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DOI 10.1007/s10762-015-0237-6

Real-Time Determination of Absolute Frequency
in Continuous-Wave Terahertz Radiation
with a Photocarrier Terahertz Frequency Comb Induced
by an Unstabilized Femtosecond Laser
Takeo Minamikawa 1,2 & Kenta Hayashi 1 &Tatsuya Mizuguchi 1 & Yi-Da Hsieh 1,2 &Dahi Ghareab Abdelsalam 1,2 & Yasuhiro Mizutani 2,3 &Hirotsugu Yamamoto 2,4 & Tetsuo Iwata 1,2 &Takeshi Yasui 1,2

Received: 25 November 2015 / Accepted: 18 December 2015 /Published online: 6 January 2016
# Springer Science+Business Media New York 2016

Abstract A practical method for the absolute frequency measurement of continuous-wave
terahertz (CW-THz) radiation uses a photocarrier terahertz frequency comb (PC-THz comb)
because of its ability to realize real-time, precise measurement without the need for cryogenic
cooling. However, the requirement for precise stabilization of the repetition frequency (frep)
and/or use of dual femtosecond lasers hinders its practical use. In this article, based on the factthat an equal interval between PC-THz comb modes is always maintained regardless of thefluctuation in frep, the PC-THz comb induced by an unstabilized laser was used to determine
the absolute frequency fTHz of CW-THz radiation. Using an frep-free-running PC-THz comb,
the fTHz of the frequency-fixed or frequency-fluctuated active frequency multiplier chain CWTHz source was determined at a measurement rate of 10 Hz with a relative accuracy of
8.2 × 10−13 and a relative precision of 8.8 × 10−12 to a rubidium frequency standard. Furthermore, fTHz was correctly determined even when fluctuating over a range of 20 GHz. The
proposed method enables the use of any commercial femtosecond laser for the absolute
frequency measurement of CW-THz radiation.
* Takeshi Yasui
yasui.takeshi@tokushima-u.ac.jp1

Institute of Technology and Science, 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 Engineering, Osaka University, 2-1, Yamadaoka, Suita, Osaka 565-0871, Japan

4

Center for Optical Research and Education, Utsunomiya University, 7-1-2, Yoto, Utsunomiya,Tochigi 321-8585, Japan

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Keywords Terahertz . Frequency comb . Absolute frequency measurement . Photoconductive
antenna . Photoconductive mixing . Frequency metrology

1 Introduction
Along with increasing demand for higher speed wireless communication, terahertz (THz)radiation (frequency = 0.1 to 10 THz) has attracted attention as a new band for wirelesscommunications [1, 2]. Recent progress in the development of continuous-wave THz (CWTHz) sources, such as the THz quantum cascade laser (THz-QCL) [3], the uni-traveling-carrier
photodiode (UTC-PD) [4], or the resonant tunnel diode (RTD) [5], have boosted research in
THz wireless communications. When the THz radiation is used for wireless communication, its
frequency allocation is important to secure necessary and sufficient bandwidth without interference with other applications. However, the allocation of frequencies higher than 0.275 THz
has not yet been established. If precise frequency allocation of the THz band is established in thesame manner as other radio waves, it will be necessary to determine the absolute frequency ofvarious types of CW-THz sources correctly in real time. However, conventional methods ofmeasuring the absolute frequency of CW-THz radiation, such as electrical heterodyne methods[6, 7] or optical interferometric methods, need cryogenic cooling of the mixer or detector tosuppress thermal noise. For practical and widespread use, a real-time method of measuring theabsolute frequency without the need for cryogenic cooling is strongly required.
One possible method that meets this requirement involves the use of a photocarrier THz
frequency comb (PC-THz comb) [8–10]. When femtosecond mode-locked laser light isincident onto a photoconductive antenna (PCA) without an electrical bias, namely a PCA
for detecting THz radiation, a PC-THz comb is generated in the PCA. Due to a coherent
photoconductive process in the PCA, the PC-THz comb is a harmonic frequency comb of thelaser repetition rate (frep) without a carrier-envelope-offset frequency (fceo), namely, an fceo-free
comb. If frep is phase-locked to a frequency standard in microwave or radio-frequency (RF)regions by laser control, the PC-THz comb can be used as a precise ruler for measuring THz
frequency. To be more specific, when measured CW-THz radiation is incident on a PCA
having a PC-THz comb, the PC-THz comb acts as a local oscillator with known multiple
frequencies covering the THz region. Therefore, the absolute frequency fTHz of the CW-THz
radiation can be determined from frep, the PC-THz comb mode number m nearest in frequency
to the CW-THz radiation, and the beat frequency fbeat generated by the photoconductive
mixing between the PC-THz comb mode and the CW-THz radiation [11–15].
The photoconductive mixing of CW-THz radiation with a PC-THz comb has been successfully applied to the absolute frequency measurement of narrow-linewidth CW-THz
sources [11–15] and even multiple CW modes in broadband THz comb [12, 16–19] at room
temperature. When a single, frep-stabilized PC-THz comb is used for the absolute frequency
determination of CW-THz radiation, two fbeat signals have to be measured before and after
shifting frep of the PC-THz comb by the laser control in order to determine m and sign of fbeat[11–13]. Such time-sequential, two-step measurement with a single, frep-stabilized PC-THz
comb has been an obstacle in applying this technique to the real-time absolute frequency
measurement of frequency-fluctuating CW-THz radiation. More importantly, the need for a
precisely stabilized femtosecond laser often makes this frequency measurement less practical.
An unstabilized femtosecond laser has been also used for high-precision frequency measurements of CW-THz radiation together with a simple and flexible algorithm of instantaneous

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frequency calculation [13]. However, use of expensive and bulky mode-locked Ti:Sapphire laser
and the associated maintenance limit the practical use of this method. Furthermore, there havebeen no attempts to perform the real-time determination of fTHz because of time-sequential, twostep measurement. Recently, to achieve real-time absolute frequency measurement withunstabilized femtosecond laser, a pair of unstabilized PC-THz combs with different frep values(frep1 and frep2), namely unstabilized dual PC-THz combs, has been effectively used for real-time
absolute frequency measurement of CW-THz radiation with rapid, large frequency variations[15]. This is based on the fact that a PC-THz comb always functions as a frequency ruler with anequal interval and a linear scale at every moment regardless of whether or not frep stabilization isused. Only if the frep is correctly monitored in real time, the PC-THz comb can be still used as aprecise ruler for measuring THz frequency. Absolute frequency measurement with a precision of
4.0 × 10−11 was achieved at a measurement rate of 100 Hz by simultaneous measurement of two
frep signals (frep1 and frep2) and two fbeat signals (fbeat1 and fbeat2) for the dual unstabilized PC-THz
combs. However, the need for dual femtosecond lasers is the last obstacle for the practical use ofthis method, even though unstabilized lasers can be used.
In the work described in this article, we demonstrated real-time, absolute frequency
measurement based on a single PC-THz comb induced by a compact, turnkey, mode-locked
fiber laser without frequency stabilization. The absolute frequency of frequency-fluctuating
CW-THz radiation was determined by rapid consecutive measurement of frep and fbeat in an
frep-modulated or frep-free-running PC-THz comb.

2 Principle of Operation
2.1 Use of frep-Modulated PC-THz Comb
When femtosecond laser light with repetition frequency frep is incident on a PCA for detecting
THz radiation, a PC-THz comb is induced in PCA. Then, when CW-THz radiation withfrequency fTHz to be measured is incident on the PCA, a group of beat signals are generated asa current signal from the PCA by photoconductive mixing between the PC-THz comb modes
and the CW-THz radiation. The photoconductive mixing between the CW-THz radiation and
the PC-THz comb mode m nearest in frequency to the CW-THz radiation generates a beatsignal at the lowest frequency, namely, fbeat. Therefore, fTHz is given byf THz ¼ m f rep " f beatð1Þ

Since frep and fbeat can be measured directly in the RF region, the value of m and the sign offbeat have to be determined to obtain fTHz.
In previous research, dual unstabilized PC-THz combs with different frequency spacing
were used for simultaneous measurement of frep1, frep2, fbeat1, and fbeat2, and the value of m andthe sign of fbeat were determined in real time based on them [15]. However, use of dual PCTHz combs is not always essential if the measurement rate of frep and fbeat is much faster than
the temporal fluctuation of fTHz. This is because two consecutive measurements of frep and fbeatwith a single PC-THz comb can be regarded as being equivalent to the simultaneous
measurement of frep1, frep2, fbeat1, and fbeat2 with dual PC-THz combs. Therefore, a single,
unstabilized PC-THz comb can be used for the real-time, absolute frequency measurement of
frequency-fluctuating CW-THz radiation.

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We next explain how to determine the value of m and the sign of fbeat with a single,
unstabilized PC-THz comb in real time. Figure 1 shows the principle of determining fTHz inreal time when the frequency spacing in a single PC-THz comb is modulated, namely, an frepmodulated PC-THz comb, where (a) shows the spectral behavior of the frep-modulated PCTHz comb and the measured CW-THz radiation (freq. = fTHz) and (b) shows the corresponding
description of frep and fbeat in the time domain. When frep is sinusoidally modulated between
frep_min and frep_max at a modulation frequency fmod, fbeat is also sinusoidally modulated between
fbeat_min and fbeat_max at fmod in synchronization with frep. If fmod is much faster than thetemporal fluctuation of fTHz, then frep_min, frep_max, fbeat_min, and fbeat_max can be regard as frep1,
frep2, fbeat1, and fbeat2 in dual unstabilized PC-THz combs [15], respectively. Therefore, the mvalue can be obtained in real time bym¼

f beat max − f beat min
f rep max − f rep min

ð2Þ

The sign of fbeat in Eq. (1) can be determined by a phase relation between modulated
waveforms of frep and fbeat. On one hand, if the sinusoidal wave of fbeat is out of phase withthat of frep, the sign is positive since fTHz > mfrep_max [see Fig. 1a, b]. On the other hand, if thesinusoidal wave of fbeat is in phase with that of frep, the sign is negative since fTHz < mfrep_min(not shown). Therefore, fTHz can be obtained byDEf−f
f rep ðout‐of ‐phaseÞ f beatf THz ¼¼ beat max beat min f rep mean þ f beat meanf rep max −f rep min
ð3Þ
DE
f beat max −f beat min
f rep mean −f beat meanf rep ðin‐phaseÞ f beat ;f THz ¼
f rep max −f rep min
where frep_mean and fbeat_mean are mean values for modulated frep and fbeat. Finally, fTHz can be
determined by measuring frep_max, frep_min, frep_mean, fbeat_max, fbeat_min, and fbeat_mean.

2.2 Use of frep-Free-Running PC-THz Comb
One may consider that the need for external modulation of the cavity length to modulate frep isstill an obstacle for the widespread use of this method, even though laser stabilization isFig. 1 Principle of real-time measurement with frep-modulated PC-THz comb. a Spectral behavior of frepmodulated PC-THz comb and measured CW-THz radiation and b the corresponding description of frep and fbeat in
the time domain

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unnecessary. In an unstabilized PC-THz comb without external modulation, the frequency
spacing frep varies every moment due to external disturbances to the laser cavity length, such astemperature changes, mechanical vibrations, acoustic vibrations, and so on. If such an frep-freerunning PC-THz comb is used for the photoconductive mixing with CW-THz radiation at fTHz
to be measured, the resulting fbeat signal also varies every moment reflecting the change of frep,
as shown in Fig. 2a, b. Such synchronized changes of frep and fbeat can also be used for the realtime determination of the value of m and the sign of fbeat if the temporal changes of frep and fbeat
are faster than the temporal fluctuation of fTHz. When we obtain frep1, frep2, fbeat1, and fbeat2 by
two consecutive measurements of frep and fbeat, m can be obtained by

Finally, fTHz can be determined by−fjf
jm ¼ !! beat2 beat1!!
f rep2 −f rep1

jf
−f
jf THz ¼ !! beat2 beat1!! f rep1 þ f beat1
f −f
rep2

rep1

−f
jf
j
f T Hz ¼ !! beat2 beat1!! f rep1 −f beat1
f −f
rep2

rep1

*

+
f beat2 − f beat1<0
f rep2 − f rep1*+
f beat2 −f beat1>0
f rep2 −f rep1

ð4Þ

ð5Þ

3 Experimental Setup
3.1 Use of frep-Modulated PC-THz Comb
Figure 3 shows a schematic diagram of the experimental setup for absolute frequency measurementwith an frep-modulated PC-THz comb. The setup included an frep-modulated femtosecond laser, a
PCA for THz detection, and data acquisition electronics. We used a mode-locked Er-doped fiber
laser (C-COMB and P100, Menlo Systems; center wavelength = 1550 nm, pulse duration = 56 fs,
frep ≈ 100 MHz) to generate a PC-THz comb in the PCA. The repetition frequency frep was not

Fig. 2 Principle of real-time measurement with frep-free-running PC-THz comb. a Spectral behavior of frep-freerunning PC-THz comb and a measured CW-THz radiation and b the corresponding description of frep and fbeat in
the time domain

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Fig. 3 Experimental setup for absolute frequency measurement with frep-modulated PC-THz comb. PPLN
periodically-poled-lithium-niobate crystal, L objective lens, PCA photoconductive antenna, PC-THz-comb
photocarrier THz frequency comb, M mixer, LPF low-pass filter, AMP current preamplifier

stabilized and could be modulated within a frequency deviation of ±50 Hz by a piezoelectric actuator(PZT; cut-off freq. ≈ 100 Hz) to change the cavity length. A portion of the laser light was detectedwith a fast photodetector (PD). The 10-th harmonic component of frep, namely 10frep, was electrically
mixed with an output signal (freq. = fLO = 980 MHz) from a local oscillator, and a beat signal
between them, namely 10frep−fLO (≈20 MHz), was extracted by a low-pass filter (LPF).
The output light from the fiber laser was converted into second-harmonic-generation (SHG)
light with a periodically-poled-lithium-niobate (PPLN) crystal. The resulting 775 nm light wasincident on a bowtie-shaped, low-temperature-grown GaAs PCA without an electrical bias,
resulting in the generation of a PC-THz comb in the PCA. In this experiment, we measured
CW-THz radiation (frequency fTHz) from an active frequency multiplier chain (Millitech AMC10-R0000, multiplication factor = 6, tuning range = 75–110 GHz, linewidth <0.6 Hz, and average
power = 2.5 mW), which multiplied the output frequency of a microwave frequency synthesizer(Agilent E8257D, frequency = 12.5–18.33 GHz, and linewidth <0.1 Hz) by six. The frequency
synthesizer was phase-locked to a rubidium frequency standard (Stanford Research Systems
FS725 with frequency = 10 MHz, accuracy = 5 × 10−11, stability = 2 × 10−11 at 1 s). When the CWTHz radiation emitted from this source was incident on the PCA together with the 775 nm light, agroup of beat signals between the CW-THz radiation and the PC-THz comb modes was generated
as an output current in the PCA by photoconductive mixing between them. The fbeat signal was
amplified by a current preamplifier (AMP; bandwidth = 40 MHz and transimpedance
gain = 100,000 V/A). The temporal waveforms for 10frep−fLO and fbeat were acquired simultaneously by a fast digitizer (resolution = 14 bit, sampling rate = 100 MHz), which used the output
signal from the frequency standard for an external clock in the digitizer. From the acquired
temporal waveforms, we obtained instantaneous values of frep and fbeat by the instantaneousfrequency-calculation algorithm involving a Fourier transform (data length = 1,000,000), digitalfrequency filtering (bandpass width = 10 kHz), an inverse Fourier transform, a Hilbert transform,
the time differential of the instantaneous phase, and signal averaging [13]. Finally, we determined
fTHz by substituting frep_max, frep_min, frep_mean, fbeat_max, fbeat_min, and fbeat_mean into Eq. (3).

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3.2 Use of frep-Free-Running PC-THz Comb
Figure 4 shows a schematic diagram of the experimental setup for the absolute frequency
measurement with an frep-free-running PC-THz comb, which is similar to that shown in Fig. 3.
Only the differences between them are described here. SHG light of another mode-locked Erdoped fiber laser (Femtolite AS-20-STD, IMRA; center wavelength = 780 nm, pulse
duration = 100 fs, frep ≈ 50.827 MHz) was used to generate an frep-free-running PC-THz comb
in the PCA. The 15-th harmonic component of frep, namely 15frep, was electrically mixed withan output signal (freq. = fLO = 763,388,000 Hz) from a local oscillator, and a beat signal
between them, namely 15frep−fLO (≈1 MHz), was measured. The fbeat signal was amplified
by a current preamplifier (AMP; bandwidth = 10 MHz and transimpedance gain = 100,000 V/A).
The temporal waveforms for 15frep−fLO and fbeat were acquired simultaneously by a digitizer(resolution = 14 bit, sampling rate = 10 MHz). Finally, we determined fTHz by substituting the
instantaneous values of frep and fbeat into Eq. (5).

4 Results
4.1 Use of frep-Modulated PC-THz Comb
First, we measured the absolute frequency of fixed-frequency CW-THz radiation(fTHz = 100,001,004,000 Hz) by using the frep-modulated PC-THz comb. To do so, frep was
sinusoidally modulated within about 3 Hz at a modulation frequency of 100 Hz (=fmod). From
Eq. (2), uncertainty of m must be less than ±0.5. To avoid the incorrect determination of m, we haveto determine |fbeat_max−fbeat_min| within a frequency error of ±1.5 Hz because |frep_max−frep_min| = 3 Hz.
From a relation between measurement rate and frequency error in our previous research (sampling
rate of the digitizer = 100 MHz) [15], the measurement rate of 10 Hz, or the measurement period ofFig. 4 Experimental setup for absolute frequency measurement with frep-free-running PC-THz comb. BS beam
splitter, L objective lens, PCA photoconductive antenna, PC-THz-comb photocarrier THz frequency comb,
M mixer, LPF low-pass filter, AMP current preamplifier

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100 ms, is suitable to suppress the frequency error below 1 Hz. Figure 5a, b show temporal changesof the instantaneous values of frep and fbeat (acquisition time = 100 ms). We consider that theincreased noise in frep after 90 ms was caused by errors in the instantaneous-frequency-calculation
algorithm rather than the data acquisition error with the digitizer. We confirmed that both frep and fbeat
were modulated at 100 Hz. The frequency deviation of fbeat should be m-times larger than that of frep
from Eq. (2). Since (frep_max−frep_min) and (fbeat_max−fbeat_min) were respectively 3.1446 Hz and3144.6 Hz, from curve fitting analysis with a sinusoidal wave for the temporal waveform during
a period of 100 ms, the m value was determined to be 1000. On the other hand, the sign of fbeat was
positive because fbeat was out-of-phase with frep. We further obtained mean values for modulated frep
and fbeat, namely frep_mean and fbeat_mean, of 100,000,007.009 Hz and 996,520.005 Hz for 100 ms. In
this way, we determined the fTHz value every 100 ms, or at a measurement rate of 10 Hz, as shown in
Fig. 5c. For 100 repetitive measurements of fTHz at a measurement rate of 10 Hz, the mean andstandard deviation of fTHz were 100,001,003,999.996 Hz and 1.5 Hz, respectively. These values
were comparable with those in the absolute frequency measurement using the frep-stabilized PC-THz
comb [15]. This result clearly indicated that the PC-THz comb correctly worked as a precise
frequency ruler even when the femtosecond laser was unstabilized and modulated. The achieved
accuracy and precision of the absolute frequency measurement were 4.0 × 10−14 and 1.5 × 10−11 ata measurement rate of 10 Hz, respectively. It should be noted that this accuracy and precisionindicate the relative values to the frequency standard because the output signal of the frequency
standard was used as a common time-base signal for the CW-THz source, the external clock in thedigitizer, and the local oscillator. The absolute accuracy and precision of frequency measurement
are determined by the absolute accuracy and stability of the frequency standard or the relativevalues, whichever is worse. Although the absolute accuracy and precision in the present systemwere limited by the rubidium frequency standard, use of another frequency standard with better
uncertainty, such as cesium frequency standard or optical frequency standard, will further improve
the absolute accuracy and precision of the frequency measurement up to the relative values.
Next, we determined the absolute frequency of the frequency-fluctuating CW-THz radiation
to demonstrate the capability of monitoring mode-hopping or free-running behavior in CWTHz sources. To do so, fTHz was made to stepwise jump at intervals of about +200 MHz fourtimes from 99,801,000,000 to 100,401,000,000 Hz. In this case, the CW-THz radiation crossed

Fig. 5 Temporal changes of instantaneous values of a frep and b fbeat for measurement time of 100 ms. c
Temporal changes of fTHz determined at a measurement rate of 10 Hz for a measurement time of 10 s

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two PC-THz comb modes in every stepwise jump of fTHz. Figure 6a shows the temporal changeof the value of m (blue plot) and the sign of fbeat (red plot) at a measurement rate of 10 Hz. Even
though fTHz crossed the PC-THz comb modes suddenly, they could be determined without
errors. Finally, we obtained the temporal change of fTHz from those values, as shown in Fig. 6b.
The temporal behavior of fTHz reflected the stepwise tuning operation of the test source
correctly. This demonstration reveals the potential of our method for measuring sudden
fluctuations of fTHz.

4.2 Use of frep-Free-Running PC-THz Comb
In the previous section, we demonstrated absolute frequency measurement with an frep-modulated PC-THz comb. However, if femtosecond lasers without the need for stabilization andmodulation of frep could be used in the proposed method, any commercial femtosecond laser
could be used for the absolute frequency measurement of CW-THz radiation. To demonstrate
the versatility of the proposed method, next we measured the absolute frequency in real time byuse of an frep-free-running PC-THz comb induced by the unstabilized femtosecond laser.
It is important to measure |frep2−frep1| and |fbeat2−fbeat1| precisely to correctly determine m based on
Eq. (4). When we use an frep-free-running PC-THz comb for absolute frequency measurement, theactual value of |frep2−frep1| depends on the frequency fluctuation of unstabilized frep. On the other
hand, the measurement precision of frep and fbeat with the instantaneous-frequency-calculation
algorithm depends on the number of averaged signals, namely the measurement rate [15]. The
measurement precision requirement of |fbeat2−fbeat1| is less strict than that of |frep2−frep1| because|fbeat2−fbeat1| is the m-time multiple of |frep2−frep1|. Therefore, we have to consider the frequency
fluctuation of unstabilized frep and the measurement precision of frep when the frep-free-running PCTHz comb is used.
We first investigated the frequency fluctuation of unstabilized frep by a RF frequency counter(Agilent 53220A) using the frequency standard as an external reference. Figure 7 shows thefrequency fluctuation of frep with respect to the gate time of the counter immediately after switchingon the femtosecond laser (0 min; red circle plot) and 35 min later (green triangle plot). Along withthe elapsed time, the frequency fluctuation was reduced due to the thermal equilibrium of the laser
cavity. On the other hand, to measure |frep2−frep1| correctly, the measurement error of frep should besmaller than the fluctuation of unstabilized frep. A relation between the measurement error and themeasurement rate in the instantaneous-frequency-calculation algorithm was given elsewhere; forFig. 6 Temporal changes of a the value of m and the sign of fbeat and b fTHz when fTHz was made to stepwise
jump at intervals of +200 MHz four times from 99,801,000,000 Hz to 100,401,000,000 Hz during 4 s. The
measurement rate was 10 Hz

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example, the frequency error was 0.15 Hz at a measurement rate of 10 Hz [15]. From thecomparison between this frequency error and the frequency fluctuation in Fig. 7, frep at 35 min afterswitching on the laser is too stable to determine the frep value without error at a measurement rate of
10 Hz. Therefore, we used PC-THz comb immediately after switching on, which is less stable thanthat at 35 min after.
We demonstrated the absolute frequency measurement of frequency-fixed CW-THz
radiation (f THz = 100,030,560,000 Hz) with the f rep -free-running PC-THz comb.
Figures 8a, b show temporal changes of frep and fbeat, in which the frep value driftedto lower frequency due to the thermal expansion of the cavity length, whereas the fbeat
value shifted to higher frequency. Such opposite behavior of frep and fbeat indicatedthat the sign of fbeat was positive. On the other hand, the m value was determined tobe 1968 during this measurement, based on Eq. (4). Finally, we determined the fTHz
value at a measurement rate of 10 Hz, as shown in Fig. 8c. The mean and standard
deviation of fTHz were 100,030,560,000.082 and 0.877 Hz in 100 repetitive measurements of fTHz at a measurement rate of 10 Hz. Therefore, the relative accuracy andprecision of the absolute frequency measurement were 8.2 × 10−13 and 8.8 × 10−12,
respectively. These values were comparable with those in the absolute frequency
measurement using the frep-modulated PC-THz comb, indicating that either an frepmodulated or frep-free-running PC-THz comb can be used for the precise frequency
measurement of CW-THz radiation.
Finally, we demonstrated the absolute frequency measurement of frequency-jumping CWTHz radiation with the frep-free-running PC-THz comb. In this experiment, fTHz was made to
stepwise jump at intervals of about +20 GHz, −500 MHz, and +5 GHz from80,004,900,000 Hz during 10 s. The first, second, and third frequency jumps crossed +394
modes, −10 modes, and +99 modes in PC-THz comb, respectively. Figure 9a shows the
temporal change of the m value (blue plot) and sign of fbeat (red plot), which correctly reflects
the expected change of them. Figure 9b shows the temporal change of fTHz. Both large changes ofseveral hundred MHz to a few tens of GHz and small changes of several Hz in fTHz [see an inset of
Fig. 9b] were successfully measured together. This frequency measurement with a wide dynamic
range was made possible by the use of a PC-THz comb with a high dynamic range of frequency.
Most importantly, the demonstrated results indicated the possibility of using any commercial
femtosecond laser for the precise frequency measurement of CW-THz radiation in real time.

Fig. 7 Frequency fluctuation of unstabilized frep at different gate time immediately after switching on the
femtosecond laser (0 min) and 35 min later

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Fig. 8 a Temporal changes of instantaneous values of a frep and b fbeat for a measurement time of 10 s. c
Temporal changes of fTHz determined at a measurement rate of 10 Hz for a measurement time of 10 s

5 Discussions
We first discuss error factors of m in the proposed method. Equations (2) and (4) hold true when two
fbeat signals (fbeat_max and fbeat_min, or, fbeat1 and fbeat2) are generated by the same mode in PC-THz
comb and signs of them are the same. On the other hand, the two fbeat signals, generated by different
modes in PC-THz comb or whose signs are different to each other, cannot satisfy these equations.
For largely fluctuating CW-THz CW-THz radiation, error of m may occur in a moment that CWTHz radiation suddenly crosses the PC-THz comb mode. For example, the lack of data plots in
Fig. 9a was due to such error of m, indicating incorrect m value outside of the range of the verticalscale. If the CW-THz radiation always fluctuates across PC-THz comb modes or the spectrum of
CW-THz radiation superimposes multiple PC-THz comb modes, the proposed method cannot beapplied. Another factor to hinder the correct determination of m is the frequency measurement
precision of frep and fbeat signals because uncertainty of m must be less than ±0.5 in Eqs. (2) and (4).
Since the measurement precision with the instantaneous-frequency-calculation algorithm depends
on the measurement rate [15], we have to select the suitable measurement rate and/or modulation
deviation of frep by considering it. Also, fbeat signals around DC and frep/2 may lead to errors because

Fig. 9 Temporal changes of a the value of m and the sign of fbeat and b fTHz when fTHz was made to stepwise
jump at intervals of +20 GHz, −500 MHz, and +5 GHz from 80,004,900,000 Hz during 10 s. The measurement
rate was 10 Hz

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of discontinuity of signal or coexistence of a mirror signal frep−fbeat. To avoid the coexistence of themirror signal, the current preamplifier functions as a low-pass filter in addition to a transimpedance
amplifier although the measurable range of fbeat is limited by the frequency bandwidth of it.
We next discuss a possibility to determine fTHz for rapidly fluctuating CW-THz radiation. In thereal-time determination of fTHz with frep-modulated PC-THz comb, we assumed that the temporalfluctuation of fTHz should be much slower than fmod. In the demonstration of Figs. 5 and 6, themeasurement rate was 10 Hz because frep is modulated at 100 Hz by PZT. For faster modulation of
frep over kHz, an electro-optic modulator can be used in the fiber laser cavity in place of PZT [20].
Also, optical frequency comb generators based on Mach-Zehnder modulator [21] or intracavity
modulator [22] will be useful for this purpose. For more rapidly fluctuating CW-THz radiation, thereal-time monitoring of the spectral shape may be important rather than the real-time determinationof fTHz. In this case, an RF spectrum analyzer will be useful for real-time monitoring of the spectral
shape of fTHz because the linewidth of PC-THz comb mode (typically, below 1 Hz) [11, 12] is muchnarrower than that of the fluctuating CW-THz radiation and hence the spectral shape of fbeat correctlyreflects that of fTHz.
We finally discuss the measurable range of the proposed absolute frequency measurement. In thisarticle, we demonstrated the real-time determination of fTHz using the CW-THz source around 0.1
THz. One may consider the availability of the proposed method above 0.275 THz because the highspeed wireless communication will be allocated at higher frequency than 0.275 THz. In principle,
the measurable range is limited by the spectral sensitivity of PCA because the proposed method isbased on the PC-THz comb induced in PCA. From the previous researches for the active frequency
multiplier chain source at 0.3 THz [14], THz-QCL at 2.5 THz [23], and electromagnetic THz comb
modes over 0.1~4 THz [11, 17], the measurable range should be extended over several THz, which
can cover the frequency bands of high speed wireless communication. The real-time determinationof such higher fTHz should maintain the same accuracy and precision as that of lower fTHz here
because they are secured by the frequency standard.

6 Conclusions
To allow commercial femtosecond lasers to be used for the absolute frequency measurement of
CW-THz radiation, we demonstrated the real-time, precise measurement of fTHz with an
frep-modulated or frep-free-running PC-THz comb. Based on the fact that an equal interval between
PC-THz comb modes is always maintained regardless of the fluctuation in frep, the PC-THz comb
induced by an unstabilized laser was effectively used to determine fTHz in fixed-frequency andfrequency-fluctuating CW-THz radiation. Using the frep-free-running PC-THz comb, the absolute
frequency fTHz of CW-THz radiation was determined with an accuracy of 8.2 × 10−13 and a
precision of 8.8 × 10−12 at a measurement rate of 10 Hz. Furthermore, even when fTHz suddenly
crossed 394 modes in the PC-THz comb due to a large fluctuation over 20 GHz, fTHz was correctly
determined in real time. Therefore, the proposed method is highly promising not only forfrequency-stabilized CW-THz sources but also practical CW-THz sources with free-running
operation or mode hopping.
Acknowledgments This work was supported by Collaborative Research Based on Industrial Demand 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. The authors thank Drs. Hideyuki Ohtake and Jun
Takayanagi of AISIN SEIKI Co., Ltd., Japan, for use of the IMRA laser.

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