APPLIED PHYSICS LETTERS 88, 241104 共2006兲

Terahertz frequency comb by multifrequency-heterodyning photoconductive
detection for high-accuracy, high-resolution terahertz spectroscopy
Takeshi Yasui,a兲 Yasuhiro Kabetani, Eisuke Saneyoshi,
Shuko Yokoyama, and Tsutomu Araki
Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka
560-8531, Japan

共Received 1 February 2006; accepted 20 April 2006; published online 13 June 2006兲
We report a terahertz spectroscopy technique based on a stable terahertz frequency comb from aphotoconductive terahertz emitter driven by a stabilized femtosecond laser. To this end, aphotocurrent frequency comb is induced in a photoconductive terahertz detector by instantaneous
photogating with another detuned femtosecond laser and is applied to read out the terahertz
frequency comb. The detailed structure of the terahertz frequency comb was clearly observed withfrequency accuracy of 2.5⫻ 10−7 and resolution of 81.8 MHz using multifrequency-heterodyningphotoconductive detection, which in turn is caused by the slightly mismatched frequency spacingbetween terahertz and photocurrent frequency combs. © 2006 American Institute of Physics.
关DOI: 10.1063/1.2209718兴
A femtosecond mode-locked laser generates a sequenceof pulses that are essentially copies of the same pulse separated by an interval equal to the inverse of the mode-locked
frequency. The highly stable femtosecond mode-locked pulse
train is synthesized by a series of frequency spikes regularly
separated by the mode-locked frequency in the optical frequency domain. This structure is referred to as a frequency
comb. Since the frequency-comb structure can be used as aprecision ruler in the frequency domain, the femtosecondlaser-based optical frequency comb has received a lot of interest as a powerful metrological tool capable of covering thevisible to near-infrared region by virtue of precise laser stabilization and the use of microstructured photonic crystal
fiber.1 Recently, the concept of the frequency comb has been
extended to the mid-infrared region by using a femtosecond
laser in combination with the nonlinear difference frequency
generation process,2 and effectively applied to a frequencycomb-based Fourier-transform infrared spectrometer 共combFTIR兲 based on a multifrequency-heterodyning interferometric technique.3,4 Furthermore, a possibility to extend combFTIR to the terahertz region is discussed. On the other hand,a terahertz electromagnetic pulse, radiating from a photoconductive antenna or nonlinear optical crystal triggered by afemtosecond laser, is also composed of a regular comb of
sharp lines in the terahertz frequency domain. This so-called
terahertz frequency comb possesses attractive features forhigh-precision terahertz spectroscopy, namely, excellent accuracy and stability, broadband selectivity, ultranarrow linewidth, and exact multiplication. Furthermore, since the terahertz frequency comb is extended to the terahertz region
without any frequency offset, it is possible to achieve absolute calibration without the use of a standard laser or a standard material. Thus the terahertz frequency comb is suitablefor identifying molecules of interest with fingerprints in theterahertz region, including gas molecules,5 illicit drugs,6 biological molecules,7 and explosives.8 There are, however, noreports of femtosecond-laser-based terahertz frequency comb
although terahertz spectroscopy based on electronica兲

Electronic mail: t-yasui@me.es.osaka-u.ac.jp

frequency-comb technique has been reported.9 In this letter,
we propose femtosecond-laser-based terahertz frequencycomb spectroscopy using multifrequency-heterodyning photoconductive detection.
Let us consider terahertz generation from a photoconductive emitter excited by a femtosecond laser 共pump laser;
mode-locked frequency= f 1兲 and terahertz detection using aphotoconductive detector gated by another femtosecond laser
共probe laser; mode-locked frequency= f 2兲. Figure 1 illustrates spectral behaviors in 共a兲 optical, 共b兲 terahertz, and 共c兲radio-frequency 共rf兲 regions. In the frequency domain, since
the photoconductive generation of the terahertz pulse can beconsidered as an ultrawideband demodulation of an opticalfrequency comb, the frequency comb is downconverted tothe terahertz region without any change to the frequencyspacing. The resulting terahertz frequency comb is a har-FIG. 1. Spectral behavior of frequency combs in 共a兲 optical, 共b兲 terahertz,and 共c兲 rf regions.

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Yasui et al.

monic frequency comb without a frequency offset, composedof a fundamental component 共frequency= f 1兲 and a series ofharmonic components 共frequency= 2f 1 , 3f 1 , . . . , nf 1兲 of amode-locked frequency. Next, we consider what happens
when the mode-locked frequency of the probe laser 共f 2 = f 1+ ⌬f兲 is slightly detuned from that of the pump laser 共f 1兲 bya certain frequency offset 共⌬f兲. Instantaneous photoconductive gating by the probe laser induces a photocurrent frequency comb having a different frequency spacing关frequency= f 2 , 2f 2 , 3f 2 , . . .,nf 2 = 共f 1 + ⌬f兲 , 2共f 1 + ⌬f兲 , 3共f 1+ ⌬f兲 , . . . , n共f 1 + ⌬f兲兴 in the photoconductive detector, which
also exists in terahertz frequency region. Under this condition, it is possible to detect the terahertz pulse as a result of
the photoconductive process occurring between the terahertz
and photocurrent frequency combs, giving rise to themultifrequency-heterodyning effect. This results in the generation of a secondary frequency comb in the rf region,termed the rf comb 共frequency= ⌬f , 2⌬f , 3⌬f , . . . , n⌬f兲.
Since the rf comb is a replica of the terahertz frequency
comb only downscaled by f 1 / ⌬f in frequency, one can utilize the terahertz frequency comb easily via direct observation of the rf comb using a rf spectrum analyzer and calibration of the frequency scale.
To confirm the above concept, we used two Kerr-lensmode-locked Ti:sapphire lasers as a pump laser and a probe
laser. The individual mode-locked frequencies in the two lasers 共f 1 and f 2兲 and the frequency difference between them
共⌬f = f 1 − f 2兲 were stabilized by two independent laser-control
systems composed of phase-locked loop 共PLL兲 and a piezoelectric transducer 共PZT兲 attached to a laser mirror. In PLL
electronics, the 100th harmonic component of a mode-locked
frequency 共100f 1 and 100f 2兲 and a synthesized signal from arubidium frequency standard 共accuracy= 5 ⫻ 10−11, stability= 2 ⫻ 10−11 at 1 s兲 are used as a control signal and a reference
signal, respectively. The resulting f 1 and f 2 are fixed at
81 800 000 and 81 800 100 Hz within a range of ±1.6
⫻ 10−3 Hz whereas the fluctuation of ⌬f is suppressed within±2.5⫻ 10−5 Hz at a gate time of 1 s. Such excellent stabilityof f 1, f 2, and ⌬f enables us to generate stable frequency
combs and achieve an exact multifrequency-heterodyning
process. We first used two bowtie-shaped, low-temperaturegrown GaAs photoconductive antennas 共bowtie length= 1 mm, gap= 5 ␮m兲 as a terahertz emitter and a terahertz
detector. The terahertz frequency comb radiated from theterahertz emitter propagated in free space and then was incident onto the terahertz detector via two hemispherical siliconlenses and two off-axis parabolic mirrors. As a result ofmultifrequency-heterodyning photoconductive detection, therf comb was directly measured with a rf spectrum analyzer
共Agilent Technologies, E4402B兲 after passing through a current preamplifier 共sensitivity= 4 ⫻ 106 V / A, bandwidth= 1 MHz兲. One can reconstruct the terahertz frequency comb
exactly by calibrating the rf comb with the frequency downscale factor 共=f 1 / ⌬f = 818 000兲.
Figure 2共a兲 shows an amplitude spectrum of the rf comb
obtained using the proposed method 共measurement time= 10 s, resolution bandwidth= 10 kHz兲, in which the upperhorizontal axis gives the frequency scale in the rf spectrum
analyzer. The spectrum was obtained by subtracting a background spectrum measured in the absence of the terahertz
electric field from a signal spectrum. The actual frequency
values in the terahertz frequency-comb spectrum are scaled

Appl. Phys. Lett. 88, 241104 共2006兲

FIG. 2. Amplitude spectrum of terahertz frequency comb obtained withmultifrequency-heterodyning photoconductive detection. 共a兲 Bowtiephotoconductive terahertz emitter and bowtie-photoconductive terahertz detector and 共b兲 bowtie-photoconductive terahertz emitter and dipolephotoconductive terahertz detector are used. An enlarged terahertz-comb
spectrum is also shown as an inset. Frequency scale in terahertz and rf
combs is indicated at lower and upper horizontal coordinates, respectively.

according to the lower horizontal axis by using the frequency
downscale factor. Considering a spectral range of 0.3 THzand a frequency spacing of 81.8 MHz, the terahertz spectrum
is composed of 3667 comb modes. The inset of Fig. 2共a兲shows an expansion of the spectral region of
0.0492– 0.0498 THz 共measurement time= 0.5 s, resolution
bandwidth= 10 Hz兲. One can clearly see seven comb-modelines having a frequency spacing of 81.8 MHz and a width of
11 MHz; these can be used as divisions in a terahertz
frequency-comb ruler with a frequency resolution of
81.8 MHz. The accuracy of the observed terahertz frequency
comb is determined by stability of frequency spacing andfrequency downscale factor. We can conclude the accuracy inthe proposed terahertz-comb spectroscopy to be 2.5⫻ 10−7
from stability of f 1 关=共1.6⫻ 10−3兲 / 81 800 000= 2.0⫻ 10−11兴
and that of ⌬f 关=共2.5⫻ 10−5兲 / 100= 2.5⫻ 10−7兴. As usual, theaccuracy in conventional terahertz time-domain spectroscopy
共THz-TDS兲 using a mechanical time-delay stage is determined by precision of step displacement 共= ⬃ 10−2 in amotor-driven stage兲. In contrast to it, the accuracy in thepresent system depends on stability of frequency spacing andfrequency downscale factor, resulting in achievement of excellent accuracy. In Fig. 2共a兲, the spectral bandwidth is limited by employing two bowtie-shaped photoconductive antennas as a terahertz emitter and detector. Next, to extend thespectral bandwidth over 1 THz, we use a dipole-shaped photoconductive antenna 共length= 7.5 ␮m, width= 10 ␮m, gap= 5 ␮m兲 as a terahertz detector and magnify the frequency
downscale factor to 16 360 000 by changing the ⌬f value of100 to 5 Hz in combination with another high-gain current

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Appl. Phys. Lett. 88, 241104 共2006兲

Yasui et al.

FIG. 3. Terahertz amplitude spectra obtained with 共a兲 stage-scanning THzTDS and 共b兲 AOS-THz-TDS. Bowtie-photoconductive terahertz emitter andbowtie-photoconductive terahertz detector are used.

preamplifier
共sensitivity= 5 ⫻ 107 V / A,bandwidth= 100 kHz兲. The resulting spectrum is shown in Fig. 2共b兲
共measurement time= 1000 s, resolution bandwidth= 1 kHz兲.
One can clearly confirm that the amplitude spectrum of terahertz frequency comb is extended over 1 THz.
To evaluate the validity of the terahertz frequency-comb
spectrum shown in Fig. 2共a兲, we compare the resultant spectrum with those obtained by stage-scanning THz-TDS
andasynchronous
opticalsampling
THz-TDS
共AOS-THz-TDS兲.10,11 The AOS-THz-TDS enables a stagefree configuration in THz-TDS and hence achieves ultrahigh
spectral resolution with rapid data acquisition. Figures 3共a兲and 3共b兲 show the terahertz spectra obtained with stagescanning THz-TDS and AOS-THz-TDS, respectively. Thefrequency resolutions in the former and latter are 9 GHz at ameasurement time of 5 min and 81.8 MHz at a measurement
time of 10 s, respectively. The spectral structure in Fig. 3共b兲is due to multiple reflection of the terahertz pulse in thehemispherical silicon lens. After comparing the terahertz amplitude spectra obtained using the three methods, we canconclude that the proposed method correctly measures theterahertz amplitude spectrum. The proposed terahertz-comb
spectroscopy and AOS-THz-TDS achieve the theoreticallimit of frequency resolution in THz-TDS, namely, modelocked frequency, at a shorter measurement time. However,
the terahertz-comb spectroscopy provides a few attractive
features compared with AOS-THz-TDS. The AOS-THz-TDS
needs an additional sum-frequency-generation 共SFG兲 crosscorrelator to generate a trigger signal as a time origin fortime-domain measurement and hence provide phase spectrum of terahertz radiation. Furthermore, even if the measurement time is much shorter for AOS-THz-TDS, one usually has to perform fast Fourier transformation 共FFT兲 on acomputer in order to obtain the terahertz spectrum of amplitude after making the measurement. In contrast to AOS-THzTDS, the proposed terahertz-comb spectroscopy can measure
the terahertz amplitude spectrum directly without a SFG
cross-correlator, similar to comb-FTIR,3,4 and FFT because itis an entirely frequency-domain measurement, which alsomeans that it does not require time coincidence or time-delayscanning between the terahertz and probe pulses. These features of terahertz-comb spectroscopy enable rapid dataanalysis and a simple, stable setup in high-accuracy, highresolution terahertz spectroscopy.
This work was supported by the SCOPE from MIC ofJapan, the ITRGP2002 from NEDO of Japan, and KAKEHHI No. 1868600 from MEXT of Japan. The authors are
grateful to Dr. Mamoru Hashimoto from Osaka University
for fruitful discussions.
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