Abstract
A single, freerunning, dualwavelength modelocked, erbiumdoped fibre laser was exploited to measure the absolute frequency of continuouswave terahertz (CWTHz) radiation in real time using dual THz combs of photocarriers (dual PCTHz combs). Two independent modelocked laser beams with different wavelengths and different repetition frequencies were generated from this laser and were used to generate dual PCTHz combs having different frequency spacings in photoconductive antennae. Based on the dual PCTHz combs, the absolute frequency of CWTHz radiation was determined with a relative precision of 1.2 × 10^{−9} and a relative accuracy of 1.4 × 10^{−9} at a sampling rate of 100 Hz. Realtime determination of the absolute frequency of CWTHz radiation varying over a few tens of GHz was also demonstrated. Use of a single dualwavelength modelocked fibre laser, in place of dual modelocked lasers, greatly reduced the size, complexity, and cost of the measurement system while maintaining the realtime capability and high measurement precision.
Introduction
Terahertz (THz) radiation covers an extremely wide electromagnetic band that potentially could be leveraged for highspeed communications, and investigation of THz radiation has attracted increasing interest^{1,2}. With the development of various continuouswave THz (CWTHz) radiation sources, such as THz quantum cascade lasers^{3} and unitravelingcarrier photodiodes^{4}, THz wireless communication is highly promising, even though frequency allocation in the THz band (0.275–3 THz) has not yet been established. For the purpose of evaluating sources and considering suitable frequency allocation, it is essential to precisely determine the absolute frequency of CWTHz radiation. Although the electrical heterodyne method^{5} and the optical interferometric method have been used for measuring the absolute frequency of CWTHz radiation, both of these methods need cryogenic cooling to reduce thermal noise, hindering the wide adoption of these methods in various practical applications. Therefore, there is a strong demand for absolute frequency measurement in the THz region without the need for cryogenic cooling.
One promising method of achieving this is the scheme based on photoconductive mixing of CWTHz radiation with a THz frequency comb of a photocarrier (PCTHz comb) in a photoconductive antenna (PCA)^{6,7,8,9,10,11}. In this scheme, the absolute frequency f_{THz} of CWTHz radiation can be determined from a PCTHz comb mode m nearest in frequency to f_{THz}, the frequency interval f_{rep} of the PCTHz comb, and the beat frequency f_{beat} between the CWTHz radiation and the mth comb mode. While f_{rep} and f_{beat} can be directly measured in the radiofrequency (RF) region, m can be determined by two different f_{rep} values and their corresponding f_{beat} values. In early research^{6,7,8}, the determination of m was based on timesequential, twostep measurement of f_{rep} and f_{beat} with a single PCTHz comb induced by an f_{rep}adjustable modelocked laser. Therefore, f_{THz} could not be determined in real time. Recently, dual PCTHz combs with different f_{rep} have been used to achieve the realtime determination of f_{THz} based on simultaneous measurement of two f_{rep} values and their corresponding f_{beat} values^{10}. In that study, by using dual stabilized or freerunning modelocked lasers with different f_{rep} for the generation of dual PCTHz combs, f_{THz} was determined precisely at a measurement rate of 100 Hz. However, use of dual laser systems hinders the wider adoption of such techniques. More recently, the realtime determination of f_{THz} was achieved by using a single modelocked laser with an actively modulated or smoothly drifting f_{rep}^{11}; however, the measurement rate remained at 10 Hz due to the timesequential, fasttwostep measurement of f_{rep} and its corresponding f_{beat} with a single PCTHz comb. If dual PCTHz combs with different f_{rep} could be generated by a single freerunning modelocked laser, the realtime capability, precision, and practicability of THz frequency measurement would be enhanced.
Recently, the use of ‘multiplexed’ modelocked erbiumdoped fibre (Er:fibre) lasers as dualcomb lasers has been demonstrated by multiplexing in the dimensions of centre wavelength, propagation direction, polarization state, or modelocking mechanism^{12,13,14,15,16,17}. Among these schemes, use of a dualwavelength (dualλ) modelocked Er:fibre laser is a promising way to generate a dual PCTHz comb because it emits two independent modelocked pulsed light beams with different wavelengths, λ_{1} and λ_{2}, from a single cavity, and their f_{rep} values are slightly detuned from each other due to dispersion in the fibre laser cavity^{18}. The pulsed light beams with wavelengths λ_{1} and λ_{2} can be easily separated by optical filters, and the difference in f_{rep} between them can be adjusted by dispersion management in the fibre cavity. Also, the commonmode noise between the λ_{1} and λ_{2} pulsed beams is effectively cancelled by copropagation of them in the same cavity^{19}. Such characteristics in dualλ modelocked Er:fibre lasers have been successfully used in asynchronous optical sampling (ASOPS) pumpprobe measurement^{18}, optical ranging^{20}, and optical spectroscopy^{19}. However, there have been no attempts to apply the technique to THz measurement. In this paper, we used a dualλ modelocked Er:fibre laser for rapid, highprecision measurement of f_{THz} based on dual PCTHz combs.
Principle of Operation
THzcombreferenced frequency measurement is based on heterodyne photoconductive mixing between CWTHz radiation and a PCTHz comb^{6,7}. Two essential conditions must be satisfied: (1) a PCA must work as a broadband heterodyne receiver with high sensitivity for THz radiation at room temperature, and (2) the generated PCTHz comb should cover the whole THz band. When CWTHz radiation (freq. = f_{THz}) is photoconductively mixed with one mode of a single PCTHz comb (freq. interval = f_{rep}, comb mode nearest in frequency to f_{THz} = m), f_{THz} is given by
where f_{beat} is the beat frequency between CWTHz radiation and the mth comb mode.
Next we consider the photoconductive mixing of CWTHz radiation with dual PCTHz combs having different frequency spacings (PCTHz comb 1, freq. interval = f_{rep1}, comb mode nearest in frequency to f_{THz} = m; PCTHz comb 2, freq. interval = f_{rep2}, comb mode nearest in frequency to f_{THz} = m). In this case, when f_{rep2} > f_{rep1}, f_{THz} is given by
where f_{beat1} is the beat frequency between the CWTHz radiation and the mth comb mode in PCTHz comb1, and f_{beat2} is the beat frequency between the CWTHz radiation and the mth mode in PCTHz comb2. From Eq. (2), m can be calculated by
where the signs of f_{beat1} and f_{beat2} are determined by the relative positions of f_{THz}, mf_{rep1}, and mf_{rep2}.
Figure 1 shows the relative position of f_{THz} (see green line) to the nearest modes mf_{rep1} (see red lines) and mf_{rep2} (see blue lines) in the dual PCTHz combs, where (a) f_{THz} < mf_{rep1} < mf_{rep2}, (b) mf_{rep1} < f_{THz} < mf_{rep2}, and (c) mf_{rep1} < mf_{rep2} < f_{THz}. Since the frequency difference between f_{rep1} and f_{rep2} ( = f_{rep2} − f_{rep1} = ∆f_{rep}) is the denominator of Eq. (3), a highly stable frequency difference is essential for accurately determining m. The relative positions of f_{THz}, mf_{rep1}, and mf_{rep2} can be determined from the simultaneous measurements of f_{rep1}, f_{rep2}, f_{beat1}, and f_{beat2} as follows:
Therefore, m can be obtained by
Finally, f_{THz} can be determined by
Results
Freerunning, dualλ modelocked Er:fibre laser
Figure 2(a) shows the configuration of the freerunning, dualλ modelocked Er:fibre laser oscillator. With birefringenceinduced filtering and loss control effects^{12,13,19}, in addition to the adjustment of the polarization state in the ring cavity, simultaneous modelocking centred on the 1530nm and 1560nm regions can be realized. As shown in Fig. 2(b), the centre wavelengths of dualλ pulses were 1531.4 nm and 1556.1 nm, with corresponding 3dB bandwidths of 2.2 nm and 3.3 nm, respectively. Because of the anomalous intracavity dispersion, the dualλ pulses had different repetition rates around 32.06 MHz (f_{rep1} = 32,066,206 Hz, f_{rep2} = 32,067,857 Hz) with a difference ∆f_{rep} ( = f_{rep2} − f_{rep1}) of ~1.63 kHz, as shown in Fig. 2(c).
In order to meet the optical power and pulse duration requirements for PCAs, the λ_{1} and λ_{2} pulses from the laser oscillator were separated by a coarsewavelengthdivisionmultiplexing bandpass filter (CWDMBPF) [not shown in Fig. 2(a)]. Figure 3(a and b) show optical spectra and RF spectra of the λ_{1} and λ_{2} pulses after passing through the CWDM bandpass filter. The dualλ modelocked fibre laser light was successfully separated into each component in the optical region and the RF region. Then, the components were amplified and spectrally broadened by erbiumdoped fibre amplifiers (EDFAs) and the following SMF, respectively. As shown in Fig. 3(c), the optical spectrum of the amplified λ_{1} pulsed light covered the whole C band, whereas that of the amplified λ_{2} pulsed light was located at the shorter wavelength side. The mean power and the pulse duration were 27 mW and 130 fs for the amplified λ_{1} pulsed light [see Fig. 3(d)] and 20 mW and 130 fs for the amplified λ_{2} pulsed light [see Fig. 3(e)] when the SMF was used to compensate for the dispersion. These output characteristics were sufficient to generate a PCTHz comb in PCA.
Before performing realtime measurement of f_{THz} with dual PCTHz combs, we investigated the frequency characteristics of this freerunning laser. We first measured the temporal fluctuations of f_{rep1} and f_{rep2} with a frequency counter (Agilent 53132 A). Figure 4(a) shows the fluctuations with respect to different gate times. Due to the freerunning operation without active frequency control, the fluctuations of f_{rep1} and f_{rep2} did not decrease over a gate time of 0.1 s. However, these fluctuations were comparable to those of other commercialized, freerunning singlewavelength lasers^{10,11}; this is clear evidence that the two modelocked operations at λ_{1} and λ_{2} do not compete with each other and are completely independent of each other. Figure 4(b) shows the temporal fluctuations of f_{rep1} and f_{rep2}, where their frequency deviations from the initial values are indicated by δf_{rep1} and δf_{rep2}. A slow drift was clearly confirmed for both, indicating changes in the environmental conditions in the fibre cavity. However, it should be emphasized that the temporal behaviours of δf_{rep1} and δf_{rep2} were the same. This is because the λ_{1} and λ_{2} pulses copropagated in the same ring cavity and experienced similar disturbances. As a result of such commonmode behaviour of δf_{rep1} and δf_{rep2}, ∆f_{rep} was highly stable, as shown in Fig. 4(c). The mean and standard deviation of ∆f_{rep} in Fig. 4(c) were 1764.97 Hz and 0.24 Hz, respectively. Such high stability of ∆f_{rep} was useful for the correct determination of m and f_{THz} based on Eqs. (4 to 6). Therefore, even though f_{rep1} and f_{rep2} were not actively stabilized, this dualλ modelocked fibre laser can be used for measuring f_{THz} in real time and with highprecision using dual PCTHz combs.
Realtime determination of f_{THz} with dual PCTHz combs
Figure 5 shows a schematic diagram of the setup for measuring the frequency of CWTHz radiation, consisting of three main parts. The first part is the laser source, including a freerunning, dualλ modelocked Er:fibre laser oscillator and two EDFAs. The second part is composed of the optical and THz systems for frequency measurement of CWTHz radiation, a CWTHz test source, a pair of lowtemperaturegrown (LT) InGaAs/InAlAs PCAs (PCA1 and PCA2), and their affiliated components. The third part is the data acquisition electronics.
The amplified λ_{1} pulsed light at f_{rep1} from one EDFA (EDFA1) was used for generating a PCTHz comb in PCA1 (PCTHz comb 1, freq. spacing = f_{rep1}), whereas the amplified λ_{2} pulsed light at f_{rep2} from another EDFA (EDFA2) was used for generating a PCTHz comb in PCA2 (PCTHz comb 2, freq. spacing = f_{rep2}). When the CWTHz radiation was incident on both PCA1 and PCA2, photoconductive mixing between the CWTHz radiation and the dual PCTHz combs and the following electronic processing resulted in the generation of beat signals with frequencies f_{beat1} and f_{beat2}. On the other hand, RF signals related to f_{rep1} or f_{rep2} (freq. = 30f_{rep1} − f_{LO} and 30f_{rep2} − f_{LO}) were obtained by the photodetectors (PD) and subsequent electric heterodyning with a local oscillator (LO, freq. = f_{LO}). Temporal waveforms of f_{beat1}, f_{beat2}, 30f_{rep1} − f_{LO}, and 30f_{rep2} − f_{LO} were simultaneously acquired by a digitizer (resolution = 14 bit, sampling rate = 20 MHz). From the temporal waveforms, we determined instantaneous values of f_{rep1}, f_{rep2}, f_{beat1}, and f_{beat2} using the instantaneousfrequencycalculation algorithm^{8}. Finally, we determined f_{THz} by substituting them into Eqs. (4 to 6). Since the CWTHz test source, the local oscillator, and the clock signals of the digitizer shared a common timebase signal from a 10 MHz rubidium (Rb) frequency standard (Stanford Research Systems FS725, accuracy = 5 × 10^{–11}, stability = 2 × 10^{−11} at 1 s), one can evaluate the relative precision of frequency measurement without the influence of the absolute precision of the frequency standard.
To confirm the three situations in Fig. 1, we measured f_{beat1} and f_{beat2} when f_{THz} was set at (a) 100,013,820,000 Hz for f_{THz} < mf_{rep1} < mf_{rep2}, (b) 100,016,340,000 Hz for mf_{rep1} < f_{THz} < mf_{rep2}, and (c) 100,020,240,000 Hz for mf_{rep1} < mf_{rep2} < f_{THz}. Figure 6 shows the temporal change of f_{beat1} and f_{beat2}, where their frequency deviations from the initial values are indicated by δf_{beat1} and δf_{beat2}, when (a) f_{THz} < mf_{rep1} < mf_{rep2}, (b) mf_{rep1} < f_{THz} < mf_{rep2}, and (c) mf_{rep1} < mf_{rep2} < f_{THz}. In all graphs, f_{beat1} and f_{beat2} fluctuated monotonically due to the drift of f_{rep1} and f_{rep2} in the freerunning operation. However, the directions of the temporal fluctuations were different from each other. In Fig. 6(a and c), f_{beat1} and f_{beat2} indicated similar behaviour to each other, namely, a monotonic decrease or increase. On the other hand, in Fig. 6(b), f_{beat1} and f_{beat2} changed in the opposite directions to each other, while their sum remained constant. These behaviours correctly reflect three situations in Fig. 1 and Eq. (4). Finally, we could correctly determine m to be all 3,119 in Fig. 6(a,b and c) based on Eqs (4 to 6).
Next, we measured f_{rep1}, f_{rep2}, f_{beat1}, and f_{beat2} when f_{THz} was fixed at 100,020,240,000 Hz. After acquiring the temporal waveforms for f_{rep1}, f_{rep2}, f_{beat1}, and f_{beat2} at a sampling rate of 20 MHz, we calculated their mean values every 10 ms, which corresponds to a measurement rate of 100 Hz. Figure 7(a,b,c and d) show the temporal changes of the mean values for them. All values temporally fluctuated due to the freerunning behaviour of the laser rather than the fluctuation of f_{THz}. By substituting f_{rep1}, f_{rep2}, f_{beat1}, and f_{beat2} in Eqs (4 to 5), the value of m was determined to be 3,119, as shown in Fig. 7(e). Finally, from Eq. (6), we determined the mean and standard deviation of f_{THz} to be 100,020,239,860 Hz and 125 Hz in repetitive measurements of f_{THz} at a measurement rate of 100 Hz, as shown in Fig. 7(f). Therefore, the relative accuracy and precision of the absolute frequency measurement were 1.4 × 10^{−9} and 1.2 × 10^{−9}, respectively.
Figure 8 shows the measurement precision with respect to the measurement rate and the corresponding measurement time. The measurement precision and the measurement rate showed a tradeoff relation within a range of measurement rates from 1 to 100 Hz. However, the correct determination of f_{THz} was impossible at measurement rates higher than 100 Hz, because the measurement error of the numerator  ± f_{beat2} ± f_{beat1} over the denominator f_{rep2} − f_{rep1} in Eq. (5) makes it impossible to determine m correctly.
Finally, we performed realtime monitoring of f_{THz} when f_{THz} was changed suddenly or slightly. Figure 9 shows the measured f_{THz} when the nominal frequency of the CWTHz test source was first set at 79,626,000,000 Hz, increased by 20,395,080,000 Hz, decreased by 513,120,000 Hz, and then increased by 2,020,260,000 Hz. The measured f_{THz} at each frequency setting was determined to be 79,626,000,029 ± 47 Hz, 100,021,079,989 ± 32 Hz, 99,507,959,988 ± 26 Hz, and 101,528,219,978 ± 36 Hz, respectively. Even though f_{THz} changed across many modes in the dual PCTHz combs, f_{THz} was determined correctly.
Discussion
One may wonder why such high precision was achieved in the realtime measurement of f_{THz} by using the dualPCTHz combs without the stabilization of f_{rep1} and f_{rep2}. The reason is that each PCTHz comb always functions as a frequency ruler with equal intervals and a linear scale regardless of whether or not f_{rep1} and f_{rep2} are stabilized. Such characteristics are inherent in frequency combs. Only if the temporal waveforms for f_{rep1}, f_{rep2}, f_{beat1}, and f_{beat2}, are acquired synchronously, f_{THz} can be determined without the influence of unstabilized f_{rep1} and f_{rep2}, as demonstrated in Figs 7(f) and 9.
The precision of 1.2 × 10^{−9} was achieved at a measurement rate of 100 Hz in the present setup; however, it was 100times worse than that of the previous experiment with two independent freerunning modelocked lasers^{10}. In the instantaneousfrequencycalculation algorithm^{8}, the precision is largely influenced by the signaltonoise ratio (SNR) of the beat signals with f_{beat1} and f_{beat2}^{10}. The beat signals measured by LTInGaAs/InAlAs PCAs in the present setup showed the much lower SNR than the signals measured by LTGaAs PCAs in the previous setup due to high darkcurrent noise in the LTInGaAs/InAlAs PCAs (not shown). Therefore, the difference in precision between them arises from the low SNR in beat signals rather than use of the freerunning dualλ modelocked Er:fibre lasers. In other words, there is still some room to enhance the precision by improving the PCAs.
∆f_{rep} (= 1.63 kHz) in the dualλ modelocked fibre laser used here was relatively high compared with that (typically, less than several tens Hz) in dual modelocked lasers used in the previous research^{10}. In this case, we cannot neglect the dead band in the determination of m. In Fig. 1 and Eqs. (1 to 6), it is assumed that the beat signals at the lowest frequency (freq. = f_{beat1} and f_{beat2}) are generated by the same mode number m of dual PCTHz combs (freq. = mf_{rep1} and mf_{rep2}). The dead band is generated when f_{beat1} and f_{beat2} are generated by different mode numbers of the dual PCTHz combs. Figure 10(a) shows the optical spectrum when f_{THz} exists within the dead band, namely
In this case, f_{beat1} is generated by photoconductive mixing between f_{THz} and (m + 1)f_{rep1}, whereas f_{beat2} is generated by photoconductive mixing between f_{THz} and mf_{rep2}. The dead bandwidth ∆f_{dead} is given by
For example, when f_{THz} = 100 GHz, f_{rep1} ≈ f_{rep2} ≈ 32 MHz, ∆f_{rep} = 1.63 kHz, and m = 3,125, ∆f_{dead} is estimated to be around 5.09 MHz, which corresponds to 16% of the measurement window with the frequency range of f_{rep1} or f_{rep2}. Figure 10(b) shows the realtime monitoring result of f_{THz} when f_{THz} was linearly tuned from 100,024,770,463 Hz to 100,044,423,685 Hz at a sweep rate of 19.653 MHz/s. One can confirm the measurement error of f_{THz} caused by the dead band.
The simplest way to reduce the dead band is to reduce ∆f_{rep}. There is still some room to further reduce ∆f_{rep} of the dualλ modelocked fibre laser down to a few hundred Hz by optimizing the fibre length and dispersion. In this case, it is expected that ∆f_{dead} can be reduced to around 0.5 MHz, which corresponds to 1.6% of the measurement window. Work is in progress to develop a dualλ modelocked fibre laser with lower ∆f_{rep}.
Conclusions
We measured the absolute frequency of CWTHz radiation using dual PCTHz combs induced by a dualλ modelocked fibre laser. To the best of our knowledge, this is the first time such a laser system has been employed for frequency measurement in THz region. Although this laser was operating in the freerunning mode without stabilization of f_{rep1} and f_{rep2}, a relative precision and accuracy of 1.2 × 10^{−9} and 1.4 × 10^{−9} were achieved at a measurement rate of 100 Hz due to the commonmode behaviour of f_{rep1} and f_{rep2}, in addition to the fact that the interval between the PCTHz comb modes was kept equal regardless of the fluctuation in f_{rep1}and f_{rep2}. Furthermore, an abrupt or slight change in f_{THz} could be accurately monitored due to the realtime capability thanks to the use of dual PCTHz combs. Although the dualλ modelocked fibre laser was used in this work for measuring the frequency of CWTHz radiation in real time, it should be possible to apply it to THz spectroscopy and other metrology applications based on dual THz combs, such as ASOPS THz timedomain spectroscopy^{21,22,23,24}, dual THz comb spectroscopy^{25,26,27}, and ASOPS THz impulse ranging^{28}. In particular, the constant ∆f_{rep} in the freerunning operation will enable correct scale conversion of the time axis or frequency axis in these spectroscopic applications. This dualλ modelocked fibre laser will open the door to enhance versatility and practicability in dualTHzcombbased THz measurement systems.
Methods
Freerunning, dualλ modelocked Er:fibre laser oscillator
As shown in Fig. 2(a), the freerunning, dualλ modelocked Er:fibre laser oscillator consists of a 980nm pumped laser diode (LD), a 980/1550 nm wavelengthdivision multiplexer (WDM), a singlemode fibre (SMF), a 2 meter length of erbiumdoped fibre (EDF, Changfei 1022), a polarizationindependent optical isolator (ISO), a homemade singlewall carbon nanotube saturable absorber (SWNTSA), a fibresqueezerbased polarization controller (PC), a 90/10 fibre output coupler (OC), and an inline polarizer (ILP) with two 0.25meterlong polarization maintaining fibre (PMF) pigtails at both ends. The lengths of the commercial singlemode fibres (SMF28 and HI 1060) in the cavity were estimated to be ~3.4 m and ~0.35 m, respectively, and therefore, the total dispersion was estimated to be ~0.063 ps/nm. The SWNTSA had a transmittance of 24% at 1540 nm and was fabricated on an FC/APC ferrule from a ~0.27 wt% SWNT solution by using the optical deposition method. By introducing the ILP with its transmission aligned along the slow axis of the PMF into the ring fibre laser, birefringenceinduced filtering and loss control effects enabled multiwavelength lasing in the cavity^{12,13,19}. With the adjustment of the intracavity polarization state, simultaneous modelocking centred on the 1530nm and 1560nm regions could be realized. ∆f_{rep} was related to the cavity dispersion of the fibre laser, whereas f_{rep1} and f_{rep2} were related to be the fibre length; their values can be further adjusted by optimizing the fibre length and dispersion.
Realtime determination of f_{THz} with dual PCTHz combs
Figure 5 shows a schematic diagram of the setup for measuring the frequency of CWTHz radiation The amplified λ_{1} pulse light at f_{rep1} from one EDFA (EDFA1) was collimated in free space and then focused onto a gap in a freespacecoupled, bowtieshaped, lowtemperaturegrown (LT) InGaAs/InAlAs PCA (PCA1, TERA15BT3, Menlo Systems) by a lens (L), whereas the amplified λ_{2} pulse light at f_{rep2} from the other EDFA (EDFA2) was directly fed into a fibrecoupled, dipoleshaped LTInGaAs/InAlAs PCA detector (PCA2, TERA 15RXFC, Menlo Systems) via an optical fibre. This resulted in the generation of dual PC THz combs: PCTHz comb 1 with a frequency spacing f_{rep1} in PCA1 and PCTHz comb 2 with a frequency spacing f_{rep2} in PCA2.
The CWTHz test source was an active frequency multiplier chain (Millitech AMC10R0000 with multiplication factor = 6, tuning range = 75–110 GHz, and mean power = 2.5 mW), which amplified the output frequency of a microwave frequency synthesizer (Agilent E8257D, linewidth < 0.1 Hz) by a factor of six. Since this test source was phaselocked to a 10 MHz rubidium (Rb) frequency standard (Stanford Research Systems FS725, accuracy = 5 × 10^{−11}, stability = 2 × 10^{–11} at 1 s), its output was CWTHz radiation with a linewidth of less than 0.6 Hz and a frequency accuracy similar to that of the frequency standard. When the CWTHz radiation was incident on both PCA1 and PCA2, photoconductive mixing between the CWTHz radiation and the dual PCTHz combs resulted in the output of a current signal from them. The current signals from PCA1 and PCA2 were amplified and filtered by current preamplifiers (AMP, bandwidth = 10 MHz, transimpedance gain = 10^{5} V/A), and the beat frequencies below half of f_{rep1} or f_{rep2} were extracted as f_{beat1} and f_{beat2}.
Portions of light from the EDFAs were detected with photodetectors (PD, Thorlabs DET01CFC, freq. bandwidth = 1.2 GHz). Since the output signal from the PDs included a fundamental component and a series of harmonic components of f_{rep1} or f_{rep2} within the frequency bandwidth of the PDs, we selected the 30th harmonic component of f_{rep1} or f_{rep2}, namely 30f_{rep1} and 30f_{rep2}, in order to magnify the frequency fluctuation. The components 30f_{rep1} and 30f_{rep2} were electrically mixed with an output signal from a local oscillator (LO, f_{LO} = 961,000,000.00 Hz) using a doublebalanced mixer (M), and the resulting beat signals 30f_{rep1} − f_{LO} and 30f_{rep2} − f_{LO} were extracted by two lowpass filters (LPF). Temporal waveforms for f_{beat1}, f_{beat2}, 30f_{rep1} − f_{LO}, and 30f_{rep2} − f_{LO} were simultaneously acquired by a digitizer (resolution = 14 bit, sampling rate = 20 MHz). From the temporal waveforms, we determined instantaneous values of f_{rep1}, f_{rep2}, f_{beat1}, and f_{beat2} using the instantaneousfrequencycalculation algorithm involving a Fourier transform, digital frequency filtering, an inverse Fourier transform, a Hilbert transform, the time differential of the instantaneous phase, and signal averaging^{8}. Finally, we determined f_{THz} by substituting these values into Eqs. (4 to 6). Since the CWTHz test source, the local oscillator, and the clock signals of the digitizer shared a common timebase signal from the frequency standard, one can evaluate the relative precision of frequency measurement without the influence of the absolute precision of the frequency standard.
Additional Information
How to cite this article: Hu, G. et al. Measurement of absolute frequency of continuouswave terahertz radiation in real time using a freerunning, dualwavelength modelocked, erbiumdoped fibre laser. Sci. Rep. 7, 42082; doi: 10.1038/srep42082 (2017).
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Acknowledgements
The work at Beihang University was supported by the 973 Program (2012CB315601), NSFC (61521091/61435002) and with Fundamental Research Funds for the Central Universities, Beihang PhD Student Funds for Shortterm Visiting Study and the Academic Excellence Foundation of BUAA for PhD Students. The work at Tokushima University was supported by the Exploratory Research for Advanced Technology (ERATO) MINOSHIMA Intelligent Optical Synthesizer Project, Japan Science and Technology Agency (JST), Japan.
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T.Y. and Z.Z. conceived the project. G.H., X.Z., Y.Y., C.L., and M.B. constructed the dualλ modelocked Er:fibre laser. G.H., Tat. Miz., Tak. Min., and Tak. Miz. performed the experiments and analysed the data. G.H., Z.Z., and T.Y. wrote the manuscript. All authors discussed the results and commented on the manuscript.
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Hu, G., Mizuguchi, T., Zhao, X. et al. Measurement of absolute frequency of continuouswave terahertz radiation in real time using a freerunning, dualwavelength modelocked, erbiumdoped fibre laser. Sci Rep 7, 42082 (2017). https://doi.org/10.1038/srep42082
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