Free-Space Terahertz Spectrum Analysis With an Optoelectronic Hybrid System

We present an optoelectronic hybrid system to perform high-resolution spectrum analysis in the terahertz regime. The concept is based on phase-locking of the difference frequencies of at least three continuous-wave (CW) distributed-feedback diode lasers by mixing the laser light with the radiation from a high-power electronic narrow-band source. Unlike for state-of-the-art spectrum analysis, no additional frequency extenders are required, keeping the system less complex and more cost-effective. Following our concept, we can generate laser difference frequencies from 0 to more than 1 THz with several hertz precision, which can be easily expanded to even higher frequencies, e.g., by cascading more lasers within our synchronization scheme. We demonstrate the systems frequency resolution and stability by measuring the first five harmonics of an electronic W-band source, and the first three of an active multiplier chain millimeter-wave source, using a CW gallium arsenide (GaAs) photoconductive antenna as a receiver.

Free-Space Terahertz Spectrum Analysis With an Optoelectronic Hybrid System Alexander Theis , Michael Kocybik , Georg von Freymann , and Fabian Friederich Abstract-We present an optoelectronic hybrid system to perform high-resolution spectrum analysis in the terahertz regime.The concept is based on phase-locking of the difference frequencies of at least three continuous-wave (CW) distributed-feedback diode lasers by mixing the laser light with the radiation from a highpower electronic narrow-band source.Unlike for state-of-the-art spectrum analysis, no additional frequency extenders are required, keeping the system less complex and more cost-effective.Following our concept, we can generate laser difference frequencies from 0 to more than 1 THz with several hertz precision, which can be easily expanded to even higher frequencies, e.g., by cascading more lasers within our synchronization scheme.We demonstrate the systems frequency resolution and stability by measuring the first five harmonics of an electronic W-band source, and the first three of an active multiplier chain millimeter-wave source, using a CW gallium arsenide (GaAs) photoconductive antenna as a receiver.

I. INTRODUCTION
R ECENTLY, advances in 5G and toward 6G commu- nication networks pose increasing challenges to highfrequency (HF) measurement techniques and the required system components.Looking at future key technologies like Internet of Things [1], machine-to-machine communications [2], or fully autonomous vehicles [3] from the perspective of hardware components, the realization of such applications demands a modification or even a radical redesign of devices, sub-systems, and systems.It is projected that in less than ten years from now, the data transfer rates will have to experience significant improvements to be well beyond 1 Tb/s [4].However, it is not possible to achieve such fast data speeds in the utilized range of 5G between 20 GHz and 100 GHz due to current transceiver designs and digital modulation techniques' limitations, such as nonlinear power amplifiers, phase noise, and poor analog-to-digital converter (ADC) resolution [5].Consequently, the development of the next generation HF components will also consider looking for new innovative test concepts to characterize and verify them.In particular, new measurement systems in the HF ranges of 6G applications (above 100 GHz and beyond) are becoming increasingly important for research and industry [6].
Nowadays, electronic spectrum analyzers (SA) are a wellestablished technique for the characterization and development of high-frequency components, and are a key measurement instrument in the microwave, millimeter-wave, and subterahertz frequency ranges.In an SA, the frequency is swept through the measurement band to determine the amplitude or power level of the input signal against the frequency.Test solutions that measure below 90 GHz are usually implemented as a single, integrated instrument [7], while extending SA capabilities to higher frequencies is typically achieved by using frequency extenders that up-convert stimulus signals and down-convert response signals to support devices that operate into the terahertz (THz) regime.The frequency extenders are based on harmonic mixers, which rely on full waveguide band THz Schottky diodes.They have the drawback that the higher the harmonic, the more the output signal is attenuated (up to more than 40 dBc) [8].To date, commercially available electronic SAs can reach frequencies up to 1.5 THz with these extender modules.However, due to the cutoff toward the lower frequencies and the multimodal behavior at the higher frequencies the bandwidth is limited to about 50% of the center frequency.To cover the range from 0.09 to 1.5 THz, at least seven different extension modules are required [8], which significantly increases the costs of the system.Moreover, when considering vector network analyzers, the usage of external mixers requires a complex calibration procedure, due to their bandwidth limitation.For instance, addressing a bandwidth from 100 GHz to 1 THz calls for recalibration of the system, whenever a source component must be exchanged for the respective frequency-subband [9].Characterizing devices over the entire possible bandwidth is therefore very tedious and expensive.
A promising idea to overcome these drawbacks is the use of optoelectronic concepts instead of purely electric ones.Two successful implementations of an optoelectronic architecture suitable for spectrum analysis in the THz range have already been published by Krause et al. [10] and Fernandez et al. [11].The first approach [10] is a photonic spectrum analyzer (PSA) that consists of two tunable laser diodes, working as a local oscillator, and an ErAs:InGaAs photoconductive mixer with integrated antenna for a heterodyne detection of a test signal.The resulting photocurrent, which corresponds to the convolution of the amplitude of the incident electromagnetic field and the conductivity, is then detected in an IF chain with a low pass cut-off frequency in the MHz range.The system is capable to analyze frequencies up to 1.25 THz with a resolution bandwidth (RBW) between 1.2 and 80 MHz.The minimum RBW of 1.2 MHz is mainly determined by the linewidth of the lasers, which is typically in the MHz range.High-resolution measurements in the kHz or even Hz range are therefore not possible with this approach.The second reported architecture of an optoelectronic SA [11] offers such HF resolution at the Hz level.It is also based on heterodyne down-conversion using ErAs:InGaAs photoconductive mixers and a photonic local oscillator.The system consists of a single DFB laser, which is amplified and split up into two branches with a polarization-maintaining splitter.In the first branch, the optical signal is phase-modulated by two cascaded electro-optical phase modulators with the frequency f RF , generating a series of sidebands around the main laser mode with distance f RF between them.An optical tunable band pass filter selects the mode number n, corresponding to the desired frequency, which is then combined with the main optical mode from the laser in the second branch.This creates a stable photonic signal composed of two modes with frequency separation of nf RF , which is sent into free space and then focused onto the photoconductive mixer for the heterodyne down-conversion of the test signal.To preserve the coherence between the optical signals, the mode propagating in the second part is delayed by sending it to a fiber of suitable length.Furthermore, a series of optical attenuators and two polarization controllers are required to match the power and the polarization state of the different modes before combing them.The system thus covers a frequency range from 50 to 90 GHz with a RBW of 1 Hz.The limiting factor here is the number and frequency spacing of the sidebands generated with the EOMs.In principle, stabilized signals with a frequency of 300 GHz and above are possible, but this requires additional cascaded EOMs or optical filters, which would significantly increase the complexity and costs of the architecture.
In this article, we introduce an easily adaptable and costefficient free-space optoelectronic SA setup for high resolution measurements in the THz range.The concept is based on the laser difference frequency stabilization scheme in [12] and employs at least two heterodyne optical phase-locked loops (OPLL) for the synchronization between two frequencycontrolled (secondary) distributed feedback (DFB) lasers and a free-running (primary) third.As in [10], the combined light of the continuous-wave (CW) DFB lasers irradiates a microscopic metal-semiconductor structure, a CW gallium arsenide (GaAs) photoconductive antenna (PCA), for the heterodyne down-conversion of the reference signal.The utilization of a triple CW laser system along with photomixers for THz spectroscopy has been reported in previous studies by Oh et al. [13] and Thirunavukkuarasu et al. [14].In [13], the difference frequencies between three lasers are employed to synchronously generate THz-transmitter and local oscillator signals for heterodyne detection of THz signals in gas sensing applications.Photomixing using three lasers is also utilized to concurrently monitor variations in the optical path lengths within a face-toface photomixer configuration, enabling precise self-normalized phase delay measurements [14].However, in both mentioned concepts, three lasers are employed specifically to generate two distinct beat signals: one between lasers 1 and 2, and another between lasers 1 and 3.These beat signals are cross-referenced to each other using a fixed frequency difference between lasers 2 and 3. Hence, there is no active synchronization between the two pairs of lasers through direct control of the individual laser output frequencies.
In contrast, our system takes advantage of the very precise frequency stability of an active electronic multiplier chain as a reference source to lock the beat signal of each laser pair.Since the beat signal of the laser pairs is phase-locked to the same reference branch, the individual lasers are also phase-locked to each other.Thus, by means of three lasers of mutually detuned wavelengths, a beat signal can be generated with a frequency corresponding to twice the output frequency of the multiplier chain.Moreover, the laser pairs can be individually locked to the reference signal between the multipliers of the chain, so that in conjunction with the frequency tunability of the multiplier chain, laser beat signals with any difference frequency up to twice the maximum reference oscillator frequency can be generated.Higher frequencies can be addressed by cascading additional laser pairs.
To demonstrate capabilities of our concept, we analyze the spurious harmonics of two different narrow-band emitters, operating from 75 to 110 GHz and from 225 to 260 GHz, respectively.Characterizing these plays a crucial role, especially for the radio certification of HF components, since one of the most common failures in these tests is due to harmonic spurious emissions (the 2nd, 3rd, …nth harmonics of the fundamental frequency) being too high [15].
The rest of this article is organized as follows.In Section II, the focus will initially be on the OPLL components, such as DFB lasers and control electronics and the associated limitations for the high-resolution spectrum analysis.Subsequently, the experimental demonstration of successful phase-locks between the lasers in the RF and THz range are shown.In Section III, the measurements of different spurious harmonics of the two electronic emitters with our developed and characterized CW SA setup are presented.In this section, we also discuss the limitations of the system in comparison to another photonic SA system and state-of-the-art electronic SAs, and present potential ideas for improvement.Finally, Section IV concludes this article.

II. LASER DIFFERENCE FREQUENCY STABILIZATION
In our laser synchronization setup, we use three DFB diode lasers (Model DL 100 DFB, Toptica Photonics) with an integrated 60-dB optical isolator, which prevents optical feedback into the laser diode.Each laser covers a wavelength range from 854.32 to 857.14 nm, which corresponds with a mode-hop-free tuning range of 1.16 THz.A maximum output power of approximately 100 mW is available after the isolator.The desired laser frequency can be set via temperature tuning (25 GHz/K) and finely adjusted by varying the operating current of the diode (1 GHz/mA).Due to spatial hole burning effects within the laser-active medium, which lead to a change in the charge carrier density and therefore the refractive index of the medium, the spectral width is larger than that of external-cavity systems (up to hundreds of kHz) [16].Additionally, residual temperature drifts and current noise increase the laser frequency fluctuations up to a few ten MHz on a time scale of milliseconds to seconds.To generate frequencies with precision on the Hz level, active frequency stabilization is therefore necessary.
For our stabilization scheme to work properly, the two most important criteria are a possibly large bandwidth of the feedback controller and short time delays between signal detection and laser frequency modulation.Therefore, we use a PID controller (mFALC 110, Toptica Photonics) with a theoretical bandwidth of 10 MHz and a response time of less than 15 ns [17].Even though the bandwidth indicates that, in theory, lasers with a linewidth of 10 MHz could be used in the feedback loop, the actual bandwidth of the controller is limited by experimental factors like the propagation time through the optical setup and the electronic components, resulting in a significantly smaller possible linewidth for the locked DFB lasers.

A. System Characterization
To get a rough estimate of what influence the factors mentioned have on the actual bandwidth of the PID controller, we first want to determine the loop propagation time.To avoid positive feedback in our control loop, the settings of the controller must be chosen such that phase lag or phase lead of the gain at all frequencies do not exceed 180 degrees.The resulting time delay consists of the propagation time of the laser light through the optical fibers (t Fiber ) and of the time the electrical signals need to pass through the RF cables (t RF ).With a fiber length of 2.5 meters (v Fiber ≈ 0.66 c), there is a time delay of about 12.6 ns for the optical path.The RF cables in the electronic part of the system are roughly 0.4 m long (v RF ≈ 0.66 c), resulting in a delay of 2 ns.This, together with the 15 ns delay provided by the PID controller and the 25 ns response time of the transimpedance amplifier, gives a total time delay t Delay of approximately 55 ns.
The phase delay τ Delay in a PID system can be calculated as where Φ(ω) is the phase shift and ω is the angular frequency.Supposing the phase delay considered here depends only on frequency-independent system parameters such as light or signal propagation times τ Delay (ω) can be replaced by t Delay .With the definition for the angular frequency ω = 2πf, this results in In our setup, this would result in phase shift of roughly 120°for a frequency of 6 MHz.Additionally, other electronic components like the laser frequency control also add time delay to the system, increasing the phase shift even more.
To ensure that the phase lag does not exceed 180°the required bandwidth of the PID and therefore the linewidth of The output of the two DFB lasers is combined by a fiber coupler resulting in a beat note that is recorded with an amplified photodiode.Feedback is applied via a PID controller to the modulation input of one of the lasers, while the other remains free-running.
the controlled lasers must be reduced.Experimentally it was elaborated that for the system to run stable, laser linewidths of less than 1 MHz are essential.In a first step, the spectral width of the secondary DFB laser diodes is determined using a delayed self-heterodyne linewidth measurement setup [18].
For both secondary diodes, we find a laser linewidth of 0.3748 MHz (secondary 1) and 0.6764 MHz (secondary 2) on a 5 µs time scale, respectively.Thus, both lasers have a linewidth significantly smaller than 1 MHz and can be used as secondary lasers in our OPLLs.

B. Phase-Locking in the RF Range
To test our laser synchronization on one hand and finding the best possible settings for the PID controllers on the other, two DFB lasers are first locked in the RF range at 10 MHz.Therefore, we use a comparable setup to the one shown earlier in [12].In the OPLL setup (see Fig. 1), a polarization-maintaining 2x2 fiber coupler is used to combine the signals of secondary and primary laser.One of the fiber outputs is directed to an amplified 150 MHz photodetector (PDA10A2, Thorlabs GmbH) for the laser synchronization, while the other one is guided to the measurement.The recorded beat signal is sent to the laser control unit, where it is mixed with a stable LO signal at 10 MHz from an RF generator.The resulting frequency difference serves as an error signal for the very fast PID controller.If there is any difference between the beat and the LO signal, the controller alters the input current and thus the frequency of the secondary laser.Thereby, the frequency of the locked laser follows the frequency of the free-running laser with an offset equal to the LO signal.
Fig. 2 illustrates the obtained spectra with and without stabilization.If the phase-lock is switched OFF (red), the beat signal drifts over several MHz on a time scale of some ms.For longer time scales, these drifts even exceed a few tens of MHz, so the available beat signal of our system changes continuously.In the phase-locked case (blue), the narrow peak at the LO frequency of 10 MHz is clearly visible, indicating that the controlled laser is following the free-running Primary laser with the expected Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.offset.The side bumps at 10 MHz ± 3 MHz, which can be explained with the limited frequency modulation bandwidth of the laser, are suppressed by nearly 45 dB.
If we look at a high-resolution measurement of the phaselocked beat signal (Inset Fig. 2), which was measured with a bandwidth of 1 kHz and an RBW of 30 Hz and also averaged 20 times, we see that the main lobe is slightly shifted by about 50 Hz compared to the selected LO frequency.This is due to the used RF generator, whose maximum output frequency should be 10 MHz, which it does not quite achieve.However, the linewidth of the stabilized beat signal is found to be limited by the 30 Hz RBW of the commercial SA, which we used for the visualization of the feedback loop signal of the OPLL.Such a narrow line is evidence that the phase-lock to the oscillator was successful.The periodical side peaks in the spectrum appear to be harmonics of the typical 50-Hz noise of the environment.The difference in the background level normalized to the central peak between the spectrum in the main panel and the high-resolution spectrum can be explained with the significantly lower RBW.

C. Adaptation of the Phase-Locking Scheme to the THz Range
In the following, the locking of the diode laser pair is adapted to a CW electronic narrow-band source emitting in the THz regime.In addition, the system was expanded to include a further secondary laser to have a significantly larger bandwidth available.The demonstrated laser synchronization technique is based on a hybrid concept that combines extremely stable high-frequency electronic components with nonlinear optical elements for the laser frequency stabilization.
A sketch of our three-laser hybrid synchronization setup is depicted in Fig. 3.The fiber-combined radiation from the three diode lasers is split up into three parts.Two are guided to the different OPLLs for the frequency locking, while the third part can be used to perform the measurements.For this approach, the laser light of the secondary diodes is first divided with a 50:50 power splitter, then superimposed with the primary laser, and finally sent to a tapered laser amplifier (BoosTA, Toptica Photonics) to reach the power level needed for the two GaAs PCAs (PCA-FD-0780-130-RX-1 photomixer with log-spiral antenna, Toptica Photonics), while maintaining the spectral properties of the seed lasers.The photomixer has a bandwidth of up to 3 THz and provides dynamic range of 80 dB at 100 GHz, and 70 dB at 500 GHz.In the free-space part of our setup, the radiation of a CW electronic THz oscillator is sent via two off-axis parabolic mirrors (OAPs) to the first PCA.After the emitter radiation has passed the first OAP, it hits a 525 μm thick Si wafer, which serves roughly as a 50:50 beam splitter for the THz signal [19].Together with the laser beat signal, the transmitted and reflected portion of the THz radiation irradiate the antenna structures of the PCA in the OPLLs, respectively.The impinging THz wave generates a bias voltage in the PCA while the laser beat modulates the conductivity in the semiconductor.The resulting photocurrent, which oscillates with the frequency difference between beat signal and the THz source, is fed to two transimpedance amplifiers (TIA) (DHPCA-100, FEMTO Messtechnik GmbH) with a selected bandwidth of 14 MHz and a gain of 10 5 V/A.Subsequently, the output signals of the TIAs serve as the error signals for the laser synchronization with the PID controllers.The system contains a reference branch based on an active frequency multiplier chain (FMC) (Transmitter TX RX-500, Radiometer Physics GmbH) with an output frequency range of 325 to 500 GHz that provides an output power around 100 μW.An analog quartz-stabilized signal generator serves as a RF input source for the CW THz multiplier chain.
As in the synchronization approach in the RF range mentioned above, a mFALC laser controller mixes the captured error signal with a 10 MHz LO signal from the RF generator.By tuning the beat frequency close to the THz signal, the controller can employ the resulting difference signal to phase-lock the laser pair to the THz emitter with a frequency offset given by the LO signal.With respect to obtain the largest possible frequency difference, one of the secondary lasers is shifted up in frequency compared to the Primary, while the other is shifted down.This could be since the portion of the THz radiation transmitted by the silicon waver is slightly larger than the reflected part.Due to the low power of the 500 GHz reference, the signal dynamics are a little lower compared to the locking in the RF range (see Fig. 2) but are still more than 20 dB above the noise level, indicating a successful phase-lock of each DFB laser pair to the 500 GHz narrow-band emitter.Both peaks are separated by 1000.02GHz, indicating a useable phase-stabilized measurement signal, generated from the superposition of the two secondary lasers, with an effective frequency bandwidth of more than 1 THz and a resolution in the tens of Hz range.
In this article, as an alternative to using PCAs, an electrooptical free-space sampling scheme was also used to synchronize the laser pairs with the THz reference branch, following [12].Fig. 5 shows an example of the beat signal of a corresponding synchronization with an active multiplier chain (AMC) (>50 mW, 225-260 GHz, 1213B-A, ACST GmbH) at 233.33 GHz.It displays the measured frequency spectra of the phase-locked (blue) and free-running (red) laser beat signals with a THz oscillator frequency of 233.33 GHz.In the phase-locked case, the central peak at the 10 MHz LO frequency has a linewidth of approximately 3 kHz, which corresponds with the set RBW of the commercial SA.In the high-resolution spectrum of the phase-locked beat signal at 233.33 GHz (Inset of Fig. 5), which was measured with a bandwidth of 1 kHz, a RBW of 30 Hz and an average of 20 sweeps, the main peak is also shifted by about 50 Hz from the selected LO frequency of 10 MHz, as in the RF range.Even though the width of the main peak is slightly wider than in the RF regime (Inset of Fig. 2), it still shows a FWHM of less than 100 Hz, indicating a very narrow linewidth of the generated laser beat signal.The periodic spurious peaks that could be caused by environmental noise also reappear in the high-resolution spectrum of the phase-locked signal at 233.33 GHz but are suppressed by more than 50 dB.
Compared to the PCA setup (see Fig. 3), the EO scheme lacks some stability of the phase-locked beat signal, especially for reference sources with low output power.Thus, it is not possible with this system to lock both OPLLs simultaneously with the available 500 GHz emitter.To overcome this drawback, the setup of the EO detection has also been modified in such a way that instead of one CW source, two different sources can be used to generate the difference frequencies.By moving both secondary frequencies above or below the primary laser, the beat frequencies can also be subtracted from each other.This allows us to generate beat frequencies between 65 to 275 GHz and 550 to 760 GHz.Additionally, only a single differential frequency between the Master laser and the respective secondary laser can be extracted from the first fiber coupler and used to generate a stabilized beat signal to cover the frequency range from 325 to 500 GHz.To also achieve the missing frequencies, the reference source can be exchanged or additional couplers between different stages of the AMCs can be employed.These couplers allow for the extraction of specific harmonics prior to the multiplication process.For instance, coupling out a portion of the signal power before the final tripler in the 325 to 500 GHz chain, enabling the generation of frequencies ranging from 110 to 170 GHz, subsequently facilitating the generation of the absent difference frequencies.In this design, the system is therefore able to deliver a highly stable and accurate CW laser beat signal at any frequency between the minimal frequency offset of 10 MHz and 760 GHz.
In the following, this setup was used for measurements of the spurious harmonics of electronic narrow-band emitters.

III. SPURIOUS HARMONICS MEASUREMENTS
To test the capabilities of our laser synchronization, a hybrid CW SA system is set up to measure the spurious harmonics Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply. of different electronic narrow-band sources using one of our GaAs PCAs as receiver for the THz radiation.Harmonics are integer multiples of an emitter fundamental and are generated by nonlinearities within the device, which can be created by either the construction of the RF signal or more likely by the RF amplifiers in the multiplier chain.Regardless of the source, harmonics must be below a certain limit to meet the electromagnetic compatibility guidelines in the radio equipment directive (RED) [20].

A. Hybrid CW Spectrum Analyzer Setup
Fig. 6 illustrates the measurement setup of our CW SA.First, the phase-locked beat signal of the two secondary lasers is guided from our laser synchronization setup to the optical amplifier, which increases the power of the linearly polarized laser beam.Afterwards, it is sent to the PCA to create charge carriers in the semiconductor material of the receiver.A 75 GHz electronic narrow-band emitter (AFM6 75-110 +10, Radiometer Physics GmbH) and an AMC millimeter-wave source (1213B-A, ACST GmbH) emitting at 233.33 GHz serve as sources for the different harmonics, that are to be detected by our SA setup.The THz beam path consists of two off-axis parabolic mirrors with an effective focal length of 101.8 mm in a standard four fconfiguration and a hyperhemispherical silicon lens (f ≈ 30 mm) in the PCA.For the measurement of the harmonics, we use a coherent detection scheme, which means down converting the DUT's radiation with a local oscillator signal-in our case the laser beat-into an electrical signal.Thereby, the optical heterodyne detection of the signal improves sensitivity and frequency selectivity of the receiver [21].Additionally, amplitude and frequency information of the device under test (DUT) signal can be determined, enabling a potential expansion of the system to perform a comprehensive S-parameter analysis like that of a vector network analyzer.
In our setup the impinging THz wave generates a voltage in the antenna while the beat signal modulates the conductivity.The resulting photocurrent is proportional to the amplitude of the THz electric field and depends on the phase difference between the optical beat and the THz wave-the measured oscillation of the photocurrent corresponds to the frequency difference between laser beat and the DUT.
To be able to determine the different harmonics, the secondary laser pair is phase-locked very close to the corresponding harmonic frequency.Therefore, different electronic narrow-band emitters were used to achieve the needed reference frequencies for the beat signals.The measured photocurrent from the receiver module is fed to the input of a low noise current preamplifier (Model SR570, Stanford Research Systems), which is connected to a lock in amplifier (HF2LI, Zurich Instruments) and a PC for the data acquisition.
For the heterodyne detection of the voltage signal, the laser beat frequency is adjusted to generate, in correlation with the incident THz signal, an intermediate frequency within the range of 10 kHz.This frequency offset was chosen, since the preamplifier only provides sufficient amplification for the detection of the higher harmonics in this range [22].The lock in amplifier serves as an ADC, digitizing the voltage signal of the preamplifier using a bandwidth of 51 kHz (frequency step size 50 Hz) and a sampling rate of 103 kSa/s.After capturing the time-domain signal, it is subsequently transformed into a frequency spectrum using the fast Fourier transform.

B. Hybrid CW Spectrum Analyzer Characterization
To characterize our system, we implement a calibration procedure similar to the one described in [10].Initially, we utilize a FMC (AFM 12 110-170 +10, radiometer physics GmbH) with a frequency range of 110 to 170 GHz and a maximum output power of approximately 10 mW as our DUT.Through this setup, we determine the linearity, displayed average noise level (DANL) RBW and 3-dB bandwidth of our SA setup.Therefore, the FMC is set to a nominal frequency of 140 GHz and the output power is varied from 10 mW down to 1 pW, by decreasing the input power of the FMC, which is provided by an RF signal generator (E8257D PSG Analog Signal Generator, Agilent Technologies).To measure the output power of the DUT, we positioned a pyroelectric detector (SLT Sensor und Lasertechnik GmbH THz 10) at the PCA location.The broadband pyroelectric detector underwent calibration at 1.4 THz at the Physikalisch-Technische Bundesanstalt in Berlin and possesses a working range of 8 μW to 10 mW.Similar to [10], we considered a systematic error of 30% arising from the disparity between the measurement and calibration frequencies.For lower power levels, we replaced the pyroelectric detector with a golay cell (Model OAP Golay cell, CDP System Corporation), capable of detecting power levels down to 1 nW.To facilitate the comparison between the measured values of the Golay cell and the calibrated pyroelectric detector, the detectors were cross-referenced within the overlapping area for multiple power values.The power levels below the noise floor of the Golay cell are estimated by extrapolating from the input versus output power measurements of the FMC, assuming a linear relationship between them.The linearity was verified in the power range down to 1 nW by simultaneously monitoring the input power level using an RF power sensor (LB5926A, Ladybug Technologies LLC) and measuring the output power with the Golay detector.To calibrate the responsivity of our hybrid SA at 140 GHz, we match the measured peak values with the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.power readings from the pyroelectric detector or the Golay cell, respectively.Fig. 7 shows an excellent linearity of the hybrid CW SA for different power levels, extending down to an FMC output power of 4.47 pW.As the output power decreases further, the signal flattens out, eventually reaching the noise power level of 1.22 pW.To calculate the DANL of SA, we need to divide this value by the measurement bandwidth, which in our case is the frequency bin size of 50 Hz.Consequently, we obtain a DANL value of −106.13 dBm/Hz for a frequency of 140 GHz.
Following that, we proceed to calibrate the measured power spectrum of our SA at an FMC frequency of 140 GHz.Therefore, the integrated spectral power of the SA is matched with the recorded signal of the pyroelectric detector.In Fig. 8, the calibrated power spectrum (±3 kHz around f FMC ) is displayed for an output power of 50 μW (−13 dBm).The spectrum was obtained using an amplification factor of 1 μA/V, an acquisition time of 200 ms (averaged ten times), and frequency steps of 50 Hz.The peak in the spectrum exhibits a 3-dB bandwidth of 101.12 Hz.It should be noted that this bandwidth represents the combined linewidth of the FMC and the LO signal.Considering that the expected linewidth of the FMC falls within the range Fig. 9. Spectral responsivity of the hybrid CW SA for frequencies between 75 to 500 GHz (black markers: calibration points). of 1 Hz [23], the determined linewidth primarily arises from the characteristics of the LO.Hence, the minimum achievable RBW with this hybrid CW SA, which is mainly determined by the spectral width of the laser beat signal, is approximately 100 Hz.
Next, we aim to characterize the frequency response of the SA setup for additional frequencies.To achieve this, we employ various multiplier chains with frequency ranges from 75 to 110 GHz (S10MS-AG 75 to 110 GHz Millimeter Wave Source Module, OML Inc.), 110 to 170 GHz (FMC), 225 to 265 GHz (1213B-A, ACST GmbH) and 325 to 500 GHz (Transmitter TX RX-500, Radiometer Physics GmbH).The DUTs are configured to provide an output power of 50 μW.Similar to the previous measurements, it is necessary to calibrate the output power of the different sources.To accomplish this, we utilize the pyroelectric detector and measure the required input power for a signal strength of 50 μW.Since, these measurements require precise adjustments, we focus on considering only 12 frequencies (black markers in Fig. 9) ranging from 75 to 500 GHz, with an approximate spacing of 50 GHz.After the power calibration, we measure the peak spectral values of the SA and correspond them with the different frequencies.
In Fig. 9, the spectral responsivity of the hybrid CW SA is illustrated for frequencies ranging from 75 to 500 GHz.The responsivity exhibits a peak around 100 GHz and gradually decreases as the frequency increases.This decrease in responsivity is primarily attributed to the roll-offs in the dynamic range of the PCA at higher frequencies [24].Unfortunately, in this article no FMCs for frequencies above 500 GHz are available.As a result, we estimate the responsivity values for higher frequencies by fitting an exponential curve to the measured spectrum.Frequencies below 75 GHz require separate consideration due to the extremely steep roll-off of the antenna for frequencies below 50 GHz.Hence, we specify a calibrated bandwidth of our SA for frequencies between 75 and 760 GHz.
The PCA used in our setup features a log spiral antenna designed for circularly polarized light.Although a log spiral antenna is generally considered to be a frequency-independent antenna, with minimal variations in radiation pattern, impedance, and polarization over a wide bandwidth, research has indicated that the axial ratio of elliptical polarization tends to increase as frequencies rise, eventually transitioning to linear polarization.This occurs when the length of the tapered section of the antenna matches the effective wavelength, causing the antenna to behave like a dipole [25].The utilized FMCs in our setup employ rectangular waveguides with a Pickett-Potter horn antenna for free-space transmission, resulting in the generation of linearly polarized beams (with a cross-polarization level typically above −20 dB [26]).Hence, we also investigate the influence of the incident radiation's polarization direction.By rotating the PCA by approximately 90°, we measure the peak voltages at various frequencies ranging from 75 to 500 GHz.However, the measured voltages differ by less than 10% for each frequency examined.Considering that the observed deviations in polarization direction are minimal compared to other sources of measurement inaccuracies, such as power calibration with the pyroelectric detector and adjustments, and since all DUTs are measured with the same polarization direction, we do not include the influence of polarization in the calibration process.However, it is important to note that the influence of the polarization direction on the measurements may become more relevant at higher frequencies, as the dipole effect increases with frequency.

C. Harmonic Measurement Results
Fig. 10 shows the obtained frequency spectra of different harmonics of the electronic narrow-band emitter at 75 GHz and the AMC millimeter-wave source emitting at 233.33 GHz.All measurements were taken using an amplification factor of 1 μA/V and an acquisition time of 200 ms for a frequency span of 10 kHz around the central peak with frequency steps of 50 Hz.
The measured voltage values are converted to power values by employing the responsivity of the receiver.This conversion process also contributes to the slope observed in the noise floor.
In the spectrum of the 75 GHz source [see Fig. 10(a)], five narrow peaks at frequencies of around 75 , 150, 225, 300, and 375 GHz are clearly visible, corresponding to the first to fifth harmonic of the fundamental frequency.The spike at 75 GHz has a peak signal power of 11.01 dBm with a signal dynamic of almost 80 dB.Looking at the other peaks in the spectrum, the measured signal powers continue to decrease from −17.23 dBm (second), −21.49dBm (third), −27.93 dBm (fourth) to −32.18 dBm (fifth).This signal reduction is to be expected since the amplitude usually decreases with increasing order of the harmonics.
For the AMC millimeter-wave source [see Fig. 10(b)], we find three narrow spikes at frequencies of about 233.34, 466.67, and 700.00 GHz.The fundamental frequency shows a maximum peak power of 17.01 dBm and a signal to noise distance of 60 dB.For the second harmonic we find a signal power of −3.67 dBm and for the third a power value of 3.06 dBm.The observation that the 3rd harmonic is 6 dBm higher than the second harmonic appears to be quite improbable.Consequently, we speculate that the responsivity for frequencies above 500 GHz behaves differently than what was assumed in the following section.Due to this discrepancy, it becomes necessary to also carry out a power calibration specifically for frequencies ranging from 500 to 760 GHz, to allow more accurate power determinations within this frequency range.
By tuning the output frequency of the DUTs, the peaks in the spectra can be shifted according to their harmonic number, showing that they correspond to the different harmonics of the emitters-for example, a 5 kHz shift in the fundamental frequency results in a shift of 10 kHz for the second harmonic, 15 kHz for the third, and so on.

D. System Limitations and Possible Improvements
Since the main focus of our work was the optimization of the laser stabilization scheme in the THz range, the presented hybrid CW SA is currently still in a highly experimental stage.Therefore, the concept has some weaknesses regarding sensitivity, calibration for accurate power measurements, acquisition speed, and resolution compared to state-of-the-art frequency extended electronic spectrum analyzers (ESA).
The measured DANL of −106.13 dBm/Hz for our optoelectronic system corresponds well with the DANL of −113.8 dBm/Hz reported for the PSA in [10].However, it is noticeably lower compared to the typical DANL range of −130 to −150 dBm/Hz for commercial systems [8].Nevertheless, it is worth mentioning that our system operates in a free-space environment, in contrast to the waveguide-coupled structure of ESAs.In our case, the DANL is mainly limited by the performance of the used PCA.One of the key requirements for efficient PCAs is high optical photon-to-charge carrier conversion efficiency, which is achieved by increasing the absorption in the photoconductive layer.One possible approach to enhance the conversion efficiency is the use of metallic nanostructures deposited on the active layer.These nanostructures are designed to couple the incident optical field to a surface plasmon wave.The surface plasmon wave is highly concentrated near the edges of the plasmonic structure, resulting in a strong enhancement of absorption and the generation of additional charge carriers in this localized region [27].For example, the sensitivity of an LT-GaAs photoconductive detector was increased by 29% by sputtering Au nanoislands on the dipole gap region [28].In addition to plasmonic structures and nano-cavities, metallic or dielectric metasurfaces have also shown their effectiveness in enhancing absorption within a thin dielectric layer without requiring additional structures [29].The sensitivity can be further increased by introducing an integrated aperture on the far side of the photoconductive region, isolating the THz field in the area of the aperture before entering the detector [30].Given the recent advancements in PCA technologies, it is anticipated that the disparity in sensitivity between optoelectronic and electronic systems will diminish in the future.
Another crucial parameter for SAs is power accuracy of the measurements.Modern ESAs offer a power calibration accuracy better than ±1 dB [31].For our SA determining the accuracy of power measurements is quite challenging due to the numerous assumptions and estimations made during the calibration process.Additionally, the system's responsivity was calibrated only at 12 frequency points within the range of 75 to 500 GHz, which introduces additional uncertainties.In principle, it is possible to overcome this drawback with a carful calibration for each frequency in the range of 65 to 760 GHz.However, the power measurements conducted for the fundamental frequencies (see Fig. 10) align quite well with the expected output power values of the two DUTs.Furthermore, in free-space measurements, there are challenges related to beam path alignment and reflections at surfaces.For instance, reflections at the silicon lens of the PCA result in approximately 30% loss of the optical power [32].Hence, it would be advantageous to also consider integrated onchip solutions to enhance the system performance in this aspect.
In terms of frequency resolution, our SA is capable of measuring signals with an RBW of a few 10 Hz.Hence, it is capable of achieving a significantly higher measurement resolution compared to the nonfrequency stabilized PSA reported in [10], with a minimum RBW of 1.2 MHz.This level of resolution is almost comparable to that of electronic SA, as their minimum RBW is typically also in the range of Hz.In our system, the minimum RBW is primarily constrained by the spectral width of the laser beat signal.However, it is worth noting that by employing lasers with narrower linewidths or utilizing a faster PID controller for frequency stabilization, it is possible to achieve a minimal RBW on the order of Hz.The maximum RBW is limited by the bandwidth of the current preamplifier used (maximum bandwidth of 1 MHz) and the data acquisition speed (maximum speed of 210 MSa/s).Yet, it is important to note that increasing the preamplifier bandwidth results in a decrease in sensitivity due to the lower amplification factor.Consequently, achieving coverage over a wide frequency range is highly time-consuming, as it requires maintaining a very narrow spacing between two frequency points at which the laser pairs need to be locked.For instance, with a locking point distance of 1 MHz and an acquisition time of 200 ms, it would take over 34 hours to complete a sweep from 75 to 760 GHz.Using an amplifier with a wider bandwidth would enable a reduction in the number of required locking points and consequently, significantly decrease the measurement time.In contrast, ESAs provide a maximum RBW in the GHz range, allowing for faster measurements of wide frequency ranges.However, this comes at the expense of significantly lower resolution.
The hybrid CW SA presented in this article has a bandwidth of nearly 700 GHz, which is slightly lower than the 1.25 THz bandwidth reported for the PSA in [10].However, an ESA would require at least of 5 frequency extender modules to cover the same frequency range.Extending the maximum bandwidth of our SA to 1 THz and beyond is easily achievable by employing reference sources with higher output frequencies or by cascading additional laser pairs.In addition, the hybrid CW SA offers a more cost-effective solution compared to established ESA approaches.Furthermore, the scalability of the concept allows for multichannel measurement solutions.

IV. CONCLUSION
In conclusion, we have demonstrated phase-locking of THz beat signals of two DFB laser pairs with PCAs as well as EO sampling in an optoelectronic hybrid system.By locking the laser signals to a single CW narrow-band emitter, we are able to generate powerful and very frequency stable beat signals.
Using the appropriate reference sources, frequencies from the millimeter-wave to the THz range can be covered with a single system unit without the need of multiple frequency extenders.This not only reduces the costs, but also the complexity of the measurement system.The concept even holds promise for frequency extensions well above 1 THz by cascading more secondary laser with appropriate frequency ranges.
Furthermore, we characterized our systems frequency stability and resolution by implementing a hybrid SA setup to investigate the spurious harmonics of two different CW THz sources.The system was calibrated for a frequency range between 75 to 760 GHz and could measure harmonics up to 700 GHz with a resolution of a few 10 Hz.This, together with the comparatively simple complexity and scalability, provide promising approaches for an extension of the hybrid THz SA to perform a complete network analysis of various HF components from the low GHz deep into the THz range with a single system platform.
Additionally, the Hz-level resolution not only allows the precise recording of frequency spectra, but also offers application options in the field of high-resolution spectroscopy.

Fig. 1 .
Fig. 1.OPLL setup for synchronizing the DFB laser pair in the RF range.The output of the two DFB lasers is combined by a fiber coupler resulting in a beat note that is recorded with an amplified photodiode.Feedback is applied via a PID controller to the modulation input of one of the lasers, while the other remains free-running.

Fig. 3 .
Fig. 3. Three-laser hybrid synchronization setup for locking in the THz regime.The beat signal of two laser pairs is phase-locked to the radiation of a 500 GHz electronic CW source with two PCA.

Fig. 4 .
Fig. 4. Frequency spectrum of the phase-locked laser beat signal at ±500.01 GHz from the central frequency f 0 = 350.6212THz (RBW: 3 kHz, 20 averages).The measurements were acquired with an SA (SA, Anritsu MS2830A) connected with the signal output of the transimpedance amplifier.

Fig. 4
Fig.4displays the measured frequency spectrum of the phaselocked laser beat signals with a THz oscillator frequency of 500 GHz and a 10 MHz LO signal.In the spectrum, two peaks at −500.01 GHz and +500.01GHz from the primary laser frequency at f 0 are clearly visible.The peaks at the 10 MHz LO frequency in both OPLLs have a linewidth of approximately 3 kHz, which corresponds with the set RBW of the commercial SA used for the measurements.Hence, the real linewidth of the phase-locked signal is smaller than this value.Furthermore, the beat signal of PCA#2 at +500.01 GHz has a slightly lower dynamic than the phase-lock with PCA#1 at −500.01 GHz.This could be since the portion of the THz radiation transmitted by the silicon waver is slightly larger than the reflected part.Due to the low power of the 500 GHz reference, the signal dynamics are a little lower compared to the locking in the RF range (see Fig.2) but are still more than 20 dB above the noise level, indicating a successful phase-lock of each DFB laser pair to the 500 GHz narrow-band emitter.Both peaks are separated by 1000.02GHz, indicating a useable phase-stabilized measurement signal, generated from the superposition of the two secondary lasers, with an effective frequency bandwidth of more than 1 THz and a resolution in the tens of Hz range.In this article, as an alternative to using PCAs, an electrooptical free-space sampling scheme was also used to synchronize the laser pairs with the THz reference branch, following[12].Fig.5shows an example of the beat signal of a corresponding synchronization with an active multiplier chain (AMC) (>50 mW, 225-260 GHz, 1213B-A, ACST GmbH) at 233.33 GHz.It displays the measured frequency spectra of the phase-locked (blue) and free-running (red) laser beat signals with a THz oscillator frequency of 233.33 GHz.In the phase-locked case, the central peak at the 10 MHz LO frequency has a linewidth of approximately 3 kHz, which corresponds with the set RBW of the commercial SA.In the high-resolution spectrum of the phase-locked beat signal at 233.33 GHz (Inset of Fig.5), which was measured with a bandwidth of 1 kHz, a RBW of 30 Hz and an average of 20 sweeps, the main peak is also shifted by about 50 Hz from the selected LO frequency of 10 MHz, as in the RF range.Even though the width of the main

Fig. 6 .
Fig. 6.Hybrid CW SA setup.The amplified phase-locked laser beat signal of the two DFB secondary lasers is employed to measure the harmonics of different narrow-band transmitters with a PCA as receiver for the DUT´s radiation.

Fig. 7 .
Fig. 7. Measured peak values of the FMC spectra at 140 GHz over the output power.

Fig. 10 .
Fig. 10.(a) Frequency spectrum of the first to fifth harmonic of a 75 GHz emitter (amplification factor: 1 µA/V, sampling rate: 103 kSa/s, averaged: 10 times, acquisition time: 200 ms per averaged spectrum, and frequency steps: 50 Hz).b) Frequency spectrum of the first to third harmonic of the AMC millimeter-wave source emitting at 233.33 GHz (amplification factor: 1 µA/V, sampling rate: 103 kSa/s, averaged: ten times, acquisition time: 200 ms per spectrum, and frequency steps: 50 Hz).