Terahertz photonic heterodyne spectral analysis with (sub-) kHz resolution and 6.5 THz frequency coverage

Domain: physics
Published: 2025-11-25
Editorial outcome: major_revision

Abstract
Spectrum analyzers and spectrometers are essential for designing sources, analyzing material properties, layer structures and fingerprinting substances. We present an ultra-wideband, continuous-wave photonic receiver with kHz-level spectral resolution in the terahertz domain for both heterodyne and homodyne detection. Employed as a spectrum analyzer frontend, it records the emitted spectrum of a source under test, assessing spectral purity, spectral shape and undesired frequency components. It outperforms state-of-the-art electronic systems in terms of frequency coverage and system cost with a competitive spectral resolution and noise floor on the few aW/Hz level at room temperature. It covers the important frequencies above 1.5 THz, yet commercially inaccessible, where sources like quantum cascade lasers operate. When combined with a comb-based photonic source, we demonstrate hetero- and homodyne spectroscopy over an unprecedented frequency range from below 100 GHz to 6.5 THz and a very low noise floor. Locking the photonic system to GPS enables tracing back the measured parameters to SI units, being of key importance for metrological applications. The presented setups offer the broadest continuous-wave frequency coverage to date, combined with a sharp spectral resolution, enabling diverse applications ranging from fast non-destructive testing, astronomic high-resolution spectroscopy, to frequency-modulated RADAR.

Introduction
Between optics and electronics, there is the terahertz (THz) frequency range, commonly defined as the frequency range between 100 GHz and 10 THz. Despite a vast growth of research activities in the past two decades, this spectral domain is still much less explored compared to optics and electronics, yet with a desperate need for more powerful sources and systems with high dynamic range and well-defined spectral properties. Key applications are future high-speed wireless communication, with several bands already defined in 6G in the lower THz region1 and more to come in follow-up standards, non-destructive testing and quality control2, as well as spectroscopy3 and imaging4, with particular focus on medically or environmentally relevant topics. The latter includes, amongst others, breath gas analysis5 for non-invasive diagnosis of illnesses, detection of pollutant trace gases6, or medical imaging, e.g., of skin cancer7. A severe obstacle for approaching these applications on a larger scale is the lack of powerful, spectrally pure sources. In order to design, characterize and optimize these, in general, spectrum analyzers are used all across the electromagnetic spectrum from high frequency electronics (electronic spectrum analyzer, ESA) all the way to visible wavelengths (optical spectrum analyzer, OSA), including the Terahertz domain, where this manuscript will demonstrate a photonic spectrum analyzer (PSA) with exceptional specifications. In order to mitigate insufficient source power, coherent systems are frequently used. They benefit from suppressed out of band noise and usually achieve a much higher signal to noise ratio than their direct detection counterparts. Both heterodyne and homodyne photonic setups will be demonstrated in the following.

Historically, the THz domain was either approached by frequency-upscaled electronic devices8 or by down-conversion of optical signals9. Electronic and photonic domains for THz generation and detection were clearly segregated. Nonlinear media and photomixers bridge this gap by combining electronic with photonic approaches. Nonlinear media benefit from high THz powers and large bandwidths, yet lack in efficiency. Resonators increase the coupling efficiency at the expense of tunability10. Photomixers, i.e., photodiodes (PDs) or photoconductors (see section photonic mixer in methods), use two signals for THz generation and detection at their difference frequency11,12. Meanwhile, photonic approaches transition into the electronic domains, e.g. in the form of a low phase noise photonic clock signal13, or photonic local oscillators14, and mixed electronic-photonic integrated circuits (EPICs)15. The highly important field of wireless THz communication benefits from opto-electronic devices directly transforming optical signals, transmitted through a fiber, to a wireless THz signal. However, engineering tools for performance analysis of THz devices, like vector network analyzers and spectrum analyzers, are still purely electronic. They consist of a microwave backbone system equipped with frequency extenders, currently available up to 1.5 THz. The extenders double or triple the microwave baseband frequency several times up to the desired THz frequency or from the THz frequency down to the base band16. These frequency multiplier chains are housed in metallic hollow core waveguides with limited bandwidths of about 50% of their center frequencies17. If a larger frequency range shall be analyzed, several extender bands have to be used. Covering the range of 100 GHz to 1.5 THz requires at least seven different extender chains, yet with strongly increasing cost with increasing frequency. Using several extenders also complicates the experiment as the setup must be altered and recalibrated for every extender band separately. In particular, revealing undesired harmonics is cumbersome. Nonetheless, the electronic system benefits from a Hz- to kHz-level spectral resolution and a very low noise floor.

Meanwhile, first alternatives to the electronic spectrum analyzer (ESA) have been demonstrated. For example, a Hilbert-transform spectrum analyzer based on a high-Tc Josephson junction18 achieves a high scanning speed of up to 4 THz/s and a frequency coverage of at least 1 THz, yet only a resolution of 50 MHz. It requires a cryogenic cooler to operate, limiting its operation to laboratory environments. Interferometer-based spectrum analyzers19 cover a frequency range of 1.5 THz but only achieve a resolution of 3.6 GHz. Pulsed-comb-referenced spectrum analyzers20,21 improve the resolution to the Hz level and cover typically 2-4 THz. Their limitation is the ambiguity of the measured signal requiring special pulsed systems with controllable repetition rates. Even then the system only manages to detect narrowband or single frequency signals. Frequency comb (FC) ptychoscopy22 has the potential to cover a similar frequency range with a resolution in the kHz range while simultaneously enabling measurements of swiftly swept sources by implementing two frequency combs or a dual-frequency comb with different repetition rates and two detectors.

The ambiguity of pulsed comb-based systems can also be overcome by locking continuous-wave lasers to specific comb lines while tuning the comb’s repetition rate, yet with a demonstrated resolution of 200 kHz and a tuning range up to 1.28 THz23. Likewise, high spectral purity can be achieved by locking the CW lasers to different resonances of a high quality factor cavity24, with a sub-Hz frequency stability demonstrated at 1.965 GHz and an accuracy of 6 kHz at 556.936 GHz. Coarse tunability of up to 1.2 THz is achieved by hopping between cavity resonances. The gaps between the resonances are closed by fine-tuning the difference frequency with a Mach-Zehnder modulator. Reference 25 references the CW lasers to a frequency comb, which itself is locked to an optical cavity achieving a terahertz frequency stability of 1.46 Hz. Removing the fiber thermal noise improves the stability further to 2 mHz. Due to the referenced frequency comb this setup is limited to THz frequencies spaced apart by the repetition rate of the FC, with a demonstrated frequency coverage of 1.1 THz. So far, these high-purity continuous-wave systems have not been demonstrated as spectrum analyzers and their maximum demonstrated operation frequency is, to date, below those of commercial ESAs (1.5 THz).

Recently, photonic heterodyne spectrum analyzers have been demonstrated26–29. These utilize continuous-wave (CW) lasers as a local oscillator (LO). An electro-optical comb based on an electro-optical phase modulator at telecom wavelengths covers a frequency range of up to 1 THz with a resolution 1 Hz26. Free-running distributed feedback (DFB) laser diodes enable a difference frequency coverage of up to 4.5 THz at a wavelength of 780 nm29, a resolution of 1.2 MHz at a center wavelength around 1550 nm27. DFB laser diodes at 850 nm referenced to an electronic THz signal reduce the resolution to 100 Hz and the frequency coverage to 1 THz28. These systems rely on CW lasers as well as photoconductive mixers. The highest frequency coverage of these – used in a spectroscopy setup – to date is 5.5 THz30,31.

Here we demonstrate a concept that combines the capability for heterodyne spectrum analysis and high-resolution spectroscopy up to 6.5 THz in a single measurement instrument while referencing the system to GPS for a high absolute frequency accuracy. The heterodyne photonic spectrum analyzer uses a newly established FC-referenced CW laser system and top-of-the-line photoconductive sources and receivers. The laser system has the capability of covering more than 10 THz32 with competitive phase stability33 at a Hz-level spectral resolution34,35 at the lower end of the THz spectrum while sweeping with maximum speeds of 1 THz/s32. The combination with a photoconductor enables characterization of sources from the microwave range all the way up to 6.5 THz and possibly beyond. The speed of the system is eventually limited by post-detection electronics and evaluation, and the tuning speed of the phase-locked CW lasers. For high resolution spectroscopy, the system is expanded in two ways. First, with a photomixer hooked up to a photonic difference FC, phase-referenced to the photonic oscillator, and second with a PD hooked up to the FC-referenced CW laser system enabling a combined frequency coverage from below 100 GHz up to 6.5 THz, the largest frequency coverage of a CW photomixing system to date.

Results
Principle of operation
We employ the same photonic local oscillator (LO) laser signal and Rh:InGaAs30 photoconductive receiver for both the heterodyne spectrum analysis as well as the high-resolution spectroscopy. The optical frequencies (\approx 193 THz) of the lasers are significantly higher than the required LO frequency in the THz region. For the generation of the LO frequency, we employ a set of CW diode lasers (Toptica DL pro and CTL) referenced to an optical FC (Fig. 1a, Toptica DFC Core+) generating two very pure optical tones with one of them tunable over a large range32–35. Heterodyning the two laser signals results in an intensity modulation at their frequency difference, i.e., the LO frequency. A photoconductor (Fig. 1b) absorbs the intensity-modulated light, causing the generation of electron-hole pairs at the same frequency and thus modulation of the conductance at the LO frequency. At the same time, an antenna attached to the photoconductor collects the THz signal of a source, generating a respective voltage at the photoconductor electrodes. The THz signal voltage is multiplied by the varying conductance according to Ohm’s law resulting in a difference frequency output current. If the LO is tuned close to the source frequency, the frequency of the current, termed intermediate frequency (IF) will be small enough in order to be detected with low-noise electronics. The photoconductor essentially mixes the envelope of the laser signal with the incoming THz-signal. In order to approach the thermal noise floor of the photoconductor, we employ a transimpedance amplifier (TEM Messtechnik PDA-S or Femto DHPCA-100) at gains between 10^6 and 10^7 V/A prior to digitizing the signal. Common spectrum analyzers show the power spectral density of this current, which is proportional to the power spectral density of the source. By simply sweeping the LO frequency, we can record the spectrum of any unknown source under test at a resolution defined by the spectral purity of the FC-referenced LO. Given that the source’s power is high enough to be detected, the maximum tuning range is limited only by the tuning range of the LO (here > 10 THz)32 and the sensitivity of the photoconductor, which becomes smaller the higher the frequency. The frequency coverage of the used photoconductors is limited by the Reststrahlen band of the InP substrate to 7 THz. Removing the substrate allows for potential coverage within or possibly even beyond the Reststrahlen band of InP and InGaAs36.

Within all measurements shown in this manuscript, the LO is additionally referenced via an oven-controlled crystal oscillator (OCXO) to a global positioning system (GPS) signal. The OCXO generates an 800 MHz reference signal that phase-locks to the 4th harmonic of the repetition rate of the FC. The additional referencing of the OCXO to the GPS gives the LO absolute frequency accuracy which we verify in a later section.

Spectrum analyzer for unreferenced sources
Spectrum analyzers are mostly used to measure signals that originate from an external source that is not referenced to the analyzer itself. We showcase a PSA by characterizing the spectra emitted from two different THz-sources. The first source is a CW waveguide-integrated (WIN)-photodiode (PD)31 from the Fraunhofer Heinrich-Hertz-Institute driven by the optoelectronic frequency-modulated CW (FMCW)-THz-spectrometer “T-Sweeper”37. Offering continuous scan speeds up to 500 THz/s with a frequency coverage from 50 GHz to more than 4 THz, the T-Sweeper is typically used as real-time THz-spectrometer or photonic THz-RADAR. In contrast to its mostly used FMCW operation, we configure the T-Sweeper to emit a fixed frequency for our measurement. Two 90° off-axis parabolic mirrors in a U-configuration guide the emitted THz-signal from the source to the photoconductive receiver of the photonic spectrum analyzer. Figure 2 shows representative measured spectra at frequencies of 532 GHz (Fig. 2a) and 1.782 THz (Fig. 2b) recorded with a spectral resolution of 240 kHz. The width of the spectral peak ranges between 31.8 ± 2.3 MHz at 532 GHz and 55.4 ± 4.0 MHz at 1.782 THz. The spectral peak ranges are a mixture of linewidth and frequency stability over the course of the measurement. They are about two orders of magnitude larger than the chosen resolution and several orders of magnitude larger than the spectral width of the beat note of the FC-referenced photonic LO which will be discussed further at a later point. Therefore, we confidently attribute the measured linewidth solely to the T-sweeper. We remark that the recorded linewidth and frequency stability of the T-sweeper operated at a fixed frequency may not reflect the performance parameters under fast sweeping. The peaks at both frequencies are well resolved with a peak power of −62 dBm and a noise power below −87 dBm at 532 GHz and a peak power of −75.5 dBm and a noise power of −78.5 dBm at 1.782 THz. The increase in noise power is the result of reduced responsivity within the photoconductive receiver in the PSA due to RC and lifetime roll-off effects12,30. In the PD transmitter, similar roll-off effects are present, leading to the reduction in signal power31. At 1.782 THz, the larger linewidth spreads the power of the THz source out more, further reducing the spectral power density recorded at each frequency point.

In order to showcase the spectral resolution of the photonic spectrum analyzer, a pulsed photonic emitter is used as source under test (SUT) in the second experiment, essentially the transmitter of a THz time-domain system. A modified, unreferenced TOPTICA difference FC (DFC Core+ 200) with an optical laser output power of 60 mW, a repetition rate of 200 MHz, and a central wavelength of 1,560 nm drives a Rh:InGaAs photoconductor38 from the Fraunhofer Heinrich Hertz Institute, biased with up to 200 V. This pulsed THz-source generates a comb of THz-lines spaced by the repetition rate up to a frequency of at least 6.5 THz. Figure 3a) depicts the laser setup schematically.

Figure 3b) shows the spectrum of an individual line at a frequency of 300 GHz of the free running, only passively locked FC. It is measured by setting the spectrum analyzer’s LO to a fixed frequency close to the SUT frequency, measuring the resulting IF signal in time and employing a fast-Fourier transformation. The combined linewidth is only 1.7 ± 1.3 Hz. As both laser systems are independent, the linewidth of 1.7 Hz is a convolution of the individual linewidths and thus represents an upper limit for both. Further, the pulsed laser is not actively locked so it can drift during the course of the measurement mimicking a larger linewidth. We therefore expect that the linewidth of the FC-referenced LO is smaller than that of the pulsed source. The phase noise of the pulsed THz source and of the LO scale about quadratically with the mode order, n35,39. Assuming an n² increase of the phase noise, the extrapolated phase noise from the combined linewidth of 1.7 Hz at 300 GHz remains below 1 kHz even at 6.5 THz. Such narrow linewidths are in agreement with previous findings in ref. 40 where we determined a combined linewidth of 20 Hz at 339.6 GHz of a Menlo Systems time domain source characterized with an electro-optic CW comb that features a linewidth below 1 Hz.

The signal to noise ratio is as huge as 65.8 dB (Fig. 2b) at a measurement time of 1 s, despite that we investigate only a singular line of about 32,500 lines between DC and 6.5 THz emitted by the pulsed source at a total power of approximately 1 mW. The first and most important reason is the about 7 orders of magnitudes smaller linewidth as compared to the previous case (Fig. 2), being similar for both systems and thus making maximum use of the equivalent noise bandwidth and system resolution. The peak is not smeared out over many frequency bins, all spectral power is concentrated in a 1.7 Hz wide narrow frequency window. Second, the frequency component under investigation at 300 GHz is close to the spectral maximum of the pulsed source between 500 GHz and 750 GHz. Above, the spectral power decreases exponentially toward higher frequencies. Third, the spectral response of the photoconductive receiver, characterized with a calibrated CW spectrometer, is lifetime and RC roll-off free below 570 GHz, offering maximum responsivity.

The spectral power is calibrated through determining the responsivity of the spectrum analyzer’s receiver in a homodyne setup where the power is referenced to a calibrated THz power meter (for details see power calibration in methods section and calibration in supplemental material). The noise floor of the calibrated power meter limits the detectable frequency range to 1.6 THz. Relevant roll-off effects of the photoconductive mixer used as receiver are in effect above 1.1 THz enabling a responsivity estimation also for frequencies above 1.6 THz. With the responsivity information and the noise levels determined with the spectrum analyzer, we calculate the displayed averaged noise level (DANL) of the PSA (Fig. 4). Hereby, the DANL represents the noise level of the PSA for a resolution bandwidth (RBW) of 1 Hz. We reach a DANL of −145.6 dBm/Hz at a frequency of 100 GHz, −134 dBm/Hz at a frequency of 1 THz, and an extrapolated DANL of −105 dBm/Hz at 6.5 THz.

kHz-level channel sounding with 4.75 THz coverage
Channel sounding is a technique of searching and identifying different channels for data communication41. Similar to a spectrum analyzer one may want to identify the absolute position, bandwidth and strength of a channel as well as undesired spurious emission into other channels. The frequency stability of the channels often benefit from referencing the signal to a GPS signal. GPS referencing also allows for comparable measurements of the same signal at different locations and times. This is experimentally simulated here by locking both the LO and the FC to the same 10 MHz GPS signal, yet each via its own OCXO (Fig. 5a). With the same THz setup as in the previous experiments, we measured several lines of the pulsed THz source.

Figure 5b) shows the measured spectrum of the pulsed source at 3.25 THz. The combined linewidth is Lorentzian with a width of 80.4 ± 10.4 Hz. Assuming purely quadratic scaling of phase noise with mode order, valid for independent FCs, the phase noise at 3.25 THz should be about 117 times higher compared to the previous 300 GHz measurement, resulting in an expected linewidth of 198 Hz. This is about twice the recorded value of 80.4 Hz. We therefore conclude that 50% of the phase noise is still uncorrelated, which stems from the additive phase noise of the optical phase locked loops, as well as the CW-laser noise outside the locking bandwidth. In other words, the CW-lasers can be considered to a large degree as independent entities despite locking to the same GPS signal. Figure 5c) (orange trace with squares) shows the development of the linewidth with respect to THz frequency for this scenario. It approximately follows a quadratic fit, in agreement with ref. 35. The highest measurable frequency in this configuration was 4.75 THz. We remark that the noise floor at 3.25 THz in Fig. 5b) of −107.8 dB (yet at an equivalent noise bandwidth of 1 Hz) shows the noise floor in direct vicinity to the signal, the actual noise floor at an offset frequency of 35 kHz to the signal is at −112 dB, i.e., another 4.2 dB lower. At a frequency resolution of 1 Hz this value is slightly larger than the estimated DANL of −117.2 dBm/Hz in Fig. 4. This is due to a combination of 1) the noise floor of the post detection electronics that play an increased role with the Fourier transformation mode used here and the frequency resolution of 1 Hz, 2) ground loop effects that influence the noise floor in our laboratory setup and 3) increasing absorbance and reflectance from the InP substrate36.

Spectrometer with 6.5 Terahertz frequency coverage
In order to measure the true signal shape, noise, and stability, a spectrum analyzer strictly requires that the LO and the signal under test are independent. In contrast, spectrometers used for devices under test benefit from locking the LO with the signal under test. Channel sounding with locking to the same GPS signal already reduce the phase noise but for even better noise suppression both source and receiver can be locked to the same OCXO (Fig. 6a). Figure 6b) shows the spectrum of the pulsed source at a frequency of 6.5 THz with a combined (relative) linewidth of only 2.3 ± 1.2 Hz and a signal-to-noise ratio of at least 7 dB for 100 averages. Figure 5c (blue line) also shows that the combined linewidth only slightly depends on the THz frequency and remains below 3 Hz over the whole frequency range. The linewidth corresponds to the remaining uncorrelated noise as well as drifts within the measurement duration irrespective of the linewidth of the individual lasers. The high correlation of both lasers drastically improves the signal-to-noise ratio, highly beneficial for spectroscopic applications. We estimate the power in the mode at 6.5 THz to 7 pW, which is now concentrated in a 2 Hz frequency bin as opposed to an 800 Hz linewidth in the non-referenced configuration, improving the signal to noise ratio by about a factor of 400. This improvement enabled the extension of the operation range very close to the current frequency limit of the photoconductive mixer, which originates from strong reflection and absorption of the Reststrahlen band of its Indium Phosphide substrate. The operation range from < 50 GHz to 6.5 THz in a single setup is by far the largest frequency coverage of any THz system with sub-10 kHz resolution.

Homodyne CW-THz-spectroscopy
Homodyne spectrometers profit from using the same LO signal for both the transmitter and the receiver, reducing common noise and enabling phase measurements. For this we replace the pulsed transmitter with a CW WIN-PD and excite it with the same LO as used for the receiver (Fig. 7a). A lock-in amplifier measures the photocurrent of the photomixing receiver while the LO sweeps the signal in frequency. Figure 7b presents the measured photocurrent of the receiver for frequencies between 100 GHz up to frequencies of 3.5 THz with frequency steps of 1.5625 MHz, acquired in a free-space reflection setup at ambient pressure with four off-axis parabolic mirrors. The measurements used an integration time of 50 µs for which the signal hits the noise floor at 3.6 THz. Longer averaging allows for accessing even higher frequencies30,37. The photocurrent decreases with the roll-off effects in the transmitter and receiver with increasing frequency as discussed earlier. Meanwhile distinct drops in the photocurrent are visible. These stem from absorption of the THz electrical field by water vapor present in the air and are based on rotational excitations of the molecules. The position and linewidth of the absorption lines are functions of the pressure and temperature (for details see method section).

In order to demonstrate the accuracy and resolution of the system, we investigate an almost Doppler-limited line of the water molecule by introducing a vacuum tube into the spectroscopy setup, adding a drop of ammonia water to the tube and evacuating to pressures between 0.020 mbar and 0.046 mbar (for more details on the measurement setup please consider the water vapour absorption spectroscopy section in the supplemental information). The absorption line of water vapor is close to 556.936 GHz (Fig. 7c) and has a linewidth of several GHz at atmospheric pressure and room temperature. Upon reducing the pressure, it becomes limited by the temperature broadened linewidth of 1.62 MHz42 (see Eq. (8) in method section) caused by the optical Doppler effect of gas molecules at thermal velocity. The blue curve in Fig. 7c illustrates the measured water vapor absorption for a pressure of 0.032 mbar with a frequency resolution of 24 kHz, a measurement speed of 11.8 GHz/s, and averaged over 6 measurements. The black curve is a Voigt fit to the measurement data, and the orange line the calculated absorption from the HITRAN database42 with a frequency resolution of 100 kHz, assuming a water vapor to air mixture of 25% ± 10%. The measured peak position is 120 kHz offset to the calculated peak position, corresponding to a relative deviation with respect to the HITRAN data of 215 ppb. The measured linewidth with 1.81 MHz is well resolved and only 1.1% smaller than the linewidth of 1.83 MHz (Fig. 7d) calculated from HITRAN. Given an estimated error of 20% on the pressure measurements, these data confirm the accuracy and reference capability of the LO.

Methods
Photonic local oscillator
The laser engine, used as the LO, combines the stability and accuracy of comb technology with widely tunable CW external cavity diode-lasers (ECDL). The ECDL is optically phase-locked to a mode-locked erbium fiber laser comb with a fixed offset. For continuous phase-lock and tuning, the frequency comb is shifted with an external frequency shifter32 based on serrodyne shifting with 2\pi phase wrapping with an electro-optic phase modulator. The tunable CW ECDL follows the applied frequency shift of the optical comb while inheriting the stability of the comb within the locking bandwidth. The CW laser covers a mode-hop free tuning wavelength range of 100 nm (> 12 THz) around 1550 nm within its and the comb’s spectrum. The external frequency shifting simultaneously minimizes spurious signals in the vicinity of the relevant mode. Pairing the tunable CW laser with a fixed CW laser enables the generation of THz difference frequencies. In this case the phase noise of the difference frequency signal is given by the quadratically scaling phase noise of the optical comb with frequency34 and the additive noise of the CW lasers. Additionally, combining the CW signals with a short pulse output of the frequency comb enables hybrid time- and frequency-domain measurements. Within the system all outputs are locked to the FC. Stabilizing the comb spectrum defines the noise properties. The comb has the option to absolutely reference it to a reference oscillator, e.g., an OCXO, which itself can be disciplined, e.g., to GPS, for SI traceable measurements. The referencing happens with a control circuit that matches the 4th harmonic of the repetition rate of the FC (200 MHz) to the frequency of the OCXO (800 MHz).

Photonic mixer
The photonic mixer driven by the comb-referenced LO is a photoconductor optimized for operation at THz frequencies. Details on the used material Rh:InGaAs as well as typical antenna and electrode designs, can be found elsewhere10,29,30. In the following we only describe the working principle of the photoconductive continuous-wave LO in general. The two tones generated by the LO result in a beat note with a time-dependent laser power of
PL(t) = PL,0(1 + cos[2\pi fLO t + \phi LO]) (1)
where we define the local oscillator frequency as the frequency difference of the two tones, fLO = |\omega 1 - \omega 2|/2\pi. \phi 1 and \phi 2 are the phases of the optical carrier waves and \phi LO = \phi 1 - \phi 2 is the resulting envelope phase. The photoconductor absorbs the beat note generated by the LO, resulting in a conductivity modulation of \sigma \propto PL(t), by generating electron-hole pairs. The proportionality factor depends on a series of parameters, such as the absorption coefficient of the photoconductive layer stack but also the carrier lifetime and mobility of the material and the electrode geometry. The antenna attached to the photoconductor receives at the same time the electric field ESUT(t) emitted by the source under test (SUT) and converts it to a voltage, resulting in a net current of
IIF(t) \propto PL(t)ESUT(t) (2)
The proportionality factor depends again on a variety of parameters, such as the antenna’s radiation resistance, the RC roll-off caused by the combination of the antenna with the photoconductor’s capacitance and a lifetime roll-off. Generally speaking, the prefactor decreases with increasing frequency beyond a few 100 GHz.

For a delta-shaped, spectrally pure LO as approximately provided by the FC-referenced system and a SUT with a frequency fSUT, ESUT(t) = ESUT,0 cos(2\pi fSUT t + \phi SUT); the IF current (i.e. the part of the signal that is not filtered out by slow post detection electronics) becomes
IIF(t) \propto PL,0 ESUT,0 cos(2\pi |fLO - fSUT| t + \phi LO - \phi SUT) (3)
If SUT and LO are not phase-locked as in case of the spectrum analyzer, the phase difference \phi LO - \phi SUT fluctuates randomly over time. Thus, the time-averaged current in Eq. (3) is zero. However, its power spectral density, PSDI remains finite, also for energy conservation reasons,
PSDI(f, fLO - fSUT) = |\mathcal{F} I(t)|2 \propto P2 L,0 E2 SUT,0 \delta(f - |fLO - fSUT|) (4)
where fIF = |fLO - fSUT| is the intermediate frequency where the power spectral density appears and \mathcal{F}(.) is the Fourier transformation. If the SUT features a finite bandwidth the process will map the THz bandwidth to the IF domain. In practice, the IF current in Eq. (3) generated by the photoconductor is pre-amplified by a transimpedance amplifier (TEM Messtechnik PDA-S or Femto DHPCA-100) and subsequently digitized by an analog-to digital conversion card (Advantech PCIE-1840L). The PSA in this manuscript employs two detection methods to determine the PSD of the SUT22. The first requires the LO to be set to one frequency during the course of the measurement. During the measurement time, the time-domain signal is acquired, Fourier transformed and finally squared, providing a “snapshot” of the spectrum around the LO frequency. To cover a larger frequency range, multiple of these are put together using slightly different LO frequencies. The second employs a (digital) low-pass filter in the IF-domain. For this the LO frequency needs to be swept from a starting to an end frequency with a known speed. Any part of the signal that falls into the low-pass filter will be acquired. Finally, squaring the signal provides the PSD \propto E2 SUT,0 of the SUT. Alternatively, the PSD can be directly read out with a low frequency electronic spectrum analyzer operating in the IF domain40. The only missing step is a power calibration in order to determine the spectral power density of the received THz wave.

If Tx and Rx are phase-locked, as in the case of the CW spectrometer operated with the same photonic LO, the phase difference in Eq. (3) does not average out. Further, for the homodyne case fLO - fSUT = 0: Thus, the IF current becomes time-independent, IIF \propto PL,0 ESUT,0 cos[\phi Tx - \phi Rx]. Usually, there is a path length difference between the point where Tx laser signal and Rx laser signal are split and the position of the Rx. This optical path length difference \Delta(nl) results in a linear frequency dependence of the phase difference, \phi Tx - \phi Rx = k0 \Delta(nl) = 2\pi c \Delta(nl) fLO \propto fLO oscillates with the THz frequency, causing homodyne fringes. Figure 7b plots the amplitude of the homodyne fringes vs. THz frequency.

Linewidth and spectral resolution
For simplicity, we assume for now Gaussian spectral shapes of the form
E(f) = E0 exp(-(f - fL)2 / \sigma2) (5)
where \sigma is the e-2 width of the spectral power (e-1 width of the field) and fL the (positive-valued) laser frequency. The envelope of the heterodyned optical wave originates from a product of the fields at the respective colors in the time domain. Spectrally, the product turns into a convolution. For two Gaussian shapes of widths \sigma L1 and \sigma L2 results in a Gaussian with a combined linewidth of the photonic LO of \sigma LO = \sqrt{\sigma2 L1 + \sigma2 L2}. Subsequently, the envelope with a spectral width of \sigma LO is convolved with the THz wave with a width of \sigma SUT. The total width is \sigma tot = \sqrt{\sigma2 LO + \sigma2 SUT}. Therefore, with the knowledge of the linewidth of either the SUT or the LO, the respective other one can be calculated. In any case, both are smaller than the measured linewidth \sigma tot. For Lorentzian or Voigt spectral profiles, it is qualitatively similar, though mathematically more complicated.

Power calibration
The power of the spectra is calibrated with the responsivity R of the Rh:InGaAs photoconductive receiver. The determination of the responsivity requires information on the resulting photocurrent IIF of a homodyne or heterodyne measurement setup with the photoconductive receiver and a measurement of the THz power Pcal of the homodyne system. The responsivity is given as
R(f) = I2(f) / Pcal(f) (6)
Generally speaking, reliable power detection in the THz domain is very challenging and afflicted by large errors. For the power calibrations, we used a pyroelectric detector, calibrated to Si-units at the German national metrology institute PTB (SLT Sensor- und Lasertechnik, THz10). Due to differences in the calibration frequency of 1.4 THz and the measured frequencies, we assume a maximum frequency-dependent error of 30%. The pyroelectric detector has a noise equivalent power of 1 \mu W which enabled the calibration of the photoconductive receiver for the frequency range between 50 GHz and 1.6 THz. For higher frequencies, the source power of the calibration source is below the detection limit of the pyroelectric detector. Therefore, we extrapolated the responsivity for higher frequencies taking into account lifetime and RC roll-off of the photoconductor above 1.1 THz. To confirm the responsivity values, we additionally investigated a CW THz source at a frequency of 95 GHz with the PSA and measured its source power.

Signal-to-noise ratio
The signal-to-noise ratio (SNR) within the measurements is dependent on the noise floor and responsivity of the receiver side, the THz power from the emitter and the linewidth of the signal-under-test and of the LO. All of the sources shown in this manuscript use photomixers (pin diodes or photoconductors) to generate the THz signal. Independent of the used optical signal (pulsed or CW), the power of the signal decreases with increasing frequency for frequencies higher than the roll-off 3 dB-frequencies. For the pulsed variant, additionally, fewer optical modes mix with each other with increasing frequency, further reducing the signal power. The signal path consists in most cases of two parabolic mirrors in a U-configuration, Si lenses and InP substrate within the photomixer’s package and a free-space path of less than 0.5 m. Along the signal path losses, reflection and absorption (i.e., water vapor, see also Fig. 7b) may occur reducing the signal strength inbound to the receiver. The photocurrent generated by the receiver depends on the strength of the incoming electrical field (see Eq. (2)) and the LO frequency. Roll-off effects within the photomixer reduce its responsivity with increasing LO frequency. The noise current of the photomixer is mostly independent of the LO frequency. The lower responsivities at higher frequencies thus require larger signals for successful detection. Additionally, the noise floor is directly proportional to the measurement bandwidth. Smaller measurement bandwidths (i.e., longer integration times) allow for the detection of smaller signals. The system-specific noise floor is therefore frequently given in the unit dB/Hz.

The system is eventually limited by the spectral power density, i.e., the power of the signal within a measurement bandwidth (frequency bin). Spectrally broad signals, as in Fig. 2a and b, distribute the signal power over many frequency bins, reducing the signal-to-noise ratio. As the responsivity of the photoconductors drops with increasing frequency, smaller SNRs lead to smaller usable bandwidths, ranging from DC to the maximum still detectable signal. The result is a lower achievable measurement bandwidth in case of a non-referenced CW signal, while the usable measurement bandwidth increases with better relative stability between the SUT and LO enabling a measurement bandwidth of 6.5 THz with all spectral power concentrated within a 2 Hz frequency bin.

Pressure and temperature broadening
The lifetime of the rotational state \tau of a molecule limits its natural linewidth (typ. 10–100 s kHz) and features a Lorentzian spectral distribution p(f),
p(f) \propto 1 / ((f - f0)2 + (1 / \pi \tau)2) (7)
When two gas molecules collide or their dipole moments perturb each other during a pass by maneuver, the lifetime of the rotational state is lowered. The more molecules per volume are present (i.e. the higher the pressure) the shorter the respective lifetime and the larger the linewidth according to Eq. (7). The pressure broadened linewidth is directly proportional to the pressure, has a Lorentzian shape and reaches linewidths in the few GHz range at normal pressure50. We remark that heavier molecules have larger impact such that foreign gases will cause a different linewidth as a pure gas. In ambient conditions the absorption also experiences Doppler broadening caused by thermal motion of the gas molecules towards and away from the THz source. The Doppler broadening \Delta fD is given by ref. 51
\Delta fD = f \sqrt{8 ln(2) k B T / (m c2)} (8)
where f is the center frequency, kB the Boltzmann constant, T the temperature and m the molecule’s mass. Based on statistical motion of the molecules, Doppler broadening features a Gaussian line shape. The theoretical Doppler limit for water vapor is 1.62 MHz at the 556.936 GHz line at a room temperature of 23 °C.

For the measurements with water vapor under vacuum, we used a spectroscopy setup with a vacuum tube in the THz beam. Beamforming equipment in the form of two lenses and photoconductive transmitter and receiver were outside the vacuum tube, purged with dry air to prevent water absorption at normal pressure outside the tube. A combined membrane pump with a turbomolecular pump enabled pressures as low as 0.001 mbar within the tube. Additional water in form of an ammonia-water solution is added in an extended part of the tube that is separated by a needle valve. For the measurements the needle valve is opened slightly to let water vapor into the tube and depending on the pressure the pumps closed off of the tube. Each measurement consists of three runs of five seconds where each run contains one up and one down scan. During each measurement we monitored the pressure with a pressure gauge. The pressure within the tube changed on average by a factor of 1.5 as the tube is quite leaky. Therefore, each measurement is compared to the maximum pressure within its measurement time window. The pressure gauge has an error of 20% due to a lack of recent calibration. The tube does not contain heating or cooling equipment and was left at room temperature (23 °C), limiting the measurements to the Doppler broadened spectra. The absorption coefficient \alpha is calculated by
\alpha = - ln(I / I0) / L (9)
where I is the measured intensity, I0 the intensity without water vapor, and L the length of the vacuum tube.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors present a comb-based THz spectrometer devised with a photonic local oscillator (LO) generating reference THz\nwaves by photo-mixing a pair of diode lasers (one is fixed, the other tuned) with phase locking to a commercial comb (DFC\nCORE+, Toptica). THZ signal detection is made using Rh:InGaAs photoconductive antenna (PCA) via a transimpedance\namplifier. A series of hetero- and homodyne tests are demonstrated over 100 GHz to 6.5 THz range. The authors claim that\ntheir comb-based setup outperforms state-of-the-art electronic systems in terms of frequency coverage and system cost with\na competitive noise floor and spectral resolution.\nThe concept of comb-based THz spectroscopy over a large spectral range is well established in the community.\nAdditionally, the generation of low-noise THz waves by phase-locking a pair of diode lasers to a stabilized comb has been\nwell demonstrated. In this context, the authors' approach is not considered particularly novel, and the achieved level of\nspectral resolution is not outstanding compared to recent records in the literature. Furthermore, the manuscript requires more\ntechnical details on the experimental setups and test results. Therefore, no favorable recommendation is given for the\nmanuscript to be accepted or considered for publication in Nature Communications.", "reviewer_2": "The authors introduce a wideband photonic analyzer that supports both heterodyne and homodyne detection over an\nimpressive part of the Terahertz domain with a sub-kHz resolution It may be used either as a spectrum analyzer to evaluate\nthe spectral shape and the spectral stability of a source under test or as a tool to perform comb-calibrated optical\nspectroscopy over an unparalleled range from below 100 GHz to 6.5 THz. The analyzer condenses technical approaches\nthat were already demonstrated by the authors, namely the comb-locked frequency swept synthesis developed by Toptica\n(Refs. 28-30) and the generation of tunable THz radiation by laser photo-mixing demonstrated by the Fraunhofer Institute for\nTelecommunications (Ref. 32). Nevertheless, since this combination is shown to provide a paradigmatic shift in the\nsynthesis and in the analysis of THz signals, I recommend the publication of this paper provided that the authors address\ntwo minor revisions and one remark.\n- I would better emphasize, perhaps with an experimental example, the metrological attitude of the spectrometer in the THz\ndomain, which naturally derives from the comb-calibrated frequency scale.\n- I would better comment the poor signal-to-noise ratios shown in Fig. 2b and 5b. This seems to conflict with the good noise\nfigures shown in Table I.\nRemark: there is an intensive advertisement in Figs. 1, 3, 5, 6.of the frequency comb source produced by Toptica, namely\nthe DFC core: name and model of the used comb source should definitely appear just once in the text (and not in the\nfigures). This is important also because the paper already enforces Toptica’s proprietary technology on the comb-calibrated\nfrequency-swept synthesizer. The paper should remain agnostic, at least to a reasonable level, with respect to industrial\ninterests.", "reviewer_3": "The work reported by Krause et al. demonstrates a THz spectrum analyzer with high resolution which covers a broad range\nof frequencies. Their concept takes advantage of a frequency comb to create two pure optical tones from two diode lasers,\none at a fixed frequency and the other with a tunable frequency. By heterodyning these two optical tones, the authors\nmodulate at a precise LO frequency the conductivity of a photoconductive antenna that is able to record THz from an\nexternal source. As the external THz signal mixes with the tunable LO frequency, low noise electronic can be used to record\nthe spectrum of the external THz source with a precision defined by the excellent spectral purity of the comb-reference LO.\nThe authors also demonstrate that their photoantenna allows the detection of frequencies up to 6.5 THz. The authors\ndemonstrate the performance of their system in 4 experiments, which are the last 4 sub-sections of the Results section. They\nuse different THz sources and configuration while reporting on the spectral resolution, noise and spectral range of their\nreceiver.\nThe manuscript contains findings that will be of interest to experimentalists working in the field of THz source\ncharacterization. However, the authors do not explicitly state the novelty aspects allowing their technique to achieve kHz-\nlevel resolution over a spectral band ranging from 0.1 to 6.5 THz. In fact, the technique seems to overlap significantly with\nsome of the previous literature. As mentioned by the authors, the concept of using photonic heterodyne spectrum analyzers\nfor THz detection has already been established in Ref [22-25]. Furthermore, details about the broadband Rh:InGaAs\nphotoconductive receiver was already reported in Ref [26]. Finally the concept referencing a CW laser to a comb was\nreported as early as 2021 by some of the same authors in Ref [28].\nComments:\nI find very interesting the concept of referencing the LO to an Oven Controlled Crystal (Xtal) Oscillator (OCXO), which is itself\nreferenced to a 10 MHz reference signal locked to GPS. This discussion and the implication of this scheme are a bit hidden\nin the current version of the manuscript. I think they could be emphasized to amplify the impact of this work.\nThe authors claim that their receiver is capable of resolving frequencies up 10 THz. It’s not clear if this is possible though,\nsince it has not been demonstrated in this work. Carrier lifetime in the photoconductor material could notably impose a\nfundamental spectral limit. The authors also mention that “the Reststrahlenband of the InP substrate of the photoconductive\nmixer will limit the frequency coverage to about 7 THz”. This might also be a fundamental limit as it is not clear how the\nreceive would perform without this substrate. Therefore, the authors must refer to a maximum frequency detection reaching\n6.5 THz (which is demonstrated in this paper) instead of 10 THz. The authors must also change the wording in their abstract\nwhich also seems to indicate that their receiver operate up to 10 THz: “ We present an ultra-wideband, continuous-wave\nphotonic receiver with kHz-level spectral resolution in the terahertz domain (100 GHz-10 THz)”.\nThe paper mentions some limitations of their receiver due to the spectral fluence of the source, e.g. at Line 149. A more in-\ndepth discussion would be necessary to determine how the fluence of the source may limit the performances of their\nreceiver.\nIn the section “Spectrum analyzer for unreferenced sources”, the authors should show the full spectrum from 0.1 to 6.5 THz\nin additional to the resolution of a single comb line in Fig. 3b.\nThe authors have showed homodyne CW THz-spectroscopy in the paper with an integration time of 50 µs where the signal\nis distinguishable until 3.5 THz. One of their previous articles show a spectrum reaching 5 THz with an integration time of\n300 ms (Ref [26]). I recommend using 300 ms here also to allow for a better comparison between this configuration and the\nprevious one used in Ref. 26.\nPlease check: the abbreviation of oven-controlled crystal (xtal) oscillator should be OCXO, not OXCO.\nRegarding the sentence: “While a spectrum analyzer strictly requires that the LO and the signal under test are independent\nin order to measure the true signal shape, noise and stability, this independence is undesired in spectrometers.”, the authors\nshould provide more information to explain why they are making these assumptions. It is advantageous (but maybe not\nnecessary) that a spectrum analyzer is independent from the signal it analyzes, but it is less clear why this independence is\n“undesired” for spectrometers. Most spectrometers don’t have any “dependence” with the source they characterize.\nThis sentence: “Fig. 6b) shows that locking to a common reference allows to extend to a maximum frequency of 6.5 THz”,\nit’s not clear. First, Fig. 6b only shows a power signal, not a comparison for locked and unlocked signals. Also, I believe that the\nauthors are making a confusing shortcut: using the same OCXO probably leads to an improved signal-to-noise, this in turns\nmight lead to an increase in the detection spectral range. This should be clarified.\nThe sentence “Key applications are future high-speed wireless communication, with several THz bands already defined in\n6G [1]” could be misleading because the Ref [1] mentions that frequencies between 1 THz and 3 THz have not yet been\ndefined as this spectral region can be used by both active and passive services. Plus, nothing is mentioned in Ref [1] about\nfrequencies above 3 THz.\nThis sentence: “For the highly important field of THz wireless communication an opto-electronic device is even a\nprerequisite to transform the optical signal, transmitted through a fiber, to a wireless THz signal.” should be removed since\nthe statement is not always true. For example, a nonlinear medium could be used to transform the optical signal into a\nwireless THz signal.\nThis sentence could be misleading: “The extenders double or triple the microwave baseband frequency several times up to\nthe desired THz frequency or from the THz frequency down to the base band [15].”. Ref 15 demonstrates this concept up to\nThere’s no verb in this sentence: “For example, a Hilbert-transform 66 spectrum analyzer based on a high-Tc Josephson\njunction [17] with a high scanning speed of up to 4 67 THz/s and a frequency coverage of at least 1 THz, yet only reaching a\nresolution of 50 MHz.”\nThis sentence is long and confusing: “These utilize continuous-wave (CW) lasers as local oscillator (LO) – namely, an\nelectro-optical comb based on an electro-optical phase modulator at telecom wavelengths with a frequency coverage of up\nto 1 THz and a resolution of 1 Hz [22], free-running distributed feedback (DFB) laser diodes with a difference frequency\ncoverage of up to 4.5 THz at a wavelength of 780 nm [25] and a resolution of 1.2 MHz at a center wavelength around 1550\nnm [23] or DFB laser diodes at 850 nm referenced to an electronic THz signal with a frequency coverage of 1 THz and a\nresolution of 100 Hz [24].”", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response to reviewers on Nature Communications manuscript NCOMMS-24-72395-T\nDear Reviewers,\nWe sincerely thank you for the comments and suggestions on the manuscript. Please find below a\ndetailed response to each of the remarks individually. We excuse for the long duration of the revision.\nIt was due to the necessity of taking new data, yet requiring to assemble a new gas spectroscopy setup.\nWe hope to have improved the manuscript to allow for further consideration.\nYours sincerely,\nBenedikt Krause\n(Corresponding author, in the name of all authors)\nReviewer #1, Concern #1: The authors’ approach is not particularly novel and the achieved level of\nspectral resolution is not outstanding compared to recent records in the literature.\nAuthor response: To address this concern of the reviewer, citations for the statement would be\nhelpful. Comparing the current work to state-of-the-art, including the references given in the paper,\nwe would like to point to the following results that significantly exceed previous work:\n1.) Frequency coverage: We achieved a frequency coverage from < 100 GHz to 6.5 THz under\ncontinuous-wave operation with semiconductor photomixing devices, excelling the state-of-the-\nart by 1 THz (5.5 THz in Refs. 26 and 27). Such frequency coverage was only accessible to date with\npulsed time domain systems that offer about a million times lower spectral resolution.\n2.) Tuning speed and no ambiguity: The system is easily tunable over the whole range in a plug & play\nconfiguration. When compared to comb-based pulsed systems, the presented system is not\nlimited to individual comb lines, there is also no ambiguity which mixing product of which comb\nlines is currently being detected. Instead, the photonic LO system, ALTAS, is easily and extremely\nquickly (up to ~1 THz/s) tunable and is truly CW.\n3.) Low noise floor: We achieve a displayed average noise level/noise floor better than -145 dBm/Hz\n(Fig. 4; corresponding to 3 aW for a 1 Hz noise bandwidth) between 100 GHz and 200 GHz and still\n-134 dBm/Hz, corresponding to 40 aW for 1Hz noise bandwidth at 1 THz. These values are by far\nthe lowest noise floors for photonic receivers in the literature and are at the same level as the\nbest electronic spectrum analyzers.\nFurther, to the best knowledge of the authors, the manuscript is the first to combine a pulsed photonic\nTHz source with a CW photonic THz receiver for spectrometer measurements. Simultaneously, the LO\nshows a competitive linewidth with 1.7 Hz at 300 GHz and less than 1 kHz at 6 THz with the option to\nlock the LO to GPS allowing for referenceable measurements basically anywhere on earth with\nexpected similar performance. We are aware that there are demonstrated combs with (much) lower\nlinewidth, but they needed complicated and expensive locking to frequency standards, e.g. hydrogen\nmasers or atomic clocks.\nFor comparison within the scope of Nature journal publications: we found recently published papers\nwith similar linewidths but considerably lower frequency coverage and considerably higher noise\nfloors: Nature Photonics 18, 1230-1231 (2024); Nature Communications 14, 7162 (2023).\nFor further improvements to our contribution with focus on metrological applications please also see\nthe responses to reviewer #2, concern #1 and reviewer #3, concern #1. We conclude that the system\npresented in our paper outperforms the state of the art in many ways, in particular in terms of\nfrequency coverage and noise floor.\nAuthor action: We incorporated measurements on the absorption spectra of an ammonia solution\nunder vacuum to compare the accuracy of the LO to nature.\n“In order to demonstrate SI unit tracability and resolution of the system, we investigate pressure\nbroadening of the ammonia molecule by introducing a vaccum tube into the spectroscopy setup,\nadding a 25% ammonia solution to the tube and evacuating to pressures between 0.018 mbar and\n20.6 mbar (for more details on the measurement setup please consider the supplemental\ninformation). The absorption line of ammonia is close to 572.5 GHz (Fig. 7c) and has a linewidth of\nseveral GHz at atmospheric pressure and room temperature. Upon reducing the pressure it becomes\nlimited by the temperature broadened linewidth of 1.72 MHz for pressures below 0.1 mbar [39] (Fig.\n7e, orange curve). The blue curve in Fig. 7c illustrates the measured absorbance for a pressure of\n0.041 mbar with a frequency resolution of 24 kHz and averaged over 6 measurements. The black curve\nis a Voigt fit to the measurement data and the orange line the calculated absorption from the HITRAN\ndatabase [39] with a frequency resolution of 100 kHz. The measured peak position is 80 kHz offset to\nthe calculated HITRAN peak position confirming the accuracy and reference capability of the LO. The\nmeasured linewidth with 2.4 MHz is well resolved and slightly larger than the theoretical Doppler\nlimited linewidth of 1.72 MHz which may be attributed to foreign broadening caused by water\nmolecules present from the ammonia solution. With increasing pressure in the tube, i.e. at 16 mbar\n(Fig. 7d), the measured linewidth increases in good agreement with the calculated absorption (Fig. 7e)\nyet faces an up-shift for the FWHM resulting from the foreign broadening. Fixing the Gaussian\ncomponent of the Voigt fit, as we do not expect a temperature change, the measured Lorentzian part,\nresponsible for the pressure broadening, (represented by Г in Fig. 7f) increases similar to the HITRAN-\ncalculated value with a similar upshift as the FWHM.” (lines 298-317)\nReviewer #1, Concern #2: The manuscript requires more technical details on the experimental setups\nand test results.\nAuthor response: We are happy to introduce more technical content. For further details, please also\nsee reviewer #2, concern #2, reviewer #3, concerns #1 and #3.\nAuthor action: We added further details within the manuscript, the method section and the\nsupplementals and believe to have captured all important information. In case we miss important\ninformation please let us know which ones, we are happy to include them.\n“Within all measurements shown in this manuscript the LO is additionally referenced via an oven-\ncontrolled crystal oscillator (OCXO) to a global positioning system (GPS) signal. The OCXO generates an\nadditional referencing of the OCXO to the GPS gives the LO excellent absolute frequency accuracy\nwhich we verify in a later section.” (lines 131-135)\n“In practice, the IF current in Eq. (3) generated by the photoconductor is pre-amplified by a\ntransimpedance amplifier (TEM Messtechnik PDA-S or Femto DHPCA-100) and subsequently digitized\nby an analog-to digital conversion card (Advantech PCIE-1840L). The PSA in this manuscript employs\ntwo detection methods to determine the PSD of the SUT [22]. The first requires the LO to be set to one\nfrequency during the course of the measurement. During the measurement time, the time-domain\nsignal is acquired, Fourier transformed and finally squared leaving us with a “snapshot” of the\nspectrum around the LO frequency. To cover a larger frequency area, multiple of these are put\ntogether using slightly different LO frequencies. The second employs a (digital) low-pass filter in the\nIF-domain. For this the LO frequency needs to be swept from a starting to an end frequency with a\nknown speed.” (lines 424-433)\n“For the measurements with the ammonia solution under vacuum we used a spectroscopy setup with\na vacuum tube in the THz beam. Beamforming equipment in the form of two lenses and\nphotoconductive transmitter and receiver were outside the vacuum tube. A combined membrane\npump with a turbomolecular pump enabled pressures as low as 0.001 mbar within the tube. The\nammonia solution is added in an extended part of the tube that is separated by a needle valve. For the\nmeasurements the needle valve is opened slightly to let ammonia vapor into the tube and depending\non the pressure the pumps closed off of the tube. Each measurement consists of three runs of five\nseconds where each run contains one up and one down scan. During each measurement we monitored\nthe pressure with a pressure gauge. The pressure within the tube changed on average by a factor of\n1.5 as the tube is quite leaky. Therefore, each measurement is compared to the average pressure\nwithin its measurement time window. The tube does not contain heating or cooling equipment and\nwas left at room temperature (23 °C) limiting the measurements to the Doppler broadened spectra.”\n(lines 521-532)\n“For the calibration of the heterodyne measurements, we employ the responsivity (see eq. (6))\nacquired from homodyne measurements with the employed Rh:InGaAs photoconductive receiver. The\nhomodyne system employs the same local oscillator signal for both the transmitter and receiver. The\ntransmitter is a waveguide-integrated photodiode provided by the Fraunhofer Heinrich-Hertz-Institute\n(HHI) and the local oscillator consists of a Keysight 81960A at 1540 nm, along with a tunable Keysight\n81608A at longer wavelengths. Their difference frequency is the local oscillator frequency. Both the\ntransmitter and the receiver are driven by an optical power of 30 mW each. A lock-in amplifier\nmodulates the transmitter bias with a sinusoidal shape that also provides the reference for\ndemodulation of the received signal. This measurement determines the photocurrent 𝐼 of the\n𝑅\nphotoconductive receiver in response to a given electrical field on the input side. Following the\nresponsivity equation (Eq. 6 in the methods section), the photocurrent is squared and the power of\nthe calibration source determined by a gauged pyroelectric detector (SLT Sensor- und Messtechnik\nTHz10). This pyroelectric detector is calibrated at a frequency of 1.4 THz at the German National\nMetrology Institute PTB and possesses a noise floor of 1 µW.” (Supplementals lines 5-18)\nReviewer #2, concern #1: I would better emphasize, perhaps with an experimental example, the\nmetrological attitude of the spectrometer in the THz domain, which naturally derives from the comb-\ncalibrated frequency scale.\nAuthor response: We thank the reviewer for the suggestion. Due to the direct locking of the LO to GPS,\nthe system should have an excellent absolute frequency accuracy. We investigate this by measuring\nthe absorbance of an ammonia solution at 572.5 GHz at pressures between 0.018 mbar and 20.6 mbar.\nAs we cannot control the temperature within the vacuum tube, we are limited by the Doppler\nbroadening which is 1.71 MHz at room temperature for ammonia. The acquired data has a selected\nfrequency resolution of 24 kHz achieving good agreement to calculated data based on the HITRAN\ndatabase.\nAuthor action: We incorporated absorption measurements of an ammonia solution under vacuum into\nthe section “homodyne CW-THz-Spectroscopy” and moved the silicon wafer reflectance measurement\nto the supplemental material.\n“Locking the photonic system to GPS enables tracing back the measured parameters to SI units, being\nof key importance for metrological applications.” (lines 23-25)\n“Here we demonstrate a concept that combines the capability for heterodyne spectrum analysis and\nhigh-resolution spectroscopy up to 6.5 THz in a single measurement instrument while referencing the\nsystem to GPS for a high absolute frequency accuracy.” (lines 90-92)\n“GPS referencing also allows for comparable measurements of the same signal at different locations\nand times.” (lines 228-230)\n“HOMODYNE CW-THz-SPECTROSCOPY\nHomodyne spectrometers profit from using the same LO signal for both the transmitter and the\nreceiver, reducing common noise and enabling phase measurements. For this we replace the pulsed\ntransmitter with a CW WIN-PD and excite it with the same LO as used for the receiver (Fig. 7a). A lock-\nin amplifier measures the photocurrent of the photomixing receiver while the LO sweeps the signal in\nfrequency. Fig. 7b) presents the measured photocurrent of the receiver for frequencies between 100\nGHz up to frequencies of 3.5 THz with frequency steps of 1.5625 MHz, acquired in a free-space\nreflection setup at ambient pressure with four off-axis parabolic mirrors. The measurements used an\nintegration time of 50 µs for which the signal hits the noise floor at 3.6 THz. Longer averaging allows\nfor accessing even higher frequencies [27, 34]. The photocurrent decreases with the roll-off effects in\nthe transmitter and receiver with increasing frequency as discussed earlier. Meanwhile distinct drops\nin the photocurrent are visible. These stem from absorption of the THz electrical field by water vapor\npresent in the air and are based on rotational excitations of the molecules. The position and linewidth\nof the absorption lines are functions of the pressure and temperature (for details see method section).\nIn order to demonstrate SI unit tracability and resolution of the system, we investigate pressure\nbroadening of the ammonia molecule by introducing a vaccum tube into the spectroscopy setup,\nadding a 25% ammonia solution to the tube and evacuating to pressures between 0.018 mbar and\n20.6 mbar (for more details on the measurement setup please consider the supplemental\ninformation). The absorption line of ammonia is close to 572.5 GHz (Fig. 7c) and has a linewidth of\nseveral GHz at atmospheric pressure and room temperature. Upon reducing the pressure it becomes\nlimited by the temperature broadened linewidth of 1.72 MHz for pressures below 0.1 mbar [39] (Fig.\n7e, orange curve). The blue curve in Fig. 7c illustrates the measured absorbance for a pressure of\n0.041 mbar with a frequency resolution of 24 kHz and averaged over 6 measurements. The black curve\nis a Voigt fit to the measurement data and the orange line the calculated absorption from the HITRAN\ndatabase [39] with a frequency resolution of 100 kHz. The measured peak position is 80 kHz offset to\nthe calculated HITRAN peak position confirming the accuracy and reference capability of the LO. The\nmeasured linewidth with 2.4 MHz is well resolved and slightly larger than the theoretical Doppler\nlimited linewidth of 1.72 MHz which may be attributed to foreign broadening caused by water\nmolecules present from the ammonia solution. With increasing pressure in the tube, i.e. at 16 mbar\n(Fig. 7d), the measured linewidth increases in good agreement with the calculated absorption (Fig. 7e)\nyet faces an up-shift for the FWHM resulting from the foreign broadening. Fixing the Gaussian\ncomponent of the Voigt fit, as we do not expect a temperature change, the measured Lorentzian part,\nresponsible for the pressure broadening, (represented by Г in Fig. 7f) increases similar to the HITRAN-\ncalculated value with a similar upshift as the FWHM.” (lines 284 – 317)\n“PRESSURE AND TEMPERATURE BROADENING\nThe lifetime of the rotational state 𝜏 of a molecule limits its natural linewidth (typ. 10-100s kHz) and\nfeatures a Lorentzian spectral distribution 𝑝(𝑓),\n𝐴\n𝑝(𝑓)= . (7)\n(𝑓−𝑓0 )2+(\n𝜋\n1\n𝜏\n)\nWhen two gas molecules collide or their dipole moments perturb each other during a pass by\nmaneuver, the lifetime of the rotational state is lowered. The more molecules per volume are present\n(i.e. the higher the pressure) the shorter the respective lifetime and the larger the linewidth according\nto Eq. (7). The pressure broadened linewidth is directly proportional to the pressure, has a Lorentzian\nshape and reaches linewidths in the few GHz range at normal pressure [49]. We remark that heavier\nmolecules have larger impact such that foreign gases will cause a different linewidth as a pure gas. For\nthe case of ammonia in water shown here, there is only minor alteration as water (18 u) and ammonia\n(18 u) have very similar molecular mass, though the amplitude, A in Eq. (7), obviously becomes smaller\nthe more water is present. In ambient conditions the absorption also experiences Doppler broadening\ncaused by thermal motion of the gas molecules towards and away from the THz source. The Doppler\nbroadening 𝛥𝑓 is given by [50]\n𝐷\n𝛥𝑓 = 𝑓√\n8ln(2)𝑘𝐵𝑇\n, (8)\n𝐷 𝑚𝑐2\nwhere 𝑓 is the center frequency, 𝑘 the Boltzmann constant, 𝑇 the temperature and 𝑚 the molecule’s\n𝐵\nmass. Based on statistical motion of the molecules, Doppler broadening features a Gaussian line shape.\nThe theoretical Doppler limit for ammonia is 1.71 MHz at the 572.5 GHz line at a room temperature of\n23 °C.\nFor the measurements with the ammonia solution under vacuum we used a spectroscopy setup with\na vacuum tube in the THz beam. Beamforming equipment in the form of two lenses and\nphotoconductive transmitter and receiver were outside the vacuum tube. A combined membrane\npump with a turbomolecular pump enabled pressures as low as 0.001 mbar within the tube. The\nammonia solution is added in an extended part of the tube that is separated by a needle valve. For the\nmeasurements the needle valve is opened slightly to let ammonia vapor into the tube and depending\non the pressure the pumps closed off of the tube. Each measurement consists of three runs of five\nseconds where each run contains one up and one down scan. During each measurement we monitored\nthe pressure with a pressure gauge. The pressure within the tube changed on average by a factor of\n1.5 as the tube is quite leaky. Therefore, each measurement is compared to the average pressure\nwithin its measurement time window. The tube does not contain heating or cooling equipment and\nwas left at room temperature (23 °C) limiting the measurements to the Doppler broadened spectra.\nThe absorption coefficient 𝛼 is calculated by\nln(\n𝐼𝑁𝐻3)\n𝛼 = − 𝐼0 , (9)\n𝑑\nWhere 𝐼 is the intensity of the reference measurement, 𝐼 the ammonia measurement and 𝑑 =\n0 𝑁𝐻3\n33 cm the mean THz path length inside the vacuum tube.” (lines 474-536)\n“AMMONIA ABSORPTION SPECTROSCOPY\nFor the absorption spectroscopy we applied the LO to both the photoconductive transmitter and\nreceiver (Fig. S3). These were positioned opposite each other, each with a TPX-lens for beam forming.\nIn between the lenses we positioned an evacuated cell that can be filled with a gas under test at a\ndesired pressure. The vacuum cell has two fused silica windows positioned under their Brewster angle\nto reduce reflections. Separated by a needle valve, we attached a probe volume to the vacuum cell\nwhere we deposited a drop of ammonia solution. On the other side the vacuum tube connects to a\nflooding vent, a pressure gauge and a valve to the pump. The pump is a combined unit of a membrane\npump and a turbomolecular pump. During the measurements the pressures of the pressure gauge are\nlogged. A bias of -1.2 V is applied to the photodiode transmitter. For the measurements the output of\nthe receiver is amplified by 3.3∙105 V/A in a TEM Messtechnik PDA-S and acquired by a LeCroy HDO\noscilloscope at 500 kSa/s. For the measurement the LO is swept for 15 GHz up and down surrounding\nthe ammonia absorption peak. Each measurement is the average of the Hilbert transformation of 3 up\nand down sweeps.\nBefore the start of the measurements we evacuated the cell to pressures below 0.01 mbar and partially\nthe probe chamber to remove remaining air. The finite gas pressure of water and ammonia filled the\nprobe volume with an ammonia-water mixture. Care was taken to slowly flood the gas chamber with\nthe ammonia-water gas mixture by slowly opening the needle valve with the pumps running and\nconnected to the vacuum chamber. Except for the lowest pressures, we cut off the vacuum pumps\nafter approximately 2 minutes and slowly let more probe into the test cell. The leak tightness of the\nvacuum cell is more in the order of 10 mbar over the course of 30 minutes, i.e. the pressure-broadened\nlinewidths contains some foreign broadening by leakage oxygen and nitrogen into the chamber.”\n(Supplementals lines 65-86)\nReviewer #2, concern #2: I would better comment the poor signal-to-noise ratios shown in Fig. 2b and\n5b. This seems to conflict with the good noise figures shown in Table I.\nAuthor response: Table I shows the noise floor for the best realization of the system, where source\nand receiver are phase-locked, common noise is almost perfectly cancelled, and all spectral power is\nessentially collected in a single spectral bin. Instead, Fig. 2b shows the case of an unlocked CW system\nwith MHz bandwidth whose spectrum is analyzed by the comb-referenced system. For spectral\nanalysis, the source under test and the characterization system must not be phase-locked in order to\nresolve the true spectrum. The CW source’s power is spread out over its whole linewidth of up to\nspectral power was collected in a single 2.3 Hz frequency bin as in Fig. 6b).\nFig. 5 b shows a partially locked case, where the same GPS reference is used but two different OXCOs.\nAs seen from the orange line in Fig. 5c, still quite some non-common noise remains between the source\nand the receiver widening the linewidth and reducing the SNR. Only in Fig. 6 we show a result with\nalmost perfect common noise cancellation that enabled increasing the spectral coverage from\n4.75 THz (Fig. 5b shows 3.25 THz) to 6.5 THz (Fig. 6b). Please also consult our response to reviewer #3\nconcern #3 for similar changes.\nAuthor action: We added some more detail within the text describing the figures (l. 162-168 and 243-\n250) in order to clarify the differences and added a section on the SNR into the methods.\n“The peaks at both frequencies are well resolved with a peak power of -62 dBm and a noise power\nbelow -87 dBm at 532 GHz and a peak power of -75.5 dBm and a noise power of -78.5 dBm at 1,782\nGHz. The increase in noise floor is the result of reduced responsivity within the photoconductive\nreceiver in the PSA due to RC and lifetime roll-off effects [12, 27]. In the PD transmitter similar roll-off\neffects are present leading to the reduction in signal power [28]. At 1,782 GHz the larger linewidth\nspreads the power of the THz source out more, further reducing the spectral power density recorded\nat each frequency point.” (lines 162-168)\n“We remark that the noise floor at 3.25 THz in Fig. 5 b) of -107.8 dB (yet at an equivalent noise\nbandwidth of 1 Hz) shows the noise floor in direct vicinity to the signal, the actual noise floor at an\noffset frequency of 35 kHz to the signal is at -112 dB, i.e. another 4.2 dB lower. At a frequency\nresolution of 1 Hz this value is slightly larger than the estimated DANL of -117.2 dBm/Hz in Fig. 4. This\nis due to a combination of 1) the noise floor of the post detection electronics that play an increased\nrole with the Fourier transformation mode used here and the frequency resolution of 1 Hz, 2) ground\nloop effects that influence the noise floor in our laboratory setup and 3) increasing absorbance and\nreflectance from the InP substrate [33].” (lines 243-250)\n“SIGNAL-TO-NOISE RATIO\nThe signal-to-noise ratio (SNR) within the measurements is dependent on the noise floor and\nresponsivity of the receiver side, the THz power from the emitter and the linewidth of the signal-under-\ntest and of the LO. All of the sources shown in this manuscript use photomixers (pin diodes or\nphotoconductors) to generate the THz signal. Independent of the used optical signal (pulsed or CW),\nthe power of the signal decreases with increasing frequency for frequencies higher than the roll-off\n3dB-frequencies. For the pulsed variant, additionally, fewer optical modes mix with each other with\nincreasing frequency, further reducing the signal power. The signal path consists in most cases of two\nparabolic mirrors in a U-configuration, Si lenses and InP substrate within the photomixer’s package and\na free-space path of less than 0.5 m. Along the signal path losses, reflection and absorption (i.e. water\nvapor, see also Fig. 7b) may occur reducing the signal strength inbound to the receiver. The\nphotocurrent generated by the receiver depends on the strength of the incoming electrical field (see\nEq. (2)) and the LO frequency. Roll-off effects within the photomixer reduce its responsivity with\nincreasing LO frequency. The noise current of the photomixer is mostly independent of the LO\nfrequency. The lower responsivities at higher frequencies require thus larger signals for successful\ndetection. Additionally, the noise floor is directly proportional to the measurement bandwidth. Smaller\nmeasurement bandwidths (i.e. longer integration times) allow for the detection of smaller signals. The\nsystem specific noise floor is therefore frequently given in the unit dB/Hz.\nThe bandwidth is limited on the lower end by the LO linewidth. The system essentially measures the\nspectral density, i.e. the power of the signal within a measurement bandwidth (frequency bin).\nSpectrally wide LOs or signals -such as the one in Fig. 2- are distributed over many frequency bins,\nreducing the power per bin and thus the signal to noise ratio. As the responsivity of the\nphotoconductors drop with increasing frequency smaller SNRs lead to smaller usable bandwidths,\nranging from DC to the maximum still detectable signal. This lead to the result that the ~50 MHz wide\nCW signal featured the lowest usable bandwidth, while the usable bandwidth increased the better the\nrelative stability of SUT and LO, yet with 6.5 THz bandwidth for close to perfect relative stability where\nall spectral power is concentrated within a 2 Hz frequency bin. “ (lines 474 – 500)\nReviewer #2, concern #3: There is an intensive advertisement in Figs. 1, 3, 5, 6.of the frequency comb\nsource produced by Toptica, namely the DFC core: name and model of the used comb source should\ndefinitely appear just once in the text (and not in the figures).\nAuthor response: We are sorry, we just wanted to clarify the system composition in order to make our\nfindings reproducible.\nAuthor action: We have replaced the wording DFC core with frequency comb (FC) in basically all cases.\nReviewer #3, concern #1: I find very interesting the concept of referencing the LO to an Oven\nControlled Crystal (Xtal) Oscillator (OCXO), which is itself referenced to a 10 MHz reference signal\nlocked to GPS. This discussion and the implication of this scheme are a bit hidden in the current version\nof the manuscript. I think they could be emphasized to amplify the impact of this work.\nAuthor response: Both CW lasers are locked to the same pulsed laser whose phase noise the CW laser\ninherit. The phase stability between the different modes of a pulsed laser are excellent even in an\nunreferenced pulsed laser. Locking the repetition rate – or a higher order of it, like done here – to a\nlow-noise radio frequency (RF) signal further reduces the relative noise between the two CW signals.\nAt the same time, the difference frequency becomes relatable to the RF reference. Referencing the\nOCXO to a 10 MHz GPS reference signal should give the repetition rate of the pulsed laser and further\nthe LO frequency the same Allan deviation as the GPS reference signal. A 10 MHz reference is a\ncommon choice for test and measurement equipment. This gives an absolute frequency accuracy of\napproximately Hz level even at multiple THz. For further details on this topic please view ref.\nhttps://doi.org/10.1063/5.0217898 and ref. 29. The direct referencing to GPS allows for metrological\napplications which we added to the manuscript. Please also see reviewer #2, concern #1.\nAuthor action: We updated the information on the locking mechanism and added further references.\nTo showcase the absolute frequency accuracy stemming from the referencing of the LO to the GPS\nsignal, we investigated the absorption line of an ammonia solution at its absorption line close to\n572.5 GHz. We achieved excellent agreement with literature data. The details are part of the\nhomodyne CW-THz-spectroscopy section including Fig. 7.\n“Within all measurements shown in this manuscript the LO is additionally referenced via an oven-\ncontrolled crystal oscillator (OCXO) to a global positioning system (GPS) signal. The OCXO generates an\nadditional referencing of the OCXO to the GPS gives the LO excellent absolute frequency accuracy\nwhich we verify in a later section.” (lines 131-135)\n“GPS referencing also allows for comparable measurements of the same signal at different locations\nand times.” (lines 228-230)\n“In order to demonstrate SI unit tracability and resolution of the system, we investigate pressure\nbroadening of the ammonia molecule by introducing a vaccum tube into the spectroscopy setup,\nadding a 25% ammonia solution to the tube and evacuating to pressures between 0.018 mbar and\n20.6 mbar (for more details on the measurement setup please consider the supplemental\ninformation). The absorption line of ammonia is close to 572.5 GHz (Fig. 7c) and has a linewidth of\nseveral GHz at atmospheric pressure and room temperature. Upon reducing the pressure it becomes\nlimited by the temperature broadened linewidth of 1.72 MHz for pressures below 0.1 mbar [39] (Fig.\n7e, orange curve). The blue curve in Fig. 7c illustrates the measured absorbance for a pressure of\n0.041 mbar with a frequency resolution of 24 kHz and averaged over 6 measurements. The black curve\nis a Voigt fit to the measurement data and the orange line the calculated absorption from the HITRAN\ndatabase [39] with a frequency resolution of 100 kHz. The measured peak position is 80 kHz offset to\nthe calculated HITRAN peak position confirming the accuracy and reference capability of the LO. The\nmeasured linewidth with 2.4 MHz is well resolved and slightly larger than the theoretical Doppler\nlimited linewidth of 1.72 MHz which may be attributed to foreign broadening caused by water\nmolecules present from the ammonia solution. With increasing pressure in the tube, i.e. at 16 mbar\n(Fig. 7d), the measured linewidth increases in good agreement with the calculated absorption (Fig. 7e)\nyet faces an up-shift for the FWHM resulting from the foreign broadening. Fixing the Gaussian\ncomponent of the Voigt fit, as we do not expect a temperature change, the measured Lorentzian part,\nresponsible for the pressure broadening, (represented by Г in Fig. 7f) increases similar to the HITRAN-\ncalculated value with a similar upshift as the FWHM.” (lines 298-317)\n“The referencing happens with a control circuit that matches the 4th harmonic of the repetition rate of\nthe FC (200 MHz) to the frequency of the OCXO (800 MHz).” (lines 392-393)\nReviewer #3, concern #2: The authors claim that their receiver is capable of resolving frequencies up\nlifetime in the photoconductor material could notably impose a fundamental spectral limit. The\nauthors also mention that “the Reststrahlenband of the InP substrate of the photoconductive\nmixer will limit the frequency coverage to about 7 THz”. This might also be a fundamental limit as it is not\nclear how the receive would perform without this substrate. Therefore, the authors must refer to a\nmaximum frequency detection reaching 6.5 THz (which is demonstrated in this paper) instead of 10\nTHz. The authors must also change the wording in their abstract\nwhich also seems to indicate that their receiver operate up to 10 THz: “ We present an ultra-wideband,\ncontinuous-wave photonic receiver with kHz-level spectral resolution in the terahertz domain (100 GHz-10 THz)”.\nAuthor response: The mentioned 10 THz relates to the definition of the terahertz domain and does\nnot show the performance of our measurements. On a side note we would like to mention that some\nof the authors have demonstrated photoconductor performance beyond 10 THz with devices where\nthe substrate (and hence absorption by its Reststrahlenband) was essentially removed [39]. This would\nprove that the photoconductor’s lifetime performance would suffice to cover the whole THz spectral\nrange.\nAuthor action: We removed the number “10 THz” in the abstract to prevent confusion.\nReviewer #3, concern #3: The paper mentions some limitations of their receiver due to the spectral\nfluence of the source, e.g. at Line 149. A more in-depth discussion would be necessary to determine\nhow the fluence of the source may limit the performances of their receiver.\nAuthor response: The signal of the source may be described with its total power and its spectral\nlinewidth. Signals with a larger linewidth spread their power over a larger spectrum than signals with\na small linewidth. The peak spectral power density of the signal with small linewidth will be\ncorrespondingly higher. Both the photomixer used for the transmitters and the receiver have roll-off\neffects (RC and lifetime) that deteriorate their performance towards higher frequencies. Please also\nview our response to reviewer #2 concern #2 for similar changes.\nAuthor action: We added a section on signal-to-noise ratio to the method section.\n“SIGNAL-TO-NOISE RATIO\nThe signal-to-noise ratio (SNR) within the measurements is dependent on the noise floor and\nresponsivity of the receiver side, the THz power from the emitter and the linewidth of the signal-under-\ntest and of the LO. All of the sources shown in this manuscript use photomixers (pin diodes or\nphotoconductors) to generate the THz signal. Independent of the used optical signal (pulsed or CW),\nthe power of the signal decreases with increasing frequency for frequencies higher than the roll-off\n3dB-frequencies. For the pulsed variant, additionally, fewer optical modes mix with each other with\nincreasing frequency, further reducing the signal power. The signal path consists in most cases of two\nparabolic mirrors in a U-configuration, Si lenses and InP substrate within the photomixer’s package and\na free-space path of less than 0.5 m. Along the signal path losses, reflection and absorption (i.e. water\nvapor, see also Fig. 7b) may occur reducing the signal strength inbound to the receiver. The\nphotocurrent generated by the receiver depends on the strength of the incoming electrical field (see\nEq. (2)) and the LO frequency. Roll-off effects within the photomixer reduce its responsivity with\nincreasing LO frequency. The noise current of the photomixer is mostly independent of the LO\nfrequency. The lower responsivities at higher frequencies require thus larger signals for successful\ndetection. Additionally, the noise floor is directly proportional to the measurement bandwidth. Smaller\nmeasurement bandwidths (i.e. longer integration times) allow for the detection of smaller signals. The\nsystem specific noise floor is therefore frequently given in the unit dB/Hz.\nThe bandwidth is limited on the lower end by the LO linewidth. The system essentially measures the\nspectral density, i.e. the power of the signal within a measurement bandwidth (frequency bin).\nSpectrally wide LOs or signals -such as the one in Fig. 2- are distributed over many frequency bins,\nreducing the power per bin and thus the signal to noise ratio. As the responsivity of the\nphotoconductors drop with increasing frequency smaller SNRs lead to smaller usable bandwidths,\nranging from DC to the maximum still detectable signal. This lead to the result that the ~50 MHz wide\nCW signal featured the lowest usable bandwidth, while the usable bandwidth increased the better the\nrelative stability of SUT and LO, yet with 6.5 THz bandwidth for close to perfect relative stability where\nall spectral power is concentrated within a 2 Hz frequency bin.” (lines 474-500)\nReviewer #3, concern #4: In the section “Spectrum analyzer for unreferenced sources”, the authors\nshould show the full spectrum from 0.1 to 6.5 THz in additional to the resolution of a single comb line\nin Fig. 3b.\nAuthor response: The power of the investigated unreferenced source has a linewidth of around\ndensity of the source will be more than 7 orders of magnitude lower compared to the locked case in\nFig. 6. A CW source ideally only emits at one frequency. Measuring a full spectrum from 100 GHz to\n6.5 THz will contain noise for almost all of the spectrum except the 50 MHz where the system emits.\nGraphically, the peak will be hard to find and the shape of the line will not be visible to the reader\nconsidering the fact that such a measurement would contain at least 260 000 data points if a maximum\nstep size of 25 MHz (Shannon Hartley limit for a 50 MHz linewidth) is chosen. We therefore opted not\nto measure the whole spectrum. Depending on the chosen resolution bandwidth, long measurements\nwill be limited by the number of data points the acquisition card can measure. Simultaneously, Fig. 7\nshows measurements with a total measurement bandwidth of more than 3 THz to emphasize the\ncapabilities of the LO.\nAuthor action: The section “principle of operation” contains information on the tunability of the LO.\n“By simply sweeping the LO frequency, we can record the spectrum of any unknown source under test\nat a resolution defined by the excellent spectral purity of the FC-referenced LO. Given that the source’s\npower is high enough to be detected, the maximum tuning range is limited only by the tuning range of\nthe LO (>10 THz) [29] and the sensitivity of the photoconductor which becomes smaller the higher the\nfrequency. The frequency coverage of the used photoconductors is limited by the Reststrahlenband of\nthe InP substrate to 7 THz. Removing the substrate allows for coverage beyond 10 THz [33].”\nReviewer #3, concern #5: The authors have showed homodyne CW THz-spectroscopy in the paper\nwith an integration time of 50 µs where the signal is distinguishable until 3.5 THz. One of their previous\narticles show a spectrum reaching 5 THz with an integration time of 300 ms (Ref [26]). I recommend\nusing 300 ms here also to allow for a better comparison between this configuration and the previous\none used in Ref. 26.\nAuthor response: We thank the reviewer for the suggestion. The measurement time increases by a\nfactor of 60,000 if using 300 ms integration time and if done with the same spacing resulting in a total\nmeasurement over multiple days. As we had to bring equipment from three labs together that was\nalso needed for further experiments, we simply could not take this much time for a single\nmeasurement. The integration time and its effect on the bandwidth of photomixing systems has been\ndescribed in plenty detail in the literature (see [34] and https://doi.org/10.1063/5.0217898 ). The long\nmeasurement would not have brought new fundamental information.\nAuthor action: We added additional literature to the manuscript for a better understanding of our\nspectroscopy results.\n“Longer averaging allows for accessing even higher frequencies [27, 34].” (lines 292-293)\nReviewer #3, concern #6: Please check: the abbreviation of oven-controlled crystal (xtal) oscillator\nshould be OCXO, not OXCO.\nAuthor response: We thank the reviewer for noticing the incorrect abbreviation.\nAuthor action: Replaced all instances of OXCO with OCXO.\nReviewer #3, concern #7: Regarding the sentence: “While a spectrum analyzer strictly requires that\nthe LO and the signal under test are independent in order to measure the true signal shape, noise and\nstability, this independence is undesired in spectrometers.”, the authors should provide more\ninformation to explain why they are making these assumptions. It is advantageous (but maybe not\nnecessary) that a spectrum analyzer is independent from the signal it analyzes, but it is less clear why\nthis independence is “undesired” for spectrometers. Most spectrometers don’t have any\n“dependence” with the source they characterize.\nAuthor response: Generally speaking both the spectrum analyzer and the spectrometer may be used\nwith or without referencing the signal under test to the LO. If a spectrum analyzer does not use\nreferencing, the SUT will be correctly represented as no common phase noise exists, assuming the\nphase noise of the SUT dominates. If the source to be analyzed is spectrally locked to the analyzer\ninstead, most of the phase noise is common-mode and thus suppressed. The recorded linewidth and\ndrifts, e.g., will then always be smaller than the true linewidth and drift, which is obvious for drifts:\nWhen source and receiver drift synchronously, which they would if phase-locked, then\ndrifts/frequency stability cannot be analyzed at all.\nThe reviewer is completely right that phase-locking is no stringent requirement for spectrometers and\neven not possible if direct detectors rather than mixers are used. Phase-locking can, however,\ndramatically reduce common noise as demonstrated in this manuscript for homodyne or heterodyne\nspectrometers: The spectrometer variant discussed in that section benefits from locking as the receiver\nmeasures primarily at the frequency of the LO.\nAuthor action: We improved the paragraphs of our spectrometer and spectroscopy variant to better\nshowcase the benefit of the shared LO.\n“In order to measure the true signal shape, noise and stability, a spectrum analyzer strictly requires\nthat the LO and the signal under test are independent. In contrast, spectrometers used for\ninvestigating devices under test benefit from locking the LO with the signal under test. Channel\nsounding with locking to the same GPS signal already reduces the phase noise but for even better noise\nsuppression both source and receiver can be locked to the same OCXO (Fig. 6a). Fig. 6b) shows the\nspectrum of the pulsed source at a frequency of 6.5 THz with a combined (relative) linewidth of only\n2.3±1.2 Hz and a signal-to-noise ratio of at least 7 dB for 100 averages. Fig. 5c) (blue line) also shows\nthat the combined linewidth only slightly depends on the THz frequency and remains below 3 Hz over\nthe whole frequency range.” (lines 261-269)\n“Homodyne spectrometers profit from using the same LO signal for both the transmitter and the\nreceiver, reducing common noise and enabling phase measurements.” (lines 285-286)\nReviewer #3, concern #8: This sentence: “Fig. 6b) shows that locking to a common reference allows to\nextend to a maximum frequency of 6.5 THz”, it’s not clear. First, Fig. 6b only shows a power signal, not\na comparison for locked and unlocked signals. Also, I believe that the authors are making a confusing\nshortcut: using the same OCXO probably leads to an improved signal-to-noise, this in turns might lead\nto an increase in the detection spectral range. This should be clarified.\nAuthor response: The reviewer is correct that using the same OCXO leads to an improved SNR. Locking\nto a common reference increases the common noise between the optical signals which in turn reduces\nthe relative phase noise between both signals. In this case the signal is concentrated in a smaller\nlinewidth boosting the signal-to-noise ratio. This is easy to see by comparing the linewidth in Fig. 6b of\n2.3 Hz (common-noise and drifts rejected) to the free-running linewidth we extrapolated for unlocked\nsources to be around 800 Hz (c.f. line 272). This enables the measurement of higher frequencies as all\nphotomixing systems show a decay in SNR towards higher frequency. If one starts with a higher SNR\nin the first place because of common noise rejection, then the system hits the noise floor at a higher\nfrequency.\nAuthor action: We updated lines 270 to 277 for clarity.\n“The high correlation of both lasers drastically improves the signal to noise ratio, highly beneficial for\nspectroscopic applications. We estimate the power in the mode at 6.5 THz to 7 pW which is now\nconcentrated in a 2 Hz frequency bin as opposed to an 800 Hz linewidth in the non-referenced\nconfiguration, improving the signal to noise ratio by about a factor of 400. This improvement enabled\nthe extension of the operation range very close to the current frequency limit of the photoconductive\nmixer, which originates from strong reflection and absorption of the Reststrahlenband of its Indium\nPhosphide substrate.” (lines 270-277)\nReviewer #3, concern #9: The sentence “Key applications are future high-speed wireless\ncommunication, with several THz bands already defined in 6G [1]” could be misleading because the\nRef [1] mentions that frequencies between 1 THz and 3 THz have not yet been defined as this spectral\nregion can be used by both active and passive services. Plus, nothing is mentioned in Ref [1] about\nfrequencies above 3 THz.\nAuthor response: Thank you for the note, this was indeed confusing.\nAuthor action: We updated the sentence in line 34.\n“Key applications are future high-speed wireless communication, with several bands already defined\nin 6G in the lower THz region [1] and more to come in follow-up standards, non-destructive testing\nand quality control [2], as well as spectroscopy [3] and imaging [4], with particular focus on medically\nor environmentally relevant topics.” (lines 33-36)\nReviewer #3, concern #10: This sentence: “For the highly important field of THz wireless\ncommunication an opto-electronic device is even a prerequisite to transform the optical signal,\ntransmitted through a fiber, to a wireless THz signal.” should be removed since the statement is not\nalways true. For example, a nonlinear medium could be used to transform the optical signal into a\nwireless THz signal.\nAuthor response: Indeed, there may be other options. To the knowledge of the authors, however,\nopto-electronic devices are the by far best technological solution so far for non-pulsed signals. Non-\nlinear media do indeed work also at CW but are very inefficient, particularly at frequencies of interest\nto 6G that are far away from the optical tone and thus heavily impacted by the Manley-Rowe limit. The\nonly continuous-wave case the authors are aware of where a non-linear medium could result in\nexcellent up-conversion or down-conversion is when placing the medium in a resonator, ideally a\ndouble-resonant (THz, NIR) setup.\nAuthor action: We changed lines 49 to 57 to account for options except the opto-electronic devices\nand added reference [10].\n“Nonlinear media and photomixers bridge this gap by combining electronic with photonic approaches.\nNonlinear media benefit from high THz powers and large bandwidths, yet lack in efficiency. Resonators\nincrease the coupling efficiency at the expense of tunability [10]. Photomixers, i.e. photodiodes (PDs)\nor photoconductors (see section photonic mixer in methods), use two laser signals for THz generation\nand detection [11, 12]. Meanwhile, photonic approaches transition into the electronic domains, e.g. in\nthe form of a low phase noise photonic clock signal [13], or photonic local oscillators [14], and mixed\nelectronic-photonic integrated circuits (EPICs) [15]. The highly important field of wireless THz\ncommunication benefits from opto-electronic devices directly transforming optical signals,\ntransmitted through a fiber, to a wireless THz signal.” (lines 49-57)\nReviewer #3, concern #11: This sentence could be misleading: “The extenders double or triple the\nmicrowave baseband frequency several times up to the desired THz frequency or from the THz\nfrequency down to the base band [15].” Ref 15 demonstrates this concept up to 400 GHz and intrinsic\ncarrier response time in materials still limit these applications to about 1 THz only.\nAuthor response: The reviewer is correct that the frequency multiplication from electronic sources is\nlimited. Commercially available extender modules reach 1.5 THz.\nAuthor action: We adjusted the sentence before in line 59 to state a limit on its current commercial\navailability.\n“They consist of a microwave backbone system equipped with frequency extenders, currently available\nup to 1.5 THz.” (line 59-60)\nReviewer #3, concern #12: There’s no verb in this sentence: “For example, a Hilbert-transform\nspectrum analyzer based on a high-Tc Josephson junction [17] with a high scanning speed of up to 4\nAuthor response: We thank the author for noticing the missing verb and apologize for it.\nAuthor action: We changed the sentence to include a verb.\n“For example, a Hilbert-transform spectrum analyzer based on a high-T Josephson junction [18]\nc\nachieves a high scanning speed of up to 4 THz/s and a frequency coverage of at least 1 THz, yet only a\nresolution of 50 MHz.” (lines 70-72)\nReviewer #3, concern #13: This sentence is long and confusing: “These utilize continuous-wave (CW)\nlasers as local oscillator (LO) – namely, an electro-optical comb based on an electro-optical phase\nmodulator at telecom wavelengths with a frequency coverage of up to 1 THz and a resolution of 1 Hz\n[22], free-running distributed feedback (DFB) laser diodes with a difference frequency coverage of up\nto 4.5 THz at a wavelength of 780 nm [25] and a resolution of 1.2 MHz at a center wavelength around\n1550 nm [23] or DFB laser diodes at 850 nm referenced to an electronic THz signal with a frequency\ncoverage of 1 THz and a resolution of 100 Hz [24].”\nAuthor response: We are sorry for implementing a long and confusing sentence.\nAuthor action: We separated the sentence (lines 82-87).\n“These utilize continuous-wave (CW) lasers as a local oscillator (LO). An electro-optical comb based on\nan electro-optical phase modulator at telecom wavelengths covers a frequency range of up to 1 THz\nwith a resolution 1 Hz [23]. Free-running distributed feedback (DFB) laser diodes enable a difference\nfrequency coverage of up to 4.5 THz at a wavelength of 780 nm [26], a resolution of 1.2 MHz at a center\nwavelength around 1,550 nm [24]. DFB laser diodes at 850 nm referenced to an electronic THz signal\nreduce the resolution to 100 Hz and the frequency coverage of 1 THz [25].” (lines 82-87)\nReviewer #4:\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part\nof the Nature Communications initiative to facilitate training in peer review and to provide appropriate\nrecognition for Early Career Researchers who co-review manuscripts.\nAuthor response: We thank you for carefully reviewing the manuscript and welcome the process of\nco-reviewing the manuscript and hope that it benefits you in your research career."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors' work is very much related to the paper \"Photonic comb-rooted synthesis of ultra-stable terahertz frequencies\"\npublished by DC Shin, BS Kim, H Jang, YJ Kim, SW Kim in Nature Communications (2023)14:790. Nonetheless, the 2023\nNature Comms paper was neither cited nor discussed even in the authors' revised manuscript -- It is strongly suggested that\nthe authors desribe how their work is differentiated and valued comparatively in terms of the THz generation system setup,\nfrequency instability, phase noise and tuneable range before making final claims on their achieved performance.", "reviewer_2": "The authors have thoroughly addressed all reviewers' concerns and well complemented the paper with missing\nmeasurements, clarifications, extensions. I am in favor of the publication of the manuscript in Nat Comm.", "reviewer_3": "I appreciate the work invested by the authors to address my comments as well as the comments from the other Reviewers.\n-I am still not convinced, based on experimental evidence, that the performance beyond 10 THz is achievable. This was my\n“concern #2”. The authors answered: “[…] some of the authors have demonstrated photoconductor performance beyond 10\nTHz with devices where the substrate (and hence absorption by its Reststrahlenband) was essentially removed [39]”. I\ncouldn’t find this photoconductor performance demonstration beyond 10 THz in reference [39], which is Gordon et al. J.\nQuant. Spectrosc. Radiat. Transfer 277, 107949 (2022). The authors also write in the text: “Removing the substrate allows\nfor coverage beyond 10 THz [33].” But reference [33], which is OE 20, 23896 (2022), doesn’t show (or even claim) to\nexperimentally demonstrate THz detection beyond 10 THz. In that previous work, the measured signals are very close to the\nnoise level after 9.5 THz. Because of the results presented in this paper and in previous work referenced by the authors\n[33, 39], I recommend removing any claims on the performance of these devices exceeding 10 THz when the substrate is\nremoved.\n-The authors propose a plausible cause to explain the slightly larger spectral linewidth of ammonia, which they attribute to\nthe presence of contaminating water molecules. However, the THz spectrum should allow them to test directly this\nhypothesis by monitoring spectral components at water molecule absorption peaks. The authors should employ this\ntechnique to confirm their hypothesis or provide a justified explanation for any limitations preventing its implementation.\n-The authors should remove the subjective word “excellent” in the added sentence: “By simply sweeping the LO frequency,\nwe can record the spectrum of any unknown source under test at a resolution defined by the excellent spectral purity of the\nFC-referenced LO."}, "author_response": "Response to reviewers on Nature Communications manuscript NCOMMS-24-72395-A\nDear Reviewers,\nWe sincerely thank you for thoroughly reviewing the manuscript and the comments and suggestions.\nPlease find below a detailed response to each of the remarks individually. We excuse for the long\nduration of the revision. We hope to have improved the manuscript to allow for further consideration.\nYours sincerely,\nBenedikt Krause\n(Corresponding author, in the name of all authors)\nReviewer #1, Concern #1: The authors’ work is very much related to the paper “Photonic comb-rooted\nsynthesis of ultra-stable terahertz frequencies” published by DC Shin, BS Kim, H Jang, YJ Kim, SW Kim\nin Nature Communications (2023)14:790. Nonetheless, the 2023 Nature Comms paper was neither\ncited nor discussed even in the authors’ revised manuscript – It is strongly suggested that the authors\ndescribe how their work is differentiated and valued comparatively in terms of the THz generation\nsystem setup, frequency instability, phase noise and tuneable range before making final claims on their\nachieved performance.\nAuthor response: We thank the reviewer for providing a reference on a similar topic. In the reference\nthe frequency comb is locked to an optical cavity and two DFB laser diodes are injection locked to the\nfrequency comb. Additional to the locking, the fiber thermal noise is compensated. This allows a THz\nlinewidth of 2 mHz or less at THz frequencies of 0.1, 0.66 and 1.06 THz. Without the fiber thermal\ncompensation the linewidth broadens to 1.46 Hz. Due to the chosen locking variant, the DFB laser\ndiodes may only lock to the comb lines and therefore only generate THz frequencies spaced apart by\nmultiples of the repetition rate of the frequency comb.\nThe LO described in this manuscript phase-locks two external cavity laser diodes to a frequency comb.\nIn order to cover any difference frequency up to 10 THz, one of the ECDLs is phase-locked to one of\nthe modes of the frequency comb while the second is phase-locked to a frequency shifted variant of\nthe frequency comb. Tuning the ECDL and the frequency shift of the frequency comb simultaneously\nachieves continuous tuning with tuning speeds up to 1 THz/s. Sweeping the LO at a rate of 11.8 GHz/s\nwe achieved an accuracy of 120 kHz at a center frequency of 556.936 GHz, with respect to HITRAN\ndata. While keeping the LO fixed we achieved an accuracy and stability of 2 Hz at a center frequency\nof 6.5 THz in comparison with a harmonic of the repetition rate of a stabilized comb.\nAuthor action: We added different LO / THz frequency synthesizer variants mentioned in the literature\nto the introduction and a short comparison to the discussion.\n“The ambiguity of pulsed comb-based systems can also be overcome by locking continuous-wave\nlasers to specific comb lines while tuning the comb’s repetition rate, yet with a demonstrated\nresolution of 200 kHz and a tuning range up to 1.28 THz [23]. Likewise, high spectral purity can be\nachieved by locking the CW lasers to different resonances of a high quality factor cavity [24], with a\nsub-Hz frequency stability demonstrated at 1.965 GHz and an accuracy of 6 kHz at 556.936 GHz. Coarse\ntunability of up to 1.2 THz is achieved by hopping between cavity resonances. The gaps between the\nresonance are closed by fine-tuning the difference frequency with a Mach-Zehnder modulator. Ref.\n[25] references the CW lasers to a frequency comb which itself is locked to an optical cavity achieving\na terahertz frequency stability of 1.46 Hz. Removing the fiber thermal noise improves the stability\nfurther to 2 mHz. Due to the referenced frequency comb this setup is limited to THz frequencies spaced\napart by the repetition rate of the FC with a demonstrated frequency coverage of 1.1 THz. So far, these\nhigh purity continuous-wave systems have not been demonstrated as spectrum analyzers and their\nmaximum demonstrated operation frequency is, to date, below those of commercial ESAs (1.5 THz).”\n(lines 82-94)\n“The additional referencing of the OCXO to the GPS gives the LO absolute frequency accuracy which\nwe verify in a later section.” (lines 147-149)\n“The FC-referenced photonic LO performs very similar in frequency stability and accuracy to other FC\nor cavity referenced photonic THz synthesizers [23, 24]. Accounting for fiber thermal noise could\nfurther improve the performance [25]. Yet the system presented in this work combines the stability\nwith by far the fastest tunability option of comparable synthesizers.” (lines 355-359)\n“Therefore, the systems give access to low pressure trace gas detection of Doppler-limited lines over\na large fraction of the THz range which we showed exemplary by investigating the water vapor\nabsorption line at 556.936 GHz.” (lines 373-375)\n[23] Mouret, G. et al. “THz photomixing synthesizer based on a fiber frequency comb”, Optics express\n17, 24, 22031-22040 (2009).\n[24] Djevahirdjian, L. et al. “Frequency stable and low phase noise THz synthesis for precision\nspectroscopy”, Nat. Commun. 14, 7162 (2023).\n[25] Shin, D.-C., Kim, B.S., Jang, H. Kim, Y.-J., Kim, S.-W. “Photonic comb-rooted synthesis of ultra-\nstable terahertz frequencies”, Nat. Commun. 14, 790 (2023).\nReviewer #2: The authors have thoroughly addressed all reviewers’ concerns and well complemented\nthe paper with missing measurements, clarifications, extensions. I am in favor of the publication of the\nmanuscript in Nat Comm.\nAuthor response: We thank the reviewer for proofreading our manuscript and for the helpful\ncomments in the previous revision.\nReviewer #3, Concern #1: I am still not convinced, based on experimental evidence, that the\nperformance beyond 10 THz is achievable. This was my “concern #2”. The authors answered: “[…] some of the authors have demonstrated photoconductor performance beyond 10 THz with devices\nwhere the substrate (and hence absorption by its Reststrahlenband) was essentially removed [39]”. I\ncouldn’t find this photoconductor performance demonstration beyond 10 THz in reference [39], which\nis Gordon et al. J. Quant. Spectrosc. Radiat. Transfer 277, 107949 (2022). The authors also write in the\ntext: “Removing the substrate allows for coverage beyond 10 THz [33].” But reference [33], which is\nOE 20, 23896 (2022), doesn’t show (or even claim) to experimentally demonstrate THz detection\nbeyond 10 THz. In that previous work, the measured signals are very close to the noise level after 9.5\nTHz. Because of the results presented in this paper and in previous work referenced by the authors\n[33, 39], I recommend removing any claims on the performance of these devices exceeding 10 THz\nwhen the substrate is removed.\nAuthor response: Firstly, we apologize for the confusion in the references. We shifted the reference\nfor OE 20, 23896 (2022) late into the response and forgot to correct it in the response letter. Secondly,\nthe reviewer is correct that mentioned reference experimentally only shows frequencies up to 10 THz.\nFor better understanding, we changed the source to Proc. SPIE 12885, Terahertz, RF, Millimeter, and\nSubmillimeter Wave Technology and Applications XVII, 1288503 (2024) as this one uses newer data\ndespite being in a less recognized journal. Fig. 3b (see below) of the reference shows a frequency\ncoverage up to 10 THz with a remaining dynamic range of at least 10 dB at 10 THz. Therefore\nshowcasing that beyond 10 THz should be possible.\nFig. 3b) from Proc. SPIE 12885, Terahertz, RF, Millimeter, and Submillimeter Wave Technology and\nApplications XVII, 1288503 (2024): “…(b) Fourier transformed pulse spectrum and measured noise\nlevel: A peak dynamic range of 105 dB and a bandwidth of 10 THz are achieved within 60 s acquisition\ntime (1000 averages).”\nAuthor action: We corrected and double checked all references to make sure they are in the correct\nposition. We also adapted the sections to state that a frequency coverage of at least 10 THz is possible\nwith the system by replacing the photoconductor substrates.\n“The frequency coverage of the used photoconductors is limited by the Reststrahlenband of the InP\nsubstrate to 7 THz. Removing the substrate allows for coverage of at least 10 THz [36].” (lines 142-144)\n“By removing the substrate the frequency coverage of the photoconductive mixer can be extended, as\ndemonstrated in ref. [36], potentially within or possibly even beyond the Reststrahlenband of InP and\nInGaAs , to cover a similar range as the FC-referenced photonic LO.” (lines 319-322)\nReviewer #3, Concern #2: The authors propose a plausible cause to explain the slightly larger spectral\nlinewidth of ammonia, which they attribute to the presence of contaminating water molecules.\nHowever, the THz spectrum should allow them to test directly this hypothesis by monitoring spectral\ncomponents at water molecule absorption peaks. The authors should employ this technique to confirm\ntheir hypothesis or provide a justified explanation for any limitations preventing its implementation.\nAuthor response: Indeed, we had underestimated the number and influence of several error sources\non the ammonia spectra. We added a droplet of ammonia water and assumed to essentially see the\nnative ammonia line with some foreign broadening mostly by air. Unfortunately, we cannot tell how\nmuch water vapor (from the evaporating droplet) and how much rest air were in the gas phase in the\nvacuum chamber. So we cannot tell for ammonia the exact foreign broadening. We did not just want\nto generate a fitted result by having all other concentrations as fit parameters as this proves essentially\nnothing (too many fit parameters, once can eventually get everything somehow in agreement). Further\nknown error sources of this measurement are: a) the pressure gauge that was not calibrated before\nthe measurements. We attribute an error of 20 % to the pressure measurements, b) Also we have no\nidea about reactions with the chamber wall resulting in difficulties to predict the partial pressures of\nthe individual gas components, c) The concentrations in the gas phase of ammonia and water will not\nbe identical to the liquid phase, d) Last but not least, the leakage of laboratory air into the chamber\nmay increase the amount of water vapor.\nAs we just intended to provide a proof for the excellent resolution of the system, we followed the\nadvice of the reviewer and inspected a water line instead. Due to the close proximity between the\nammonia absorption line (572.5 GHz) and the water line (557 GHz), we had indeed captured both\nwithin the same measurements. The measurement of the water line at low pressures shows much less\nerrors for the following reasons: Within our setup the transmitter and the receiver are mounted\noutside the pressure chamber. Any humidity remaining in the surrounding air will influence the\nlinewidth of the signal. For this reason the area surrounding the transmitter and receiver were flooded\nwith dry air essentially removing any water vapor in the free space THz path outside the pressure\nchamber, providing just a very minor error source. The amount of ammonia in the gas phase is\n(expected to be) much smaller than water vapor for a 25% ammonia water. As water and ammonia\nhave almost identical molar mass eigen broadening and foreign broadening are very similar.\nEssentially, we measure water vapor foreign broadened by air. For the calculations we assumed a\nwater vapor content of 25 % with an error of up to 10 %. At the lowest investigated pressures, errors\nin the pressure gauging have less influence. We thus get much better agreement with HITRAN data for\nthe water line as the new Fig. 7c) shows for a pressure of 0.032 mbar.\nFig. 7: c) Absorption measurement (blue curve) and Voigt fit (black curve) with simulated absorption\n(orange curve) of water vapor at 0.032 mbar. d) Measured (blue circles) and simulated (orange\ntriangles) absorption full width half maximum (FWHM).\nThe measured water vapor absorption spectra (blue line) with a Voigt fit (black line) and the calculated\ndata from HITRAN (orange line) for the same pressure agree very well. The fitted center frequency is\n556.936 12 GHz and the calculated one is 556.936 GHz showing a difference of 120 kHz. We\npurposefully only show the water vapor results for the lowest pressures where the lines are mostly\nDoppler broadened and the uncertainty of the pressure error has less influence. In Fig. 7d we compare\nwith measured FWHM to the HITRAN FWHM. For the pressures between 0.020 mbar and 0.046 mbar\nthe difference in FWHM are less than 45 kHz between the calculated and the measured spectra. For\nboth peak position and FWHM, the deviation with respect to the HITRAN data is just a fraction of the\nFWHM, namely a relative deviation of 215 ppb for the peak position and only 1.1% for the FWHM at\n0.032 mbar.\nAuthor action: We exchanged the ammonia data shown within the previous version of the manuscript\nwith the water vapor data for the pressure ranges with a low measurement uncertainty.\n“In order to demonstrate the accuracy and resolution of the system, we investigate an almost Doppler-\nlimited line of the water molecule by introducing a vacuum tube into the spectroscopy setup, adding\na drop of ammonia water to the tube and evacuating to pressures between 0.020 mbar and 0.046 mbar\n(for more details on the measurement setup please consider the supplemental information). The\nabsorption line of water vapor is close to 556.936 GHz (Fig. 7c) and has a linewidth of several GHz at\natmospheric pressure and room temperature. Upon reducing the pressure it becomes limited by the\ntemperature broadened linewidth of 1.62 MHz [42] (see Eq. (8) in method section) caused by the\noptical Doppler effect of gas molecules at thermal velocity. The blue curve in Fig. 7c illustrates the\nmeasured water vapor absorption for a pressure of 0.032 mbar with a frequency resolution of 24 kHz,\na measurement speed of 11.8 GHz/s and averaged over 6 measurements. The black curve is a Voigt fit\nto the measurement data and the orange line the calculated absorption from the HITRAN database\n[42] assuming a water vapor to air mixture of 25%±10%. The\nmeasured peak position is 120 kHz offset to the calculated peak position, corresponding to a relative\ndeviation with respect to the HITRAN data of 215 ppb. The measured linewidth with 1.81 MHz is well\nresolved and only 1.1% smaller than the linewidth of 1.83 MHz (Fig. 7d) calculated from HITRAN. Given\nan estimated error of 20% on the pressure measurements, these data confirm the accuracy and\nreference capability of the LO.” (lines 312 – 328)\n“Therefore, the systems give access to low pressure trace gas detection of Doppler-limited lines over\na large fraction of the THz range which we showed exemplary by investigating the water vapor\nabsorption line at 556.936 GHz.” (lines 373-375)\n“We remark that heavier molecules have larger impact such that foreign gases will cause a different\nlinewidth as a pure gas. In ambient conditions the absorption also experiences Doppler broadening\ncaused by thermal motion of the gas molecules towards and away from the THz source.” (lines 526-\n529)\n“The theoretical Doppler limit for water vapor is 1.62 MHz at the 556.936 GHz line at a room\ntemperature of 23 °C.\nFor the measurements with water vapor under vacuum we used a spectroscopy setup with a vacuum\ntube in the THz beam. Beamforming equipment in the form of two lenses and photoconductive\ntransmitter and receiver were outside the vacuum tube, purged with dry air to prevent water\nabsorption at normal pressure outside the tube. A combined membrane pump with a turbomolecular\npump enabled pressures as low as 0.001 mbar within the tube. Additional water in form of an\nammonia-water solution is added in an extended part of the tube that is separated by a needle valve.\nFor the measurements the needle valve is opened slightly to let water vapor into the tube and\ndepending on the pressure the pumps closed off of the tube. Each measurement consists of three runs\nof five seconds where each run contains one up and one down scan. During each measurement we\nmonitored the pressure with a pressure gauge. The pressure within the tube changed on average by a\nfactor of 1.5 as the tube is quite leaky. Therefore, each measurement is compared to the maximum\npressure within its measurement time window. The pressure gauge has an error of 20% due to a lack\nof recent calibration. The tube does not contain heating or cooling equipment and was left at room\ntemperature (23 °C) limiting the measurements to the Doppler broadened spectra. The absorption\ncoefficient 𝛼 is calculated by\nln(\n𝐼𝐻2𝑂\n)\n𝛼 = − 𝐼0 , (9)\n𝑑\nWhere 𝐼 is the intensity of the reference measurement, 𝐼 the water vapor measurement and 𝑑 =\n0 𝐻2𝑂\n33 cm the mean THz path length inside the vacuum tube. ” (lines 533-552)\nReviewer #3, Concern #3: The authors should remove the subjective word “excellent” in the added\nsentence: “By simply sweeping the LO frequency, we can record the spectrum of any unknown source\nunder test at a resolution defined by the excellent spectral purity of the FC-referenced LO.\nAuthor response: We thank the reviewer for spotting subjective wording.\nAuthor action: We rewrote sections with subjective wording to be more objective wherever possible.\nFor a better understanding of the context, we also added a discussion on linewidths of similar THz\noptical synthesizer (please see reviewer 1, concern 1 for the details).\n“The presented setups offer the broadest continuous-wave frequency coverage to date, combined\nwith a sharp spectral resolution, enabling diverse applications ranging from fast non-destructive\ntesting, astronomic high-resolution spectroscopy, to frequency-modulated RADAR.” (lines 24-27)\n“Nonetheless, the electronic system benefits from an Hz- to kHz-level spectral resolution and a very\nlow noise floor.” (lines 68-69)\n“The laser system has the capability of covering more than 10 THz [32] with competitive phase stability\n[33] at a Hz-level spectral resolution [34, 35] at the lower end of the THz spectrum while sweeping with\nmaximum speeds of 1 THz/s [32].” (lines 108-110)\n“By simply sweeping the LO frequency, we can record the spectrum of any unknown source under test\nat a resolution defined by the spectral purity of the FC-referenced LO.” (lines 138-140)\n“Commercially available electronic spectrum analyzers only reach frequencies up to 1.5 THz. As tab. 1\nshows the presented photonic system significantly exceeds the frequency range of the electronic\nvariants while achieving slightly better spectral resolution and comparable noise floors.” (lines 342-\n345)\n“The result is a lower achievable measurement bandwidth in case of a non-referenced CW signal, while\nthe usable measurement bandwidth increases with better relative stability between the SUT and LO\nenabling a measurement bandwidth of 6.5 THz with all spectral power concentrated within a 2 Hz\nfrequency bin.” (lines 513-516)"}, {"round": 3, "reviewer_comments": {"reviewer_1": "The authors have addressed the reviewer's concern by adding other relevant LO / THz frequency synthesizer methods to the introduction with a short comparison in the revised manuscript. Now this reviewer agrees to accept the manuscript for publication.", "reviewer_3": "I appreciate the effort the authors have made to address the reviewers’ comments, and I believe this manuscript merits publication in Nature Communications. That said, I would still encourage the authors to reconsider the claim that the presented THz detection technology can operate effectively beyond 10 THz. As it stands, this assertion is not directly supported by the data in the manuscript, and relies solely on a single conference paper: Proceedings Volume 12885, Terahertz, RF, Millimeter, and Submillimeter-Wave Technology and Applications XVII; 1288503 (2024)\nWhile figure 3b from that conference paper does show a THz signal above the noise floor extending to 10 THz, the nature of this signal is ambiguous. Since the spectrum reflects the absolute value of the Fourier-transformed time-domain signal, the high-frequency components, 6 to 7 orders of magnitude weaker than the low-frequency signal, could plausibly arise from minor amplitude fluctuations of a time-resolved signal containing only low frequencies. This contribution is distinct from the “noise” indicated in the figure. In previous experiments, such high-frequency artifacts could be entirely suppressed by applying a spectral filter (high pass) that reduces the low-frequency contribution of the THz signal (e.g. see Fig. 2a in Light Sci Appl 14, 44 (2025))\nThis is why I find the repeated claim of >10 THz operation mildly problematic. Although not a cause for rejection, reiterating this claim in a Nature Communications article risks prematurely solidifying the notion that this device has been demonstrated to operate in that regime. I am not suggesting the claim is incorrect, only that the supporting evidence is very weak. The concern is that future researchers may cite this work as a definitive proof of >10 THz operation, potentially motivating follow-on studies based on an unverified premise."}, "author_response": "Response to reviewers on Nature Communications manuscript NCOMMS-24-72395-B\nDear Reviewers,\nWe sincerely thank you for thoroughly reviewing the manuscript, the comments and suggestions and\nfor accepting the manuscript. We would still like to take the opportunity to thank each reviewer\nindividually and comment on the final remarks.\nPlease note that, in preparation for the editorial compliance, we uploaded the figures separately and\nmoved the table and figure descriptions to the end of the manuscript.\nYours sincerely,\nBenedikt Krause\n(Corresponding author, in the name of all authors)\nReviewer #1: The authors have addressed the reviewer's concern by adding other relevant LO / THz\nfrequency synthesizer methods to the introduction with a short comparison in the revised manuscript.\nNow this reviewer agrees to accept the manuscript for publication.\nAuthor response: We thank the reviewer for proofreading our manuscript and for the helpful\ncomments in the previous revisions.\nReviewer #2: The authors have thoroughly addressed all reviewers’ concerns and well complemented\nthe paper with missing measurements, clarifications, extensions. I am in favor of the publication of the\nmanuscript in Nat Comm.\nAuthor response: We thank the reviewer for proofreading our manuscript and for the helpful\ncomments in the previous revision.\nReviewer #3: I appreciate the effort the authors have made to address the reviewers’ comments, and\nI believe this manuscript merits publication in Nature Communications. That said, I would still\nencourage the authors to reconsider the claim that the presented THz detection technology can\noperate effectively beyond 10 THz. As it stands, this assertion is not directly supported by the data in\nthe manuscript, and relies solely on a single conference paper: Proceedings Volume 12885, Terahertz,\nRF, Millimeter, and Submillimeter-Wave Technology and Applications XVII; 1288503 (2024)\nWhile figure 3b from that conference paper does show a THz signal above the noise floor extending to\nFourier-transformed time-domain signal, the high-frequency components, 6 to 7 orders of magnitude\nweaker than the low-frequency signal, could plausibly arise from minor amplitude fluctuations of a\ntime-resolved signal containing only low frequencies. This contribution is distinct from the “noise”\nindicated in the figure. In previous experiments, such high-frequency artifacts could be entirely\nsuppressed by applying a spectral filter (high pass) that reduces the low-frequency contribution of the\nTHz signal (e.g. see Fig. 2a in Light Sci Appl 14, 44 (2025))\nThis is why I find the repeated claim of >10 THz operation mildly problematic. Although not a cause for\nrejection, reiterating this claim in a Nature Communications article risks prematurely solidifying the\nnotion that this device has been demonstrated to operate in that regime. I am not suggesting the claim\nis incorrect, only that the supporting evidence is very weak. The concern is that future researchers may\ncite this work as a definitive proof of >10 THz operation, potentially motivating follow-on studies based\non an unverified premise.\nAuthor response: We thank the reviewer for proofreading our manuscript and for the helpful\ncomments throughout all revisions. In fact, this statement as well as the measurement in ref [36] up\nto 10 THz is not really relevant for the current manuscript and therefore we softened the statement.\nAuthor action: We reworded the claim to not directly mention a specific frequency for the\nphotoconductive mixers:\n“Removing the substrate allows for potential coverage within or possibly even beyond the\nReststrahlenband of InP and InGaAs [36].” (lines 144-145).\n“By removing the substrate the frequency coverage of the photoconductive mixer can be extended, as\ndemonstrated in ref. [36], potentially within or possibly even beyond the Reststrahlenband of InP and\nInGaAs , to cover a similar range as the FC-referenced photonic LO.” (lines 319-322)\nBetween the lines:\nWe agree with the reviewer that stating an unsupported or only mildly supported claim may be\nmistaken as a definite proof and the authors had seen cases themselves in our own lab as well as false\ndata in publications where an imperfectly corrected time axis led to fake echoes/artifacts at the high\nfrequency end after Fourier transformation. We agree that such artifacts become particularly apparent\nwhen there is a high dynamic range at low frequencies as the artifacts are essentially attenuated copies\nof the low frequency part caused by the FFT that makes the low frequency end reappear at the high\nfrequency end. Yet, we still believe that the statement of potential usability even beyond 10 THz is\ncorrect and might be relevant for future work for the following reasons:\n1.) There is no plausible reason why photoconductors should not work beyond 10 THz.\n2.) Fourier artifacts can easily be identified by the absence of absorption lines. Fig. 1b of ref [36]\nshows a TDS measurement of a sample with InP substrate. One can see a perfectly flat noise\nfloor within the Reststrahlenband, starting around 6.5 THz up to ~8 THz where this specific\nmeasurement ended. The slight raise of the signal just at 8 THz is indeed supported by the FTIR\ndata. In contrast, when the substrate is removed (Fig 3b), there is no apparent noise at these\nfrequencies, but there still seems to be some mild absorption between 6.5 and 7.8 THz,\npossibly originating from the photoconductive material’s Reststrahlenband (just an ~1.5 µm\nthick film, so no excessive attenuation). Indeed, we cannot make a rock-solid statement for\nfrequencies beyond 8 THz as the measurement in Fig. 1b contains no data beyond 8 THz.\nGiven there is little to no papers with experimental data on photoconductive mixers beyond 10 THz\nbesides from authors within this manuscript, we encourage other groups or authors to investigate the\nbehavior."}]

Decision letter