We constructed a widely and continuously tunable terahertz frequency synthesizer traceable to a hydrogen maser linked to coordinated universal time. Photomixing of two optical frequency synthesizers, linked to the hydrogen maser via dual optical frequency combs, gave this THz synthesizer frequency uncertainty of 10−12. To demonstrate the potential of wide and continuous tunability in the THz synthesizer, we tuned its output frequency up to 50 GHz discretely and 1.26 GHz continuously in the F-band while maintaining the unprecedented frequency uncertainty by using a uni-traveling-carrier photodiode as a photomixer. This THz synthesizer will be a powerful tool for broadband, high-precision THz spectroscopy and THz frequency metrology.
©2011 Optical Society of America
Accurate, stable, and tunable single-frequency signal generators operating in the terahertz (THz) region, which we call THz synthesizers, are powerful tools serving as sources for high-precision spectroscopy and local oscillators for heterodyne receivers in the fields of astronomy and molecular gas analysis. To achieve universal identification power in these spectroscopic applications, uncertainty of the output frequency should be guaranteed by referencing the base unit of time defined by The International System of Units (SI), that is, the microwave frequency standard. A THz synthesizer traceable to the microwave frequency standard also plays an important role for establishment of THz frequency metrology . However, conventional tunable continuous-wave (CW) THz sources based on the photomixing process of two CW near-infrared laser beams at adjacent wavelengths with a photomixer [2,3] or an optical parametric process involving two nanosecond pulsed laser beams in an optical nonlinear crystal  are not traceable to the frequency standard. Therefore, it is necesary to calibrate the output frequency using a standard material for a frequency reference, such as the absorption lines of low-pressure water vapor. Lack of frequency traceability in THz synthesizers will be a hindrance to widening the scope of THz spectroscopic applications with high reliability. Although frequency multiplier sources  can be synchronized to a frequency standard via a microwave frequency synthesizer, it is difficult to use them at frequencies over 1 THz due to the limited output power and tunable range.
Frequency combs in the optical  and THz  regions are attractive frequency references to realize THz synthesizers traceable to the microwave frequency standard because they enable us to transfer the excellent uncertainty of the microwave frequency standard to the THz region via coherent frequency linking . One possible approach for constructing a THz synthesizer is based on a combination of a THz quantum cascade laser (THz-QCL) and a THz frequency comb. Recently, a THz-QCL has been actively phase-locked to one mode of a THz comb ; however, it is still difficult to tune the frequency in a broad range due to the band structure of the THz-QCL . Another approach is based on a combination of the photomixing technique and an optical comb. Recently, an accurate, stable, phase-locked CW-THz radiation has been generated by photomixing of two CW laser beams phase-locked to a single optical comb . Furthermore, the output frequency was tuned continuously by scanning the frequency spacing of the optical comb while phase-locking the CW lasers to the comb; however, the reported range of continuous tuning was limited to several kHz. In this case where the two CW lasers share the same optical comb, when scanning the comb spacing, the optical frequencies of the two CW lasers change simultaneously. This common-mode change cancels most of the optical frequency change in the two CW lasers. As a result, the continuous tuning range of the CW-THz radiation is much smaller than that of the optical frequency in the CW lasers. Although a wider continuous tuning range was attempted by changing the offset frequency of one CW laser phase-locked to one of the comb modes in place of the comb spacing, the continuous tuning range was still limited to several tens of MHz . This is because phase information between the CW laser and the comb is lost when the CW laser frequency sweeps across one of the comb modes. Further expansion of the continuous tuning range is essential in spectroscopic applications.
One promising approach to increase the continuous tuning range while maintaining excellent frequency uncertainty is photomixing of two independent optical frequency synthesizers (OFSs) phase-locked to a microwave frequency standard via dual optical combs. An OFS is realized by phase-locking a tunable single-frequency CW laser to one of the comb modes . When the frequency spacing and carrier-envelope-offset frequency in the comb and the beat frequency between the CW laser and one of the comb modes are fully phase-locked to the microwave frequency standard, the optical frequency of the OFS can be determined at the uncertainty of the optical comb. Furthermore, the optical frequency can be widely and continuously tuned by scanning the comb spacing while maintaining the phase-locking. Therefore, if the outputs from a tunable OFS and a fixed, non-tunable one are optically heterodyned with a photomixer, the generated CW-THz radiation is widely and continuously tunable while its frequency is always determined, referenced to the microwave frequency standard. Based on this concept, we have constructed a continuously tunable, phase-locked CW-THz generator [1,13]. The tuning rate of this generator was enhanced by three orders of magnitude compared with that of the THz synthesizer using the single comb . However, because the carrier-envelope-offset frequency of the fiber comb used for the fixed OFS was not stabilized, the generated CW-THz radiation was not traceable to the microwave frequency standard, and hence its frequency uncertainty was still insufficient for a high-precision THz synthesizer. Furthermore, although the demonstrated continuous tuning was within a range of a few tens of MHz, the generator possesses the possibility of achieving a continuous tuning range within the range of 100 GHz.
In the study described in this paper, we constructed a widely and continuously tunable THz synthesizer traceable to the microwave frequency standard by stabilizing all parameters of two OFSs and photomixing them with a uni-traveling-carrier photodiode (UTC-PD). We demonstrated discrete tuning of 50 GHz and continuous tuning of 1.26 GHz in the F-band, ranging from 90 to 140 GHz.
2. Principle of operation
Let us consider the optical frequency fofs1 of a fixed OFS (OFS1), composed of a CW laser (CWL1) and a fiber-based optical comb (FC1), as shown in the upper part of Fig. 1 . The optical frequency fofs1 is represented by 
On the other hand, the optical frequency fofs2 of a tunable OFS (OFS2), composed of another CW laser (CWL2) and another fiber comb (FC2), as shown in the lower part of Fig. 1, is given by
When a THz synthesizer is realized by photomixing OFS1 and OFS2 with a photomixer, its output frequency (fTHz) is given by
Here, it is important to emphasize that the absolute value of fTHz can be determined at the uncertainty of the microwave frequency standard by measuring fceo1 (fixed), fceo2 (fixed), frep1 (fixed), frep2 (variable), m1 (fixed), m2 (fixed), fbeat1 (fixed), and fbeat2 (fixed). This is the main advantage over other THz synthesizers [2–4]. The continuous tuning range of fTHz (ΔfTHz) is represented as
The value of m2 reaches 3,880,000 when the optical frequency of CWL2 is 194 THz (corresponding wavelength = 1550 nm) and frep2 is 50 MHz. For example, when Δfrep2 = 500 kHz, which is 1% of frep2, ΔfTHz could reach about 2 THz from Eq. (4). Therefore, the proposed method can also be used for widely and continuously tunable THz synthesizers.
3. Experimental setup
The experimental setup of the THz synthesizer is shown in the upper part of Fig. 2 . We first constructed two OFSs operating at a wavelength of 1542 nm for photomixing. The fixed OFS (OFS1) was composed of a distributed feedback fiber laser (CWL1; Koheras A/S, Inc., AdjustiK E15-PM) and a custom-built optical comb including a mode-locked Er-doped fiber laser , namely, a fiber comb (FC1). On the other hand, the tunable OFS (OFS2) was composed of an external cavity laser diode (CWL2; Optical Comb, Inc., LT-5001) and another fiber comb (FC2). The frequencies fceo1, fceo2, frep1, frep2, fbeat1, and fbeat2 were all phase-locked to the microwave frequency reference synthesized from a hydrogen maser linked to coordinated universal time (UTC), operated by the National Metrology Institute of Japan (UTC-NMIJ). Details of the phase-locking process in the OFSs are given elsewhere . The mode numbers m1 and m2 were selected depending upon the frequency of the generated CW-THz radiation. An optical wavemeter (Advantest Corp., Q8326) was used to determine m1 and m2. In our previous THz synthesizer, the continuous tuning range of OFS2 (∆fofs2) without losing phase-locking of CWL2 to FC2 was limited to less than 110 GHz due to the stroke of a piezoelectric (PZT) actuator used to tilt a diffraction grating for optical frequency tuning of CWL2, although the optical frequency of the m2–th mode could be continuously tuned over 1.7 THz by making full use of the scanning range of frep2 (Δfrep2 = 450 kHz) . In the present system, the continuous tuning range of ∆fofs2 was increased up to 990 GHz by expanding the tuning range of CWL2 using a combination of a PZT actuator and a linear translation stage.
Promising photomixers for the THz synthesizer include a UTC-PD  and a photoconductive antenna (PCA) . The former has the advantages of high power characteristics and good compatibility with laser sources in the 1.5 µm telecommunication band, whereas the latter can achieve higher frequency response and broader tunability by use of 0.8 µm laser sources. Furthermore, the available frequency range in the UTC-PD could be extended to over 1 THz . We here used an F-band UTC-PD (NTT Electronics, frequency range = 90–140 GHz) as a photomixer for actual proof of the proposed method; however, it should be emphasized that it is possible to easily use another UTC-PD or PCA in place of the F-band UTC-PD if THz synthesizers with higher frequency and/or broader tunability are required. After adjusting the polarization overlap with a half-wave plate (λ/2) and a quarter-wave plate (λ/4), the output beams from OFS1 (fofs1 = 194.4 THz, power = 7.3 mW) and OFS2 (fofs2 = 194.3 THz, power = 9.4 mW) were combined with a fiber coupler and then optically heterodyned with a fiber-coupled, F-band UTC-PD equipped with a horn antenna. We estimated from the observed photocurrent value (7 mA) and the set bias voltage (–2.5 V) of the UTC-PD that the average power of generated CW-THz radiations was around 250 µW in the F-band.
To evaluate the spectral characteristics of the THz synthesizer, we used a THz-comb-referenced spectrum analyzer [1,15,16] composed of a third fiber comb whose frequency frep was stabilized (FC3 with frep3 = 56,122,639 Hz), a bow-tie-shaped, low-temperature-grown GaAs PCA for THz detection, and RF frequency instruments, as shown in the lower part of Fig. 2. The frequency frep3 and RF frequency instruments were synchronized to the microwave frequency reference. This spectrum analyzer was based on frequency beat measurement between the CW-THz radiation and the photocarrier THz (PC-THz) comb via a photoconductive heterodyne mixing process . The free-space-propagating CW-THz radiation passing through a pair of THz lenses (Pax Co., Tsurupica) was made incident on the PCA. The PCA was triggered by second-harmonic-generation (SHG) light (center wavelength = 775 nm, average power = 10 mW) from FC3. This resulted in the generation of a photoconductive self-beat signal of FC3 in the PCA, namely, the PC-THz comb. Photoconductive heterodyne mixing between the CW-THz radiation and the PC-THz comb in the PCA generated beat signals in the RF region. The beat signal of the current from the PCA was amplified by a high-gain current preamplifier (bandwidth = 10 MHz, sensitivity = 105 V/A) and was measured with an RF spectrum analyzer (Agilent E4402B) and frequency counter (Agilent 53132A). Details of the THz-comb-referenced spectrum analyzer are given elsewhere [1,15,16]. The spectral behavior and frequency instability of the CW-THz radiation were measured with the THz-comb-referenced spectrum analyzer. On the other hand, the absolute frequency of the CW-THz radiation was determined based on Eq. (3).
To evaluate the spectral characteristics in our THz synthesizer, we first generated frequency-locked CW-THz radiation at upper and lower frequency limits within the F-band, ranging from 90 GHz to 140 GHz. Figures 3(a) and 3(b) show spectra of the beat signal for CW-THz radiation around 91.97 GHz and 140.0 GHz, respectively. The lower horizontal axes give the frequency scale (fbeat3) measured with the RF spectrum analyzer. One can clearly confirm that the CW-THz radiation spectra have similar Gaussian-like shapes at these two frequencies. The linewidth of the CW-THz radiation was 599 kHz at 91.97 GHz and 631 kHz at 140.0 GHz when a Gaussian function was fitted to the spectral shape by regression analysis based on the Levenberg–Marquardt algorithm. If narrower-linewidth CW lasers with fast feedback control are employed for the OFSs, the linewidth of the CW-THz radiation will be further decreased, as reported in another paper .
We next assigned an absolute frequency to each CW-THz spectrum in Fig. 3. In our previous paper, the absolute frequency of CW-THz radiation was determined according to a procedure used for the THz-comb-referenced spectrum analyzer because fceo2 in the fixed OFS was not stabilized . In this procedure, the absolute frequency of the CW-THz radiation (fTHz) is given by15,16]. However, when the linewidth of the CW-THz radiation became broader, around 1 MHz, fitting analysis of the beat signal spectrum to determine its center frequency included an error of a few kHz . This resulted in an uncertainty of 10−3 in the absolute frequency measurement even though the actual frequency of the CW-THz radiation was more stable and accurate. Conversely, if all parameters in Eqs. (1) and 2 are known, the absolute frequency of the CW-THz radiation can be simply determined from Eq. (3) without the need for the THz-comb-reference spectrum analyzer or Eq. (5). Therefore, we decided to determine the absolute frequency using Eq. (3). Parameters of OFS1 and OFS2 are summarized in Tables 1 and 2 when fTHz = 91.97 GHz and 140.0 GHz in Fig. 3. From these values, center frequencies for those two CW-THz radiation spectra were 91,974,517,201 Hz and 140,003,403,918 Hz, respectively. The upper horizontal axes in Figs. 3(a) and 3(b) shows the actual scale of the absolute frequency determined by Eq. (3). Here, it is important to note that their absolute frequency is traceable to the hydrogen maser because two OFSs are fully phase-locked to the maser and the phase-noise in photomixer is negligible.
We also evaluated the frequency instability of the CW-THz radiation set at 132.0 GHz by measuring the frequency fluctuation of the beat signal with the RF frequency counter. Figure 4 shows the fluctuation of the beat frequency, represented by the Allan standard deviation , with respect to various gate times. A power law relationship in the form Y = X−1 between gate time X and frequency fluctuation Y was found. The inverse proportionality between them clearly indicates that the output frequency of the THz synthesizer was phased-locked to the hydrogen maser. Here, we consider whether the frequency fluctuation of the THz synthesizer is consistent with that of the OFS. The THz synthesizer had a frequency fluctuation of about 10 kHz at a gate time of 1 s (see Fig. 4). Conversely, since the frequency uncertainties of fceo1 (or fceo2), frep1 (or frep2), and fbeat1 (or fbeat2) in OFS1 (or OFS2) were respectively 10−17, 10−12, and 10−13 at a gate time of 1 s , the frequency fluctuation in the OFS was estimated to be a few hundreds of Hz from the uncertainty of m1frep1 (or m2frep2), which is mainly due to the uncertainty of the frequency synthesis of frep1 (or frep2). We consider that the discrepancy of frequency fluctuation between THz and optical synthesizers is mainly due to electrical noise caused in the amplification processes of the considerably weak beat signal in the THz-comb-referenced spectrum analyzer.
Next, we show the result of incremental tuning of the CW-THz radiation around 133 GHz by scanning frep2 at 0.2 Hz intervals. The resulting consecutive spectra of the CW-THz radiation are shown in Fig. 5 (sweep time = 2.483 s, RBW = 10 kHz, number of integrated signals = 50), in which the horizontal coordinate is scaled by Eq. (3). It is important to note that a tiny increment of 0.2 Hz in frep2 causes a large change of 762,281.6 Hz in fTHz due to a large tuning rate in Eq. (4) (m2 = 3,811,408 in this demonstration). This tuning rate is three orders of magnitude larger than that of the conventional THz synthesizer using the single comb .
Finally, we demonstrated continuous tuning of the CW-THz radiation over 1 GHz. The initial value of fTHz was set at 131.71 GHz. Figure 6(a) shows the display on the RF spectrum analyzer before starting tuning; here, the frequency span of the RF spectrum analyzer was set to be 60 MHz. Two beat signals between the CW-THz radiation and PC-THz comb were confirmed at 7.4 MHz and 48.7 MHz. Conversely, a signal around 56.1 MHz arose from self-beating of FC3 with frep3 of 56,122,639 Hz, used for the THz-comb-reference spectrum analyzer. Frequency dependence of the gain and the noise characteristics in the current preamplifier used in the THz spectrum analyzer cause the power difference between the two beat signals and the raised background floor, respectively. The spectral configuration of the CW-THz radiation and PC-THz comb before tuning is illustrated in the upper part of Fig. 6(b). The mode number mTHz of the PC-THz comb mode nearest in frequency to the CW-THz radiation was estimated to be 2,347 from fTHz and frep3. Then, the fTHz value was continuously tuned to 132.97 GHz during 60 s by scanning frep2. Since mTHz after tuning was 2,369, as illustrated in the lower part of Fig. 6(b), the CW-THz radiation traverses the PC-THz comb modes at 23 points. The actual spectral behavior of the beat signals during continuous tuning is shown as a movie in Media 1 (full span = 60 MHz, sweep time = 83.55 ms, and RBW = 560 kHz). It was confirmed that two beat signals appeared and disappeared one after another. The beat signal at the lower frequency was generated by mixing the CW-THz radiation with the PC-THz comb mode number mTHz nearest in frequency, whereas the beat signal at the higher frequency was due to mixing with mTHz + 1 or mTHz-1. Since zero crossing of the beat signal means that the CW-THz radiation traverses the PC-THz comb mode, scanning of fTHz by 1.26 GHz should cause zero crossing of the beat signal 23 times. The actual number of zero crossings was 23 in the movie of Media 1, which was exactly the same as the expected number. In this way, we confirmed from both Eq. (3) and THz spectrum analyzer that the continuous tuning of 1.26 GHz was surely performed. This continuous tuning range can be extended to the full frequency bandwidth of the F-band UTC-PD photomixer because we also generated CW-THz radiation at the lower limit (91.97 GHz) and the upper limit (140.0 GHz) of frequency in the F-band (see Fig. 3).
We demonstrated a widely and continuously tunable THz synthesizer traceable to the hydrogen maser linked to UTC-NMIJ. A combination of dual optical combs and the photomixing technique achieved a frequency uncertainty of 10−12 in the THz frequency range. Furthermore, photomixing of a tunable OFS and a fixed one enabled us to extend the continuous tuning range of the CW-THz radiation up to 1.26 GHz while maintaining the unprecedented frequency uncertainty. We believe that it should be possible to further extend the tuning range to 990 GHz in the THz frequency region by use of a broadband photomixier, such as a PCA [3,18], because we have already achieved continuous tuning of 990 GHz in the tunable OFS. This THz synthesizer will be a powerful tool for broadband, high-precision THz spectroscopy, such as analysis of multiple chemical species in gas-phase spectroscopy . Furthermore, the combination of the developed THz synthesizer and THz-comb-referenced spectrum analyzer will pave the way for establishment of frequency metrology in the THz region .
This work was supported by the Ministry of Education, Culture, Sports, Science, and Technology of Japan (Grants-in-Aid for Scientific Research Nos. 20560036, 21360039, and 21650111). We also gratefully acknowledge financial support from the Renovation Center of Instruments for Science Education and Technology in Osaka University, Japan.
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