radiation within a frequency range from 0.2 to 1.5 THz. We demonstrated THz frequencydomain spectroscopy of gas-phase acetonitrile CH3CN and its isotope CH313CN in the frequency
range of 0.600–0.720 THz using this THz synthesizer. Their rotational transitions were assignedwith a frequency accuracy of 8.42 × 10−8 and a frequency resolution of 520 kHz. Furthermore, theconcentration of the CH3CN gas at 20 Pa was determined to be (5.41 ± 0.05) × 1014 molecules/cm3
by curve fitting analysis of the measured absorbance spectrum, and the mixture ratio of the mixed
CH3CN/CH313CN gas was determined to be 1:2.26 with a gas concentration of 1014–1015 molecules/cm3. The developed THz synthesizer is highly promising for high-precision THz-FDS of lowpressure molecular gases and will enable the qualitative and quantitative analyses of multiple gases.
Keywords Terahertz . Optical frequency comb . Photomixing . Synthesizer . Spectroscopy . Gas
analysis . Rotational transition

1 Introduction
Gas analysis is one of the typical applications of optical spectroscopy. Up to now, infrared
spectroscopy, which can observe vibrational transitions of gas molecules, has been widely used
for this purpose [1]. However, when the gas molecule is composed of many atoms, the number ofvibrational transitions increases considerably. Also, when the target gas molecule is mixed with other
different gas molecules, the observed spectrum becomes more complicated. In these cases, it isdifficult to identify the gas molecule from a single vibrational transition. Therefore, gas molecules
have to be identified by referencing multiple vibrational transitions. Furthermore, we have toconsider the influence of pressure broadening (typically, MHz to GHz order, depending on thegas pressure) and Doppler broadening (typically, a few to a few tens of GHz) on the absorption
spectrum. Although pressure broadening can be suppressed by reducing the gas pressure, Doppler
broadening still remains and causes adjacent absorption lines to be superimposed, making it difficult
to discriminate them. To avoid Doppler broadening, we have to use complicated optical configurations for Doppler-free spectroscopy [2, 3], which decreases the practicability of gas analysis. On
the other hand, from the viewpoint of practical applications, when the target gas is mixed with
undesired aerosols (smoke, soot, dust, mist, fog, haze, fumes, and so on), optical scattering by theseaerosols degrades the performance of infrared spectroscopy.
Recently, terahertz (THz) radiation (frequency = 0.1–10 THz, wavelength = 30–3000 μm)
has attracted attention for optical gas analysis [4]. Many rotational transitions of polar gas
molecules appear as spectral fingerprints in the THz region. The contribution of far more
atoms to the rotational transition makes the absorption spectrum in the THz region simpler
than that in the infrared region, leading to higher selectivity of the target gas molecule. For
example, it is possible to assign the target molecule in a gas sample mixed with other different
gas molecules using only a single rotational transition. More interestingly, Doppler broadening
in the THz region (typically, a few MHz) is much smaller than that in the infrared region
because it is proportional to the optical frequency of the probing radiation. Therefore, higher
molecular discrimination of the target gas can be achieved at low pressure without the need forcomplicated Doppler-free spectroscopy configurations. In addition, from the relationshipbetween the wavelength of THz radiation and the size of aerosols, there is less susceptibility
to optical scattering by aerosols compared with infrared spectroscopy [5, 6].

Author's personal copy
J Infrared Milli Terahz Waves (2016) 37:903–915

905

The THz spectral fingerprints of gas molecules are concentrated below 3 THz, and theabsorption linewidth is on the order of a few GHz at atmospheric pressure and on the order ofseveral MHz at low pressure. Observing such THz spectral features in detail requires a spectral
coverage of more than 1 THz, a spectral resolution of less than 1 MHz, and a spectral accuracyof 10−6. A tunable narrow-linewidth CW-THz generator, namely, a THz frequency synthesizer,
is a powerful tool for achieving precise THz frequency-domain spectroscopy (THz-FDS) ofgas molecules. So far, there have been THz synthesizers based on electrical approaches [4, 7,
8] and optical approaches [9, 10].
In the former approaches, frequency-multiplied microwave sources (FMMS) [7, 8] enable
fast sweeping of high-brightness CW-THz radiation. The generated CW-THz radiation istraceable to a microwave or radio-frequency (RF) standard via frequency synthesizing andmultiplication, and its linewidth is below 1 Hz. However, the output power of this method
decreases as the frequency becomes higher. Furthermore, the tuning range of a single FMMS isusually limited to within 10 to 20 % of the center frequency. THz-FDS using a backward wave
oscillator (BWO) [4], also called the fast-scan submillimeter spectroscopy technique(FASSST), can extend the frequency coverage while maintaining similar resolution; however,its frequency accuracy is limited by the performance of the Fabry-Perot cavity used for
frequency monitoring of the BWO. Furthermore, in these methods, it is difficult to fully cover
the frequency range from 0.1 THz to a few THz at once due to the limited tuning range.
Therefore, it is necessary to select suitable FMMS or BWO tubes depending on the frequency
band used.
On the other hand, an optical THz synthesizer is realized by photomixing two near-infrared(NIR) CW lasers with an optical frequency difference of sub-THz to THz order [9, 10]. If CWNIR lasers with tunable optical frequency and fixed optical frequency are used forphotomixing, the frequency of the CW-THz radiation can be tuned over a range of 1 THz.
However, since photomixing THz synthesizers often use free-running CW-NIR lasers, thefrequency accuracy and stability of CW-THz radiation are relatively low. Thus, the performance of conventional THz synthesizers has been insufficient for high-precision THz-FDS of
multiple gas molecules.
Recently, optical frequency combs (OFCs) have appeared as a new optical frequency
reference traceable to a frequency standard [11]. An OFC can be used as a frequency ruler
in optical frequency regions by phase-locking the laser repetition rate, frep, and carrierenvelope-offset frequency, fceo, to the frequency standard. Therefore, if two CW-NIR lasers
for photomixing are phase-locked to an OFC, it is possible to achieve high frequency accuracy
and high stability. A combination of the photomixing technique and an OFC can realize a THz
synthesizer traceable to the frequency standard. For example, single-OFC-based photomixing
THz synthesizers have been achieved by phase-locking two CW-NIR lasers to different modesin the same OFC and photomixing them [12–14]. Continuous tuning of the CW-THz radiation
was demonstrated by changing frep while phase-locking the two CW-NIR lasers to an OFC.
However, the frequency range of the continuous tuning was limited to a few hundred MHz at
most because the optical frequencies in the two phase-locked CW-NIR lasers simultaneously
change, and most of the optical frequency changes are canceled due to the common-mode
behavior, like an accordion. If the optical frequency of only one CW-NIR laser is tuned whilethat of the other is fixed based on the OFC, the continuous tuning range would be greatly
increased.
In order to further expand the continuous tuning range while maintaining the traceability to
the frequency standard, dual-OFC-based photomixing THz synthesizers have been proposed

Author's personal copy
906

J Infrared Milli Terahz Waves (2016) 37:903–915[15, 16]. A beam of CW-NIR laser light, phase-locked to an frep-fixed OFC, was photomixed
with another beam of CW-NIR laser light, phase-locked to another frep-tunable OFC, by a unitraveling carrier photodiode (UTC-PD) in the F-band (freq. = 90–140 GHz). The continuous
frequency tuning range could be expanded up to the bandwidth of the F-band UTC-PD.
Unfortunately, since rotational transitions of the polar gas molecules are not so rich in the Fband, there have been no attempts to employ this dual-OFC-based photomixing THz synthesizer for THz spectroscopy of low-pressure gas molecules.
In the work described in this article, we constructed a dual-OFC-based photomixing THz
synthesizer continuously tunable over 120 GHz by using a broadband UTC-PD (freq. = 0.2–
1.5 THz). The constructed THz synthesizer was applied to THz-FDS of low-pressure acetonitrile gas in a frequency range from 0.600 to 0.720 THz to demonstrate the high potential ofthis technique for gas analysis. After assigning multiple rotational transitions, we determinedthe concentration of acetonitrile gas by applying curve fitting analysis to the measured
absorbance spectrum. Furthermore, we also determined the concentration and the mixture
ratio of a mixed gas of acetonitrile and its isotope.

2 Materials and Methods
2.1 Experimental Setup
The principle of operation of the dual-OFC-referenced photomixing THz synthesizer has been
described in detail elsewhere [15, 16]. A key component here is an optical frequency synthesizer(OFS) [17]. An OFS is a CW-NIR laser phase-locked to an OFC, and its optical frequency, fofs, istraceable to a frequency standard via laser control. Furthermore, fofs can be continuously tuned bychanging frep while phase-locking the CW-NIR laser to the OFC. For the dual-OFC-referenced
photomixing THz synthesizer, two OFSs, namely, dual OFSs, were prepared, and these wererespectively used as an fofs-fixed OFS (OFS1; optical freq. = fofs1) and an fofs-tunable OFS (OFS2;
optical freq. = fofs2) for photomixing. The frequencies fofs1 and fofs2 were determined from thefollowing equations:f o f s1 ¼ f ceo1 þ m1 f rep1 þ f beat1

ð1Þ

f o f s2 ¼ f ceo2 þ m2 f rep2 þ f beat2 ;ð2Þ

where fceo1 and fceo2 are the carrier-envelope offset frequencies of the dual OFCs, m1 and m2
are the mode numbers of the dual OFCs to which the dual CW-NIR lasers are respectively
phase-locked, frep1 and frep2 are the repetition rates of the dual OFCs, and fbeat1 and fbeat2 are thebeat frequencies between the dual OFCs and the dual CW-NIR lasers.
As shown in the upper part of Fig. 1, the fofs-fixed OFS was composed of an frep-locked Erfiber OFC (OFC1; Menlo Systems, FC1500-250, center wavelength = 1550 nm, mean output
power = 40 mW, fceo1 = −20,000,000.000 Hz, frep1 = 250,000,000.00 Hz) and an extended
cavity laser diode (ECLD1; Redfern Integrated Optics, RIO PLANEX, center
wavelength = 1550 nm, mean output power = 10 mW, spectral linewidth = 15 kHz). ECLD1
was phase-locked to an optical frequency mode m1 (=773,099) of OFC1 with a frequency
offset fbeat1 (=30,000,000.000 Hz) by means of the current control. On the other hand, in theAuthor's personal copy
J Infrared Milli Terahz Waves (2016) 37:903–915

907

Fig. 1 Experimental setup. Rb-FS rubidium frequency standard, OFC1 and OFC2 mode-locked Er-fiber opticalfrequency combs, ECLD1 and ECLD2 extended cavity laser diodes, OFS1 and OFS2 optical frequency
synthesizers, λ/2 half-wave plate, λ/4 quarter-wave plate, EDFA erbium-dropped optical fiber amplifier, UTCPD uni-traveling-carrier photodiode for photomixing, L THz lenses, OC optical chopper

fofs-tunable OFS, another extended cavity laser diode (ECLD2; Optical Comb, Inc., LT-5001,
wavelength = 1500–1600 nm, mean output power = 20 mW, spectral linewidth = 500 kHz) was
phase-locked to an optical frequency mode m2 of the frep-tunable Er-fiber OFC (OFC2; Menlo
Systems, FC1500-250, center wavelength = 1550 nm, mean output power = 80 mW,
fceo2 = −20,000,000.000 Hz, frep2 = 250,000,000.00 Hz) with a frequency offset fbeat2(=30,000,000.000 Hz). frep2 could be tuned over a frequency range of 2 MHz. Therefore, fofs2
could be set to an arbitrary value by selection of m2 and/or by changing frep2. Since ECLD2
was equipped with a piezoelectric actuator (PZT) for tilting a diffraction grating for opticalfrequency tuning, fofs2 could be continuously tuned within a frequency range of 120 GHz bychanging frep2 while keeping m2 constant. Since the frequencies fceo1, fceo2, frep1, frep2, fbeat1, andfbeat2 were all phase-locked to a rubidium frequency standard (Rb-FS; FS725, Stanford
Research Systems, accuracy = 5 × 10−11 and instability = 2 × 10−11 at 1 s), fofs1 and fofs2 were
determined with a frequency uncertainty equal to that of Rb-FS based on Eqs. (1) and (2). An
optical wavemeter (Advantest Corp., Q8326) was used to determine m1 and m2. The fiber
outputs of the dual OFSs were combined with a fiber coupler and amplified by an erbiumdoped optical fiber amplifier (EDFA) after adjusting the polarization overlap with a half-wave
plate (λ/2) and a quarter-wave plate (λ/4).
The optical beat signal with a beat frequency fTHz (=fofs2 − fofs1) was generated from the two
output beams of OFS1 and OFS2 in a single-mode fiber and was delivered to the experimental
setup for THz-FDS of low-pressure gas molecules, as shown in the lower part of Fig. 1. To increase
fTHz and widen its tuning range, we used an antenna-integrated, broadband UTC-PD (NTTElectronics, frequency range = 0.2–1.5 THz) as a photomixer. We generated tunable CW-THz
radiation (nominal output power = 3 μW) within a frequency range from 0.600 to 0.720 THz. The
generated CW-THz radiation was fed into a low-pressure gas cell after passing through an opticalchopper (OC, chopping freq. = 50 Hz) and a collimating THz lens (Pax Co., Tsurupica, focal
length = 50 mm, diameter = 50 mm). The gas cell (length = 362 mm, diameter = 40 mm, pressure
range = 0.2 Pa to 101.3 kPa, pressure leakage = 0.98 Pa/h) was made of a cylindrical metal
enclosure and two white polyethylene windows. The CW-THz radiation passing through the gas

Author's personal copy908

J Infrared Milli Terahz Waves (2016) 37:903–915

cell was detected by a combination of a pyrometer (CDP Corp., PD-1) and a lock-in amplifier (NF
Corporation, LI5640, time constant = 100 ms). To obtain the THz power spectrum with an accuracy
and precision guaranteed by the frequency standard, frep2 was incrementally tuned while
performing frequency stabilization control. To be more specific, we (1) set the value in the frep2
control system, (2) shifted frep2 and stabilized it at the set value by referencing the frequency
standard, and then (3) measured a single data point in the spectrum with the lock-in amplifier. We
obtained the spectrum by repeating this procedure. Therefore, frep2 and hence fTHz were phaselocked to the frequency standard.
We performed broadband THz-FDS and high-precision THz-FDS of gas molecules.
For the broadband THz-FDS, we scanned fTHz from 0.600 to 0.720 THz incrementallyby changing fofs2 from 193,874,760.00 to 193,994,760.00 MHz at intervals of 5 MHz
while fofs1 was kept at 193,274,760.00 MHz. To this end, frep2 was changed from
250,000,000.00 to 250,154,739.00 Hz while maintaining m2 = 775,499. In this case,since the frequency interval of 5 MHz was larger than the linewidth of 520 kHz of
the CW-THz radiation, the effective spectral resolution was limited by the frequency
interval rather than the linewidth. Since the data acquisition time was 40 min for the
spectrum with a frequency span of 120 GHz, the scanning speed of the THz
synthesizer was 50 MHz/s. In the case of the high-precision THz-FDS, we finetuned fTHz within a frequency range of 200 or 140 MHz. Since the frequency
increment was set to 30.8 kHz, the spectral resolution was limited by the linewidthof the CW-THz radiation (=520 kHz). The scanning speed of the THz synthesizer was
0.3 MHz/s in this experiment.

2.2 Sample Gas
We selected gas-phase acetonitrile (CH3CN) as a sample gas to demonstrate the capability ofthe present THz-FDS system to simultaneously probe multiple absorption lines. CH3CN is an
important molecular gas in astronomic and atmospheric gas analyses because it is a very
abundant species in the interstellar medium and is also a volatile organic gas compound foundin the atmosphere. Since CH3CN is a symmetric-top molecule with a rotational constant, B, of
9.199 GHz and a centrifugal distortion constant, DJK, of 17.74 MHz [18], the frequencies ofrotational transitions are given byv ¼ 2Bð J þ 1Þ−2D J K K 2 ð J þ 1Þ

ð3Þ

where J and K are rotational quantum numbers. From this equation, the molecule displays two
characteristic features in its THz spectrum. The first term in Eq. (3) indicates that many
manifolds of absorption lines regularly spaced by 2B (=18.398 GHz) appear. The second term
indicates that each manifold includes a series of closely spaced absorption lines of decreasing
strength due to 2DJK. In this way, CH3CN gas indicates the widths of characteristic spectral
structures with both GHz and MHz orders.
In practical gas analysis, it is often necessary to determine the concentrations and the
mixture ratio of multiple gases. To investigate the potential of our approach in satisfying thisrequirement, we prepared an isotope of CH3CN (CH313CN, B = 9.194 GHz, DJK = 17.67 MHz)[18] and mixed it with CH3CN. Although these two gas molecules have similar symmetric-top
molecular structures, their B and DJK values are slightly different from each other. TheseAuthor's personal copy
J Infrared Milli Terahz Waves (2016) 37:903–915

909

slightly different spectral features should be discriminated at low pressure by high-precision
THz-FDS.

3 Results
3.1 Basic Performance
To evaluate the linewidth of an optical beat signal between OFS1 and OFS2, we generated an
optical beat signal with a frequency difference of 1 GHz. To achieve this, fofs1 and fofs2 were set
at 193,274,760.00 and 193,275,760.00 MHz (frep2 = 250,000,000.00 Hz, m2 = 773,103), respectively. The generated optical beat signal (freq. = fofs2 − fofs1 = 1 GHz) was detected with ahigh-speed photodetector (freq. bandwidth = 1.2 GHz). Figure 2a shows the RF spectrum of
the optical beat signal measured by an RF spectrum analyzer (Agillent E4402B,
RBW = 10 kHz). The RF spectral linewidth was determined to be 520 kHz by curve fitting
analysis with a Lorentzian function (see the blue line in Fig. 2a). Since the OFS1 and OFS2
had linewidths of 492 and 192 kHz, respectively (not shown), the measured linewidth wasreasonably consistent with the root-sum-square value of them (=528 kHz). We consider thatthe difference in linewidth between the free-running operation and the phase-locking operationin ECLD1 was mainly due to the insufficient feedback speed in the phase-locking control offbeat1. If faster feedback control could be employed for ECLD1, the linewidth of the phaselocked ECLD1, and hence the optical beat signal, would be further decreased.
Next, we evaluated the frequency stability of the optical beat frequency fofs2–fofs1 with an
RF frequency counter (Agillent 53230A). Figure 2b shows the frequency instability and thecorresponding frequency fluctuation of fofs2–fofs1 with respect to the gate time of the frequency
counter. As the gate time increased, the frequency fluctuation decreased. This indicates thatfofs2–fofs1 is phase-locked to the Rb-FS. Therefore, the proposed THz sythesizer is phasedlocked to the frequency standard.
One might query whether the linewidth and frequency instability of the beat signal at 1 GHz
is maintained when the frequency of the beat signal increases to the 600-GHz band. The
linewidth of the photomixing CW-THz radiation depends on the fluctuation of fofs2–fofs1 andthe convoluted linewidth of OFS1 and OFS2. Since fofs2–fofs1 was phase-locked to the Rb

Fig. 2 a RF spectrum of the optical beat signal at 1 GHz (RBW = 10 kHz). b Frequency instability and thecorresponding frequency fluctuation of the optical beat signal at 1 GHz with respect to the gate time of thefrequency counter

Author's personal copy
910

J Infrared Milli Terahz Waves (2016) 37:903–915

frequency standard with an instability of 2 × 10−11 at 1 s, its frequency fluctuation was
estimated to be 20 mHz for the 1-GHz beat (see Fig. 2b) and 12 Hz for the 600-GHz beat.
On the other hand, the convoluted linewidth was common to all beat frequencies. Since thefrequency fluctuation (=12 Hz) was much smaller than the convoluted linewidth (=520 kHz)of OFS1 and OFS2, the convoluted linewidth should be dominant in the linewidth of thephotomixing CW-THz radiation. In other words, the linewidth of the 1-GHz beat should be
identical to that of the 600-GHz beat regardless of the beat frequency. Although phase noise in
the UTC-PD may have increased the linewidth in the photomixing process, its influence isnegligible compared with the measured linewidth. On the other hand, the frequency stability of
the 1-GHz beat signal should be equal to that of the 600-GHz beat signal due to phase-lockingof fofs2–fofs1 to the Rb-FS. Therefore, the frequency stability and linewidth of the beat signal at
1 GHz should also be achieved in the THz region.
Finally, to estimate the frequency accuracy of this THz synthesizer, we considered thefrequency accuracy of OFS1 and OFS2. Since fofs1 and fofs2 were phase-locked to the Rb-FS
via laser control, their absolute frequency accuracy should be identical to that of the Rb-FS(=5 × 10−11). In this case, the frequency deviation in fofs1 and fofs2 from the true value wasestimated to be within 1 kHz. Since the root-sum-square value of them is 1.4 kHz, thefrequency accuracy of the CW-THz synthesizer is expected to be 2.3 × 10−9 at 0.6 THz. The
reason for the lower accuracy than that of the Rb-FS and the OFS is the cancelation ofsignificant digits due to the optical frequency difference in the photomixing process.

3.2 THz-FDS of Low-Pressure CH3CN Gas
To demonstrate the utility of the THz synthesizer in gas spectroscopy, we performed broadband THz spectroscopy of gas-phase CH3CN with unknown concentration in a gas cell. To
avoid pressure broadening and resolve the spectral features given in Eq. (3), we set thepressure of the CH3CN gas at 20 Pa. Figure 3a shows the transmittance spectrum of theCH3CN gas at 20 Pa within a frequency range from 600 to 720 GHz at a spectral resolution of
5 MHz. Seven periodic manifolds of rotational transitions were clearly confirmed with aconstant frequency spacing, which was exactly equal to 2B (=18.398 GHz) in Eq. (3). From acomparison with the literature values in the JPL database [19], we assigned them to J = 32 toFig. 3 a Broadband transmittance spectrum of CH3CH gas at 20 Pa (spectral range = 120 GHz, spectral
resolution = 5 MHz). b High-precision absorbance spectrum of CH 3 CH gas at 20 Pa (spectral
range = 200 MHz, spectral resolution = 520 kHz). The blue line indicates the curve fitting result with multiple
Lorentzian functions

Author's personal copy
J Infrared Milli Terahz Waves (2016) 37:903–915

911

J = 38, respectively (see the green text in Fig. 3a). Satellite manifolds appearing at the higher
frequency side of the main manifolds (see the green asterisks in Fig. 3a) were due to therotational transition of the vibrationally excited molecules. In this way, we confirmed that thewidths of the spectral structures with GHz order were characterized by the rotational constant
B in the first term of Eq. (3).
To confirm the spectral features of MHz order characterized by the centrifugal distortion
constant DJK in the second term of Eq. (3), we fine-tuned fTHz from 624.75 to 627.95 GHz
across a part of the transition J = 34 → 33. Figure 3b shows the absorbance spectrum of
CH3CN at 20 Pa with a spectral resolution of 520 kHz. For comparison, literature values of
CH3CN in the JPL database [19] are indicated by the dashed green lines in Fig. 3b. Four sharp
absorption lines with a linewidth of a few MHz appeared with a frequency spacing of a few
tens of MHz. We determined the center frequencies of these four absorption lines byperforming curve fitting analysis with multiple Lorentzian functions. Table 1 summarizes
the determined center frequencies and the literature values in the JPL database [19]. From acomparison between them, these peaks could be assigned to K = 0, 1, 2, and 3 in the transition
J = 34 → 33. The frequency discrepancy of the determined values from the literature values isalso shown in Table 1. The mean and standard deviation of the frequency discrepancy were52.6 ± 77.5 kHz for K = 0, 1, 2, and 3, corresponding to a spectral accuracy of 8.42 × 10−8 at
625 GHz.
We next quantified the concentration of CH3CN gas by determining the line area of theabsorption spectrum [20]. The line area was obtained by fitting the measured absorbance
spectrum α(ν)L to a Lorentzian profile as follows:
"
#
A
Δν
ð4Þ
αðvÞL ¼
π ðv−v0 Þ2 þ Δν 2
where A is the line area, ν0 is the center frequency, and Δν is the half width at half maximum.
Then, the gas concentration N (molecules/cm3) can be determined from the following
equation:
N¼

A
SL

ð5Þ

where S is the line intensity and L is the interaction length. Figure 4 shows themagnified absorbance spectrum of K = 2 in the J = 34 → 33 transition and the corresponding literature value in the JPL database (see the dashed green line) [19]. We
fitted it to the Lorentzian profile of Eq. (4), as indicated by the blue line in Fig. 4,
and determined N to be (5.41 ± 0.05) × 10 1 4 molecules/cm 3 by substituting

Table 1 Comparison of CH3CN absorption line positions as reported in the literature [19] and obtained using
high-precision THz-FDS in this work
J

K

Literature value (GHz)

Experimental value (GHz)

Discrepancy (kHz)34 → 333
2624.8193573
624.8788542

624.8195125
624.8788270

155.2
−27.2

1

624.9145620

624.9146239

61.9

0

624.9264662

624.9264868

20.6

Author's personal copy
912

J Infrared Milli Terahz Waves (2016) 37:903–915

Fig. 4 High-precision absorbance
spectrum of the J = 34 → 33, K = 2
transition in CH3CN gas at 20 Pa(spectral range = 40 MHz, spectral
resolution = 520 kHz). The blueline indicates the curve fitting
result with a Lorentzian function

2.00 × 10−4 cm−1, 1.02 × 10−20 cm−1/(molecule•cm−2), and 36.2 cm for A, S, and L in
Eq. (5).

3.3 THz-FDS of a Mixture Gas of CH3CN and CH313CN at Low Pressure
Next, we demonstrated THz spectroscopy of a mixture gas of CH3CN and its isotope(CH313CN). Because CH313CN is a symmetric-top molecule with a slightly different B value(=9.194 GHz) and DJK value (=17.67 MHz) from those of CH3CN (B = 9.199 GHz,DJK = 17.74 MHz) [17], the absorption lines appear in the THz frequency with a slightfrequency offset. We mixed the CH3CN and CH313CN at an unknown mixture ratio in a gas
cell. To observe the spectral features characterized by DJK in these two molecules, we precisely
tuned fTHz from 624.50 to 624.64 GHz across a part of the J = 34 → 33 transition. Figure 5
shows the absorbance spectrum of the mixed CH3CN/CH313CN gas with a spectral resolutionof 520 kHz. For comparison, the literature values in the JPL database [19] are also indicated by
the dashed green line for CH3CN and the dotted purple lines for CH313CN. A comparison
between them allowed us to assign one transition of CH3CN (J = 34 → 33, K = 5; see greentext) and four transitions of CH313CN (J = 34 → 33, K = 0, 1, 2, and 3; see purple text). In thisway, the difference in the spectral features between CH3CN and CH313CN was clearlyFig. 5 High-precision absorbance
spectrum of the mixed gas of
CH3CN and CH313CN gas(spectral range = 140 MHz,
spectral resolution = 520 kHz). The
blue line indicates the curve fitting
result with multiple Lorentzianfunctions

Author's personal copy
J Infrared Milli Terahz Waves (2016) 37:903–915

913

observed, indicating the potential of this approach for qualitative analysis of multiple gas
molecules.
Finally, we determined the mixture ratio of the CH3CN and CH313CN by performing fitting
analysis of multiple Lorentzian functions for the transition J = 34 → 33, K = 5 in CH3CN andthe transition J = 34 → 33, K = 2 in CH313CN. Table 2 summarizes the line area A, the line
intensity S, the interaction length L, and the gas concentration N for these two molecules. From
Table 2, the mixture ratio of the gases was estimated to be 1:2.66.

4 Discussion
The spectral accuracy of low-pressure THz gas spectroscopy in Fig. 3b and Table 1 remained
at 8.42 × 10−8, although the frequency accuracy of the THz synthesizer was guaranteed to be
2.3 × 10−9 by the Rb-FS. This inconsistency is mainly due to errors in the curve fitting analysis.
As usual, determining the center frequency with curve fitting analysis involves an error ofseveral percent to a few tens of percent of the spectral linewidth, depending on the signal-tonoise ratio of the measured spectrum. Since each spectrum in Fig. 3b has a linewidth of a few
MHz, an error of several tens of kHz to a few hundred kHz is included. The full accuracy of
the THz synthesizer will be achieved in Doppler-free THz gas spectroscopy at a lower gas
pressure.
Next, we discuss the possibility of further extending the continuous tuning range of the THz
synthesizer. The continuous tuning range in the present system was 120 GHz (see Fig. 3a).
This continuous tuning range is 400 times larger than that in the previous research on a singleOFC-referenced photomixing THz synthesizer [14] and is 10 times larger than that in previous
research on a dual-OFC-based photomixing THz synthesizer [16]. If this 120-GHz continuous
tuning is repeated 9 times every time the m2 value is changed in units of 480, a total tuning
range of over 1 THz can be achieved. However, to highlight the advantages of thisphotomixing THz synthesizer over an electrical THz synthesizer, it is desired to enhance thecontinuous tuning range to over 1 THz without changing the m2 value because the electrical
THz synthesizer can tune the output frequency within 10 to 20 % of the center frequency. The
continuous tuning range, ΔfTHz, in the present THz synthesizer depends on three factors: thespectral bandwidth of the photomixer, ΔνPM, the continuous tuning range of the m2th mode in
the OFC2, Δνm2, and the continuous tuning range of ECLD2, ΔνECLD2. First, since thefrequency range of the UTC-PD used here was 0.2–1.5 THz, a ΔνPM of over 1 THz can beachieved. Indeed, a ΔνPM of a few THz was achieved by a photoconductive mixer operating in
the 1.5-μm band [21, 22]. Second, the Δνm2 value is given byΔvm2 ¼ m2 Δf rep2

ð6Þ

Table 2 Line area A, line intensity S, interaction length L, and gas concentration N for CH3CN and CH313CN

Line area A (cm−1)−1

CH3CN (J = 34 → 33, K = 5)

CH313CN (J = 34 → 33, K = 2)

2.54 × 10−4

2.32 × 10−4

−21Line intensity S (cm /(molecule•cm )6.09 × 10

1.48 × 10−20

Interaction length L (cm)

36.2

36.2

Gas concentration N (molecules•cm−3)

4.32 × 1014

1.15 × 1015

-2

Author's personal copy914

J Infrared Milli Terahz Waves (2016) 37:903–915

where Δfrep2 is the tuning range of frep2. The m2 value was 775,499 in the experiment involving
THz-FDS of CH3CN. Since Δfrep2 = 2 MHz for OFC2, Δνm2 could reach about 1.55 THz from
Eq. (6). If another fofs-tunable OFS with the opposite scanning direction is used for OFS1, thetotal tuning range achieved by both OFS1 and OFS2 will double. Also, if an OFC2 with alower frep2 is used for OFS2, Δνm2 can be increased due to higher m2 value. For example, when
frep2 = 50 MHz and Δfrep2 = 500 kHz, Δνm2 could reach about 2 THz [17]. The third factor,
ΔνECLD2, is the actual limiting factor of the continuous tuning range in the present THz
synthesizer. Here, ΔνECLD2 was limited to less than 120 GHz due to the stroke of the PZT used
to tilt the diffraction grating for optical frequency tuning of ECLD2. Although we can findcommercial ECLDs with a wider tuning range, it is still difficult to achieve both wide tuning
and fine tuning without losing the phase-locking of ECLD2 to OFC2. In the previous research,an ΔνECLD2 of over 1 THz was achieved without losing the phase-locking of ECLD2 to OFC2,
by using a combination of a PZT and a motor actuator [17]. Other approaches may be used toextend ΔνECLD2 [23, 24]. In this way, the proposed THz synthesizer has the potential toachieve a continuous tuning range of over 1 THz. Work is currently in progress to achieve this.

5 Conclusion
We demonstrated THz-FDS of CH3CN gas and mixed CH3CN/CN313CN gas at low pressureby using a photomixing THz synthesizer traceable to a Rb frequency standard. A combinationof the photomixing technique with dual OFCs in the broadband UTC-PD enabled us toachieve a linewidth of 520 kHz, a frequency accuracy of 2.3 × 10−9, and a continuous tuning
range of 120 GHz for CW-THz radiation in a spectral range of 0.2–1.5 THz. The spectral
signatures, characterized by the rotational constant, B, and centrifugal distortion constant, DJK,in CH3CN and CN313CN, were clearly observed within a frequency range from 0.600 to 0.720
THz and were assigned with a frequency accuracy of 8.42 × 10−8. We also performed
quantitative analysis of the gas concentration and the mixture ratio by curve fitting analysis.
The demonstrated results clearly indicated the high potential of the proposed THz synthesizer
for the qualitative and quantitative analyses of multiple gases.
Acknowledgments This work was supported by grants for Collaborative Research Based on Industrial
Demand, Exploratory Research for Advanced Technology (ERATO), from the Japan Science and Technology
Agency, and a Grant-in-Aid for Scientific Research No. 26246031 from the Ministry of Education, Culture,
Sports, Science, and Technology of Japan. We also gratefully acknowledge financial support from The CanonFoundation. The authors thank Mr. Makoto Shimizu of NTT Electronics Corp., Japan, for use of the broadband
UTC-PD. The authors are grateful to Dr. Yoshiaki Nakajima of Univ. Electro-Commun., Japan, and Dr. Sho
Okubo of Natl. Inst. Adv. Ind. Sci. Tech., Japan, for fruitful discussions on the laser control. The authors also
wish to acknowledge Ms. Yumi Sumino of Tokushima Univ., Japan, for her help in preparation of the manuscript.

References
1. B. Stuart, Infrared Spectroscopy (John Wiley & Sons, 2005).
2. S. R. Bramwell, A. I. Ferguson, and D. M. Kane, “Doppler-free two-photon absorption spectroscopy with afrequency-modulated dye laser,” Opt. Lett., vol. 12, pp. 666-668, 1987.
3. D. W. Preston and C. E. Wieman, “Doppler-free saturated absorption: Laser spectroscopy,” Am. J. Phys., vol.
64, pp. 1432-1436, 1996.
4. D. M. Mittleman, Sensing with THz Radiation (Springer-Verlag, 2003).

Author's personal copy
J Infrared Milli Terahz Waves (2016) 37:903–915

915

5. N. Shimizu, K. Kikuchi, T. Ikari, K. Matsuyama, A. Wakatsuki, S. Kohjiro, and R. Fukasawa, “Absorption
spectra of smoke emitted from heated nylon fabric measured with a continuous-wave sub-terahertz spectrometer,” Appl. Phys. Express, vol. 4, art. 032401, 2011.
6. Y.-D. Hsieh, S. Nakamura, D. G. Abdelsalam, T. Minamikawa, Y. Mizutani, H. Yamamoto, T. Iwata, F.
Hindle, and T. Yasui, “Dynamic terahertz spectroscopy of gas molecules mixed with unwanted aerosol underatmospheric pressure using fibre-based asynchronous-optical-sampling terahertz time-domain spectroscopy,”
Sci. Rep., in revision.
7. B.J. Drouin, F.W. Maiwald, and J.C. Pearson, “Application of cascaded frequency multiplication tomolecular spectroscopy,” Rev. Sci. Instrum., vol. 76, art. 093113, 2005.
8. J.C. Pearson, B.J. Drouin, A. Maestrini, I. Mehdi, J. Ward, R.H. Lin, S. Yu, J.J. Gill, B. Thomas, C. Lee, G.
Chattopadhyay, E. Schlecht, F.W. Maiwald, P.F. Goldsmith, and P. Siegel, “Demonstration of a room
temperature 2.48–2.75 THz coherent spectroscopy source,” Rev. Sci. Instrum., vol. 82, art. 093105, 2011.
9. A.S. Pine, R.D. Suenram, E.R. Brown, and K.A. McIntosh, “A terahertz photomixing spectrometer:
application to SO2 self broadening,” J. Mol. Spectrosc., vol. 175, pp. 37-47, 1996.
10. A.J. Deninger, T. Göbel, D. Schönherr, Th. Kinder, A. Roggenbuck, M. Köberle, F. Lison, Th. Müller-Wirts,
and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum., vol. 79, art. 044702, 2008.
11. Th. Udem, R. Holzwarth, and T.W. Hänsch, “Optical frequency metrology,” Nature, vol. 416, pp.
233-237, 2002.
12. Q. Quraishi, M. Griebel, T. Kleine-Ostmann, and R. Bratschitsch, “Generation of phase-locked and tunable
continuous-wave radiation in the terahertz regime,” Opt. Lett., vol. 30, pp. 3231-3233, 2005.
13. G. Mouret, F. Hindle, A. Cuisset, C. Yang, R. Bocquet, M. Lours, and D. Rovera, “THz photomixing
synthesizer based on a fiber frequency comb,” Opt. Express, vol. 17, pp. 22031-22040, 2009.
14. F. Hindle, G. Mouret, S. Eliet, M. Guinet, A. Cuisset, R. Bocquet, T. Yasui, and D. Rovera, “Widely tunable
THz synthesizer,” Applied Physics B, vol. 104, pp 763-768, 2011.
15. T. Yasui, H. Takahashi, Y. Iwamoto, H. Inaba, and K Minoshima, “Continuously tunable, phase-locked,
continuous-wave terahertz generator based on photomixing of two continuous-wave lasers locked to two
independent optical combs,” J. Appl. Phys., vol. 107, art. 033111, 2010.
16. T. Yasui, H. Takahashi, K. Kawamoto, Y. Iwamoto, K. Arai, T. Araki, H. Inaba, and K. Minoshima, “Widelyand continuously tunable terahertz synthesizer traceable to a microwave frequency standard,” Opt. Express,
vol. 19, pp. 4428-4437, 2011.
17. H. Takahashi, Y. Nakajima, H. Inaba, and K. Minoshima, “Ultra-broad absolute-frequency tunable lightsource locked to a fiber-based frequency comb,” in Conference on Lasers and Electro-Optics (CLEO) 2009,
Technical Digest (CD) (Optical Society of America, 2009), paper CTuK4.
18. J.C. Pearson and H.S.P. Müller, “The submillimeter wave spectrum of isotopic methyl cyanide,” Astrophys.
J., vol. 471, pp. 1067-1072, 1996.
19. H.M. Pickett, R.L. Poynter, E.A. Cohen, M.L. Delitsky, J.C. Pearson, and H.S.P. Muller, “Submillimeter,
millimeter, and microwave spectral line catalog,” J. Quant. Spectrosc. Radiat. Transf., vol. 60, pp.
883–890, 1998.
20. F. Hindle, A. Cuisset, R. Bocquet, and G. Mouret, “Continuous-wave terahertz by photomixing: applications
to gas phase pollutant detection and quantification,” C. R. Phys., vol. 9, pp. 262-275, 2008.
21. T. Göbel, D. Stanze, B. Globisch, R. J. B. Dietz, H. Roehle, and M. Schell, “Telecom technology based
continuous wave terahertz photomixing system with 105 decibel signal-to-noise ratio and 3.5 terahertz
bandwidth,” Opt. Lett., vol. 38, pp. 4197-4199, 2013.
22. A. J. Deninger, A. Roggenbuck, S. Schindler, and S. Preu, “2.75 THz tuning with a triple-DFB laser system
at 1550 nm and InGaAs photomixers,” J. Infrared Millim. Terahertz Waves, vol. 36, p. 269-277, 2015.
23. E. Benkler, F. Rohde, and H. R. Telle, “Endless frequency shifting of optical frequency comb lines,” Opt.
Express, vol. 21, pp. 5793-5802, 2013.
24. F. Rohde, E. Benkler, T. Puppe, R. Unterreitmayer, A. Zach, and H. R. Telle, “Phase-predictable tuning of
single-frequency optical synthesizers,” Opt. Lett., vol. 39, pp. 4080-4083, 2014.