Chip-scale electrically pumped optical frequency combs (OFCs) are expected to play a fundamental role in applications ranging from telecommunications to optical sensing. To date, however, the availability of such sources around 2 μm has been scarce. Here, we present a frequency-modulated OFC operating around 2060 nm of wavelength exploiting the inherent gain nonlinearity of single-section GaSb-based quantum well diode lasers. A 2 mm long device operating as a self-starting comb outputs 50 mW of optical power over more than 10 nm of bandwidth while consuming <1 W of electrical power. Using the shifted-wave interference Fourier transform spectroscopy technique, we characterize the generated frequency-modulated waveform and demonstrate a linearly chirped intermodal phase relationship among the entire emission optical bandwidth. Furthermore, by compensating for the linear chirp using a single-mode optical fiber with opposite dispersion, 6 ps long optical pulses are generated. The frequency stability of the devices with ∼19.3 GHz repetition rates allows us to perform mode-resolved free-running dual-comb spectroscopy. All rights reserved.

Optical frequency combs (OFCs) have revolutionized the field of metrology by enabling measurement of optical frequencies with unprecedented precision.1 An OFC consists of a set of equidistant mutually coherent modes and has predominantly been generated by mode-locked lasers. In the time-domain, mode-locked lasers produce a train of pulses with a strongly amplitude-modulated (AM) character.2,3 The underlying physical phenomena involved in the synchronization of the cavity modes are saturable absorption and Kerr lensing. However, amplitude modulation is not a prerequisite for the source to have frequency comb properties. Instead, it is sufficient for the optical waveform just to be periodic. For example, frequency modulation (FM) produces a waveform that is constant in intensity with an instantaneous frequency that is swept across the source bandwidth in a repetitive fashion, which in the frequency domain possesses the equidistance property of an OFC. This mode of operation is favorable for many single-section semiconductor lasers with fast gain dynamics that precludes energy storage over a roundtrip time required for AM comb generation. Spatial hole burning (SHB) responsible for multimode lasing and nonlinear four wave mixing (FWM) enabling their synchronization have been identified as key contributors to self-starting FM OFC generation in a semiconductor laser cavity.4–6 SHB initially promotes lasing on multiple longitudinal modes with non-equidistant spacing governed by the cavity dispersion. However, FWM enables equalization of the spacing down to a sub-kilohertz level over large optical bandwidths, as long as the intracavity dispersion is sufficiently low. It was recently suggested that FM operation enables more efficient use of the semiconductor laser gain compared to AM operation in some media.6,7 Furthermore, passive mode locking based on saturable absorption in semiconductor lasers typically requires a strong negative bias applied to the absorber section of the cavity,8 which inevitably lowers the average optical power. Consequently, for frequency comb applications that require high average optical power and quasi-continuous-wave intensity, FM operation is preferred.

To date, different FM comb platforms have been demonstrated, in particular, based on quantum dash (QDash),9 quantum dot (QD),5 quantum well (QW),10,11 quantum cascade (QC),12 and interband cascade (IC) lasers.13,14 Some of them have also supported AM operation in the same medium under strong microwave injection15 or multi-section bias.16 In principle, the wavelength portfolio of FM combs is still expanding, yet there are some wavelength ranges of large practical relevance that have been unexplored.

For instance, the 2 μm region is of large interest for the next-generation telecommunication systems, eye-safe light detection, and molecular spectroscopy, in particular, for monitoring global emissions of carbon dioxide. From an application standpoint, 2 μm combs can enable spectrally efficient orthogonal-frequency division multiplexing (OFDM) in optical interconnects17 to be implemented in a new spectral window, while in sensing applications, they would allow measurement of broadband and high-resolution spectra on extremely short time scales using the dual-comb technique.3,18 Although this spectral region is underdeveloped compared to typical telecommunication wavelengths around 1.5 μm, it is still more mature than at mid-infrared wavelengths beyond 2.5 μm. Convenient availability of thulium19 and holmium20 optical fiber amplifiers accompanied by recent advances in fast modulator21 and photodetector22 technology promises a rapid expansion of systems operating in this spectral range. In this context, the development of compact coherent light sources at 2 μm is of large importance.

Whereas technologically mature optically pumped fiber23 and semiconductor disk24 lasers operate reliably in this spectral region, greatly desired are small-footprint electrically pumped chip-scale combs with high optical power. Recently, several groups have successfully demonstrated passive mode locking of a 2 μm GaSb-based quantum well diode laser (QWDL),25–27 which has the advantage of emitting high peak powers over picosecond timescales. These sources, however, have average optical powers lying in the single milliwatt regime, and their suitability for demanding heterodyne measurements requiring narrow optical linewidths is yet to be evaluated.

In this work, we present QWDL devices based on a monolithic single-section Fabry–Pérot cavity design emitting a frequency-modulated THz-spanning OFC with ∼50 mW of optical power centered around 2060 nm at less than 1 W of electrical power consumption at room temperature. These devices emit ten times more average optical power than the previously demonstrated mode-locked 2 μm QWDL devices25–27 due to the lack of intracavity saturable absorption losses. Their excellent stability and high line-to-line coherence allows for completely free-running near-infrared dual-comb spectroscopy (DCS), as demonstrated here on a low-finesse etalon. Using the shifted-wave interference Fourier transform spectroscopy (SWIFTS) technique,28 we retrieve the spectral phase, instantaneous optical intensity, and frequency. Despite the linearly chirped waveform generated by the laser, we obtain quasi-pulsed emission with an external dispersion compensation optical fiber. Experimental results presented here play an important role in the understanding of FM comb generation in semiconductor diode lasers.6,29 To date, no clear picture of this phenomenon in QWDL has been drawn; therefore, it would be of large relevance to validate agreement between the experiment and recently developed theories.6,30

The 2 mm long Fabry–Pérot devices studied here were designed, grown, and fabricated using procedures reported previously for single-mode devices.31 More details are given in Sec. IV. Figure 1(a) shows a QWDL Fabry–Pérot cavity along with the generated optical spectrum [Fig. 1(b)], P-I-V characteristics, and intermode beat note spectrum acquired with 1 kHz resolution bandwidth [Figs. 1(b) and 1(c)]. At less than 500 mW of electrical power, the device produced a quasi-flat optical spectrum with most of the power carried in 10 nm bandwidth, whereas the total coverage (40 dB relative to maximum) reached 20 nm (∼1.5 THz). In the dominant 10-nm-wide part of the spectrum, ∼35 comb lines spaced by 19.37 GHz are emitted with an average optical power greater than 1 mW per line. Without any dispersion engineering, effective nonlinear phase-locking at high optical intensities in the cavity produces a narrow near-kilohertz stable intermode radio-frequency (rf) beat note over extended current and temperature ranges. Unlike QD/QDash, QCL, or ICL devices that promote multi-mode operation shortly above threshold, our device develops multimode and frequency comb spectra only at injection currents exceeding threshold multiple times (5–7). A more detailed analysis of this peculiar behavior can be found in the supplementary material, Note I.

FIG. 1.

(a) Photo of a QWDL comb on a gold-plated copper–tungsten submount. (b) Optical spectrum in a low phase noise regime. (c) P-I-V characterization of the device at room temperature. (d) Electrical intermode beat note spectrum acquired simultaneously with (b) measured on an external high-speed detector.

FIG. 1.

(a) Photo of a QWDL comb on a gold-plated copper–tungsten submount. (b) Optical spectrum in a low phase noise regime. (c) P-I-V characterization of the device at room temperature. (d) Electrical intermode beat note spectrum acquired simultaneously with (b) measured on an external high-speed detector.

Close modal

To characterize the intermodal phases and source coherence, we employed the SWIFTS technique, which relies on measuring the interferometrically modulated microwave intermode beat note (see Sec. IV for experimental details). Figure 2(a) plots the recorded normal (zero-frequency/DC) and SWIFTS (microwave) interferograms (IFGs) where a characteristic minimum around the zero path difference (ZPD) point [Fig. 2(a)] can be observed, which is a signature of FM comb operation.12,32 An AM comb would instead produce a waveform similar to the normal IFG15 because its intermodal phases Δφ(ω) add constructively.

FIG. 2.

SWIFTS interferograms (a) along with the corresponding amplitude and phase spectra (b). A characteristic minimum around the zero path difference (ZPD) point visible in the SWIFTs traces confirms the FM character. Additionally, the phase difference between neighboring lines varies almost linearly from π to –π, as expected for a maximally chirped comb state.

FIG. 2.

SWIFTS interferograms (a) along with the corresponding amplitude and phase spectra (b). A characteristic minimum around the zero path difference (ZPD) point visible in the SWIFTs traces confirms the FM character. Additionally, the phase difference between neighboring lines varies almost linearly from π to –π, as expected for a maximally chirped comb state.

Close modal

First, excellent agreement between the spectral product Ssp(ω) and the SWIFTS spectrum |S+(ω)| unequivocally proves the comb nature of the source—virtually all lines contribute to the microwave intermode beat note. By using the interferometer to spectrally resolve the amplitude and phase of the beat note, we determine which of the laser’s frequency components are separated by the synthesizer frequency exactly. Second, the distribution of the SWIFTS phases Δφ(ω) supports the conclusion drawn from the unprocessed SWIFTS IFGs: the QWDL comb exhibits a maximally chirped FM state with intermodal phases distributed linearly between −π and π. Despite different gain dynamics, this state seems to be found across many FM comb platforms.12,14,16,29

Knowledge of the intermodal phases Δφ(ω) can be used to retrieve the optical phase φ(ω) + φ0 through a cumulative summation, albeit with an arbitrary global offset φ0. Therefore, only quantities weakly dependent upon the global phase can be reconstructed. Figure 3(a) plots the parabolic optical phase computed from Δφ(ω), which is expected for a negatively chirped source. A least-squares fit to the data yields a group delay dispersion (GDD) estimate of −10.4 ps2. Note that this value refers to the GDD of the generated FM comb waveform and does not describe the intracavity group velocity dispersion (GVD) covered in the supplementary material, Note III. Interestingly, the measured field GDD can be quite accurately predicted a priori from the optical spectrum.32 Assuming the source exhibits a FM behavior and develops a 25 cm−1 wide spectrum (fBW ≈ 750 GHz) with a 19.37 GHz repetition rate frep, the field GDD can be approximated through

GDD^=12πfrepfBW.
(1)

This yields an estimate of −11 ps2, which is in excellent agreement with the measured value of −10.4 ps2.

FIG. 3.

(a) Optical phase with an arbitrary global offset obtained by a cumulative integration of Δφ. A linear modal phase difference corresponds to a second order dispersion. A least-squares fit to the parabolic phase yields a field GDD of −10.4 ps2 (b) Calculated instantaneous intensity and frequency based on the modal intensities and phases. Shaded regions indicated a standard deviation obtained via Monte–Carlo simulation.47 A quasi-continuous wave output periodic with the repetition frequency has a strong amplitude modulation component with pronounced spikes of intensity when the laser changes the direction of its frequency sweep. Spikes in the instantaneous frequency correspond to instances when the intensity drops to zero.

FIG. 3.

(a) Optical phase with an arbitrary global offset obtained by a cumulative integration of Δφ. A linear modal phase difference corresponds to a second order dispersion. A least-squares fit to the parabolic phase yields a field GDD of −10.4 ps2 (b) Calculated instantaneous intensity and frequency based on the modal intensities and phases. Shaded regions indicated a standard deviation obtained via Monte–Carlo simulation.47 A quasi-continuous wave output periodic with the repetition frequency has a strong amplitude modulation component with pronounced spikes of intensity when the laser changes the direction of its frequency sweep. Spikes in the instantaneous frequency correspond to instances when the intensity drops to zero.

Close modal

The spectrally resolved intensities and phases of the comb lines enable the reconstruction of the instantaneous intensity |E(t)|2 and frequency d(arg{E(t)})/dt of the electric field shown in Fig. 3(b). As shown in Fig. 3(b), the laser frequency sweeps the spectral window linearly from lower to higher frequencies over a roundtrip time. Strikingly, the accompanying field intensity has a significant amplitude modulation caused by the non-uniformity of the comb intensities and local flattening of the intermodal phases. Lines centered at the high-frequency end tend to have more power than the average, while their phases tend to be less chirped that the global fit. This non-negligible AM component explains why one can observe the intermode beat mode, which would have not been possible to measure for a constant-intensity perfect FM source without a phase discriminator. The AM component is expected for a semiconductor laser due to nonlinear gain/loss modulation resulting in mode amplitude variation.33 

Although the GDD of the optical waveform’s electric field is relatively high, it is possible to compensate for it to promote pulsed operation. In contrast to the long-wavelength mid-infrared region, external pulse compressors at 2 μm can be conveniently realized using optical fibers instead of free-space grating compressors.34 Here, we used a dispersion-tailored single-mode fiber (SMF, Nufern SM2000D) with a nominal dispersion parameter of −55 ± 10 ps/(nm km) at 2000 nm. It allows us to introduce a positive dispersion of 0.10 ps2/m–0.12 ps2/m at 2060 nm. Therefore, at least 100 m of fiber are needed to compensate for the waveform’s GDD of −10.4 ps2. The robust all-fiber dispersion compensation scheme enables pulse generation at relatively low optical losses at 2050 nm (∼5 dB/100 m).

Figure 4 plots the results of the experiment. After 110 m of propagation in the SMF (whose length was found to maximize the peak power of the SWIFTS IFGs |x(τ) + iy(τ)|2 around ZPD), we obtained quasi-pulsed emission with a strong AM component. The normal IFG does not change since the intensity spectrum remains intact in this passive compensation scheme; however, the SWIFTS IFGs differ quite significantly from those uncompensated because of the altered phase. First, a slowly varying oscillatory term appears in both SWIFTS channels (which relates to the conventional autocorrelation35), while the maxima of the in-phase (x) component correspond to the maxima of the normal IFG. This is an indication of intermodal phase synchronization, as confirmed in the spectral analysis plotted in Fig. 4(c)—the linear intermodal phase trend is eliminated. The optical phases remained non-uniformly scattered over a range of 0.31 · 2π that indicates the presence of higher order dispersion terms and precludes the formation of clean single-peaked pulses. Figure 4(d) shows the unwrapped optical phase corresponding to ordinary group delay with significant deviations from the ideal linear behavior.

FIG. 4.

Chirp compensation using a dispersion-tailored single-mode fiber. (a) Normal and SWIFTS IFGs of the device operating at 20 °C and 360 mA in a comb state analogous to that in Fig. 2. The comb shows a highly chirped FM character with a characteristic SWIFTS and rf beat note IFG (|x(τ) + iy(τ)|2) minima around ZPD. (b) Device in the same comb state measured after 111 m of propagation in SM2000D dispersion-tailored fiber. While the normal IFG is simply noisier (due to attenuation in the fiber) without any changes in the shape, the microwave IFGs look completely different. Around ZPD, the rf beat note IFG has a sharp peak indicating strong amplitude modulation, whereas the SWIFTS IFGs have a strong slowly varying oscillatory term. (c) SWIFTS spectra. The linear chirp of the intermodal phases is compensated; however, significant deviations from a flat profile persist. The phases are splayed over 0.31 · 2π, while their distribution directly relates to the shape of the spectrum and local variations in modal intensities. (d) Unwrapped optical phase using data from (c). Instead of the parabolic shape, a linear trend dominates (corresponding to an ordinary group delay). Nonetheless, deviations from the line clearly reveal the presence of higher order dispersion. (e) Reconstructed intensity profile. The waveform takes form of multiple pulses with 6 ps of FWHM duration. The central part of the multi-peaked pulse is ∼2.8 ps wide. Higher order dispersion prevents the laser from emitting a clear single-peaked pulse.

FIG. 4.

Chirp compensation using a dispersion-tailored single-mode fiber. (a) Normal and SWIFTS IFGs of the device operating at 20 °C and 360 mA in a comb state analogous to that in Fig. 2. The comb shows a highly chirped FM character with a characteristic SWIFTS and rf beat note IFG (|x(τ) + iy(τ)|2) minima around ZPD. (b) Device in the same comb state measured after 111 m of propagation in SM2000D dispersion-tailored fiber. While the normal IFG is simply noisier (due to attenuation in the fiber) without any changes in the shape, the microwave IFGs look completely different. Around ZPD, the rf beat note IFG has a sharp peak indicating strong amplitude modulation, whereas the SWIFTS IFGs have a strong slowly varying oscillatory term. (c) SWIFTS spectra. The linear chirp of the intermodal phases is compensated; however, significant deviations from a flat profile persist. The phases are splayed over 0.31 · 2π, while their distribution directly relates to the shape of the spectrum and local variations in modal intensities. (d) Unwrapped optical phase using data from (c). Instead of the parabolic shape, a linear trend dominates (corresponding to an ordinary group delay). Nonetheless, deviations from the line clearly reveal the presence of higher order dispersion. (e) Reconstructed intensity profile. The waveform takes form of multiple pulses with 6 ps of FWHM duration. The central part of the multi-peaked pulse is ∼2.8 ps wide. Higher order dispersion prevents the laser from emitting a clear single-peaked pulse.

Close modal

The reconstructed optical intensity shows optical pulses with a FWHM of 6 ps. This is slightly less than 12% of the roundtrip time and less than 31% expected based on the range occupied by the intermodal phases. Due to the significant nonlinear chirp of the waveform, the peak to average ratio is merely 5.5, which corresponds to ∼27 mW of peak power due to losses at the optical isolator, fiber coupling efficiency, and attenuation in the fiber itself. Compared to state-of-the-art monolithically integrated passively mode-locked GaSb devices,27 our device emits pulses that are 2.5× broader and have >10× less peak power. Nevertheless, the comb has more average power (∼5 mW) while its repetition rate stability Δfrep/frep is an order of magnitude higher.

In this context, it is useful to compare our results to other semiconductor lasers with free-space chirp compression. For instance, passive chirp compensation of a broadband (3 THz wide) mid-infrared QCL allowed us to reach 12 ps long pulses with ∼16 dB optical losses.34 Just like in our case, the waveform was plagued by higher order dispersion terms precluding the formation of chirp-free clean single-peaked pulses. While currently there is no increase in peak power, this experiment undoubtedly confirms the validity of the waveform’s GDD inferred from the SWIFTS data and paves the way for pulse shaping of QWDL sources. For applications requiring truly monolithic pulsed 2 μm sources, passively mode-locked QWDL devices with a smooth Gaussian-like optical spectrum may be of preference,27 albeit with a higher timing jitter.

Arguably, one of the most promising applications of chip-scale OFCs driving their development is compact dual-comb spectroscopy (DCS).18,36,37 To date, semiconductor lasers have been widely employed in DCS at longer wavelengths with record levels of optical power per mode36 and low electrical power consumption.38 However, it is somewhat surprising that in the near-infrared region, no demonstrations of DCS with electrically pumped monolithic OFC sources have been presented.37 Here, we fill this niche by multi-heterodyning two QWLD combs on a fast InGaAs detector to perform proof-of-principle DCS measurements of a low-finesse n-GaSb etalon (see Sec. IV). The results of the experiment are shown in Fig. 5.

FIG. 5.

Free-running DCS using a pair of QWDLs. (a) Rf dual-comb spectrum obtained by multi-heterodyning the two devices within 1 ms. The raw and computationally phase-corrected spectra are plotted. (b) Temporal structure of the electrical dual-comb interferogram showing ∼9 consecutive burst within 200 ns. (c) Optical spectra of the devices in the DCS experiment. (d) Retrieved DCS transmission spectrum along with a low-finesse GaSb etalon fit. An independent transmission measurement using an optical spectrum analyzer (OSA) is plotted for comparison. Error bars in the DCS measurement correspond to a 2σT confidence interval. The standard deviation of the fit residual is 6.3%.

FIG. 5.

Free-running DCS using a pair of QWDLs. (a) Rf dual-comb spectrum obtained by multi-heterodyning the two devices within 1 ms. The raw and computationally phase-corrected spectra are plotted. (b) Temporal structure of the electrical dual-comb interferogram showing ∼9 consecutive burst within 200 ns. (c) Optical spectra of the devices in the DCS experiment. (d) Retrieved DCS transmission spectrum along with a low-finesse GaSb etalon fit. An independent transmission measurement using an optical spectrum analyzer (OSA) is plotted for comparison. Error bars in the DCS measurement correspond to a 2σT confidence interval. The standard deviation of the fit residual is 6.3%.

Close modal

The unprocessed free-running rf dual-comb spectrum plotted in Fig. 5(a) has a typical beat note linewidth of 1 MHz within 1 ms. It corresponds to a ∼700 kHz optical comb linewidth assuming a lack of correlation between the beating combs. This value is several times higher than reported for distributed feedback (DFB) single-mode devices following the same design39 but still sufficiently low for many demanding high resolution applications. Although the strongest of the 34 easily resolvable lines have relative intensities reaching 40 dB, some of them are significantly weaker. Thus, to unlock the full potential of the acquired DCS data, we processed it using the computational coherent averaging algorithm (CoCoA).40 It digitally phase locked the comb lines and hence concentrated their spectral amplitudes in a narrow bandwidth. The rf spectrum was globally phase-corrected using two computationally extracted signals and yielded an acquisition-limited rf linewidth for all lines. Their simultaneous narrowing unequivocally proves the high phase noise correlation between the lines expected for a comb.

Figure 5(b) plots the temporal structure of the electrical dual-comb interferogram. It shows a highly chirped signal with no silent intervals encountered in DCS using mode-locked AM combs that validate the chirped quasi-cw comb operation inferred from SWIFTS measurements. The lack of high-power bursts is beneficial in spectroscopy applications since it allows for more efficient use of the analog-to-digital converter’s dynamic range and lowers photodetector’s nonlinearities. Unfortunately, FM combs often have uneven comb teeth power, which may introduce difficulties in power normalization and cause data heteroscedasticity.

Figure 5(d) shows the retrieved transmission spectrum of a low-finesse GaSb etalon measured using a pair of closely matched QWDL combs in a DCS setup. The optical frequency axis calibration relied on the unique spectral amplitude pattern inferred from the optical spectra plotted in Fig. 5(c). For DCS data retrieval in Fig. 5(d), we used 34 lines with relative intensities varying between ∼15 dB and ∼60 dB. This irregularity in relative line strengths causes the error bars to have variations across the spectrum, and here, the 2σ transmission intervals range from 10% down to 0.15% for the strongest lines. Overall, good agreement between the fitted model (red line) and the DCS data is obtained. An independent etalon transmission measurement using an optical spectrum analyzer (OSA) confirms the validity of the DCS measurement. The standard deviation of the DCS fit residual is 6.3% over millisecond time scales in the entire span and 4.2% between 2066 nm and 2073 nm, which agrees with similar experiments using other DCS platforms in free-running mode. This makes QWDLs promising candidates for low-drive-power sensors of environmentally important molecular species like carbon dioxide or ammonia in the 2 μm region. On the one hand, the obtainable spectroscopic bandwidth (∼0.7 THz) and sampling resolution (∼19.37 GHz) are short of spectrally broadened fiber combs,41 reaching 40 THz of coverage with 160 MHz comb tooth spacing. On the other hand, the high power per tooth yields a high average spectroscopic signal-to-noise ratio of 3360/s compared to 24.5/s for the nonlinear Si3N4 platform. This permits measurements over much shorter time scales (even microseconds), which is well suited for studying reaction kinetics, but unfortunately in a much narrower spectral window.

We have demonstrated quantum well diode laser optical frequency combs operating in the 2 μm region with more than 1 mW per comb tooth. Optical frequency comb generation is possible at higher optical currents and exploits self-starting frequency modulation (FM). Although the initial free-running stability of the ∼19.37 GHz repetition rate is excellent and lies in the near-kilohertz range over 40 ms, the stability can be further improved down to a sub-hertz level using a fast optical phase locked loop (OPLL). Interferometric characterization of the devices revealed a strongly chirped waveform with a GDD on the order of −10 ps2, which was compensated externally to generate 6 ps long optical pulses limited by the high order dispersion of the optical waveform. Finally, a pair of devices was used to demonstrate proof-of-concept free-running dual-comb spectroscopy of a low-finesse Fabry–Pérot etalon.

Our results support earlier theoretical considerations of FM comb generation in QWDLs and reproduce difficulties in multi-mode operation due to suppressed SHB, which is activated only at high optical intensities in the cavity. Future comb designs will focus on facilitating multi-mode operation at lower levels of electrical injection and increasing the comb bandwidth through dispersion engineering of the waveguide and gain medium.42 

Lasers used here were fabricated using standard III/V micro fabrication techniques. After device fabrication, the facets of 2 mm long Fabry–Pérot devices were coated with a highly reflective (HR) and anti-reflective (AR) coating on the back and front facet, respectively. The latter had 2% reflectivity provided by thin layers of TiO2 and Al2O3. Devices were mounted epi-up on gold-coated copper–tungsten blocks. Next, light from the front facets was collimated using an AR-coated Black Diamond-2 lens and coupled into a single-mode fiber for spectral and radio-frequency (rf) beat note characterization. The low phase-noise operation regime is ensured by using a low-noise laser driver (Vescent Photonics, D2-105) and an optical isolator for optical feedback management.

To perform SWIFTS measurements, light from the QWDLs was coupled into a Fourier transform spectrometer (FTIR, Bruker Vertex 80). A fast InGaAs photodetector (Newport, 818-BB-51) located at the external detector output of the FTIR was used to analyze the signal. The normal (DC) and SWIFTS (∼19.37 GHz) interferograms (IFGs) were simultaneously recorded as a function of optical delay τ. The experimental setup and data processing path are analogous to that used in Refs. 28 and 43. During the experiment, the intermode beat note remained phase locked to a microwave reference down to sub-hertz levels (see the supplementary material, Note II for details). The lockin demodulated in quadrature the interferometrically modulated beat note located at frep = 19.37 GHz, which was available after down-conversion at 20 MHz. The acquisition was performed in the slow continuous mirror scan mode with 3 kHz low-pass filters for all signals.

After acquisition, the interferometric traces were analyzed in the frequency domain. From the normal IFG, using the Fourier transform, we calculated the normal intensity spectrum S0(ω). By multiplying S0(ω) by its Δω = 2πfrep-shifted version S0(ω + Δω), we obtain a normalized spectral product Ssp(ω)=S0(ω)S0(ω+Δω), which can be directly compared to the microwave SWIFTS spectrum S+(ω) for evaluation of the comb coherence. S+(ω) is simply the Fourier transform of the complex SWIFTS IFG s+(τ) = x(τ) − iy(τ) with an amplitude |S+(ω)| and a non-zero phase Δφ(ω) = arg{S+(ω)} term.

A pair of free-running devices was operated in comb regimes favoring spectral flatness and mutual overlap, which involved thermal tuning of the signal (SIG) comb with respect to the local oscillator (LO). The devices were biased at 340 mA and 367 mA for the SIG and LO, respectively, while their heatsink temperatures were 24.6 °C and 20 °C. The combs differed in repetition rates by Δfrep = 44.24 MHz; therefore, the electrical beating signal was periodic every 22.6 ns. To avoid saturating the fiber-coupled photodetector and minimize measurement nonlinearities, the optical power was heavily attenuated by optical irises preceding the fiber coupler to ∼100 μW.

After recording a reference 1 ms long time-domain electrical signal using a fast oscilloscope, we introduced to the SIG comb path a low-finesse Te-doped n-GaSb wafer serving as a Fabry–Pérot etalon with a measured thickness of 514 ± 1 μm and recorded the DCS interferogram again. The substrate’s carrier concentration of 2 × 1016 cm−3 was responsible for a non-negligible absorption α ≈ 5 cm−1, as extrapolated from Ref. 44. Despite lowering the fringe contrast, it was actually advantageous because only small intensity variations were measured, as opposed to complete attenuation of some of the comb lines for high-finesse optical cavities.

The optical spacing between the comb lines was readily available from the rf intermode beat note of the SIG comb and used in the spectral fitting routine. For spectroscopy, we used beat notes with an amplitude standard deviation σA lower than 3% and calculated the corresponding transmission uncertainty based on formulas in Ref. 45. The etalon model was obtained by fitting the group index ng, absorption coefficient α, and angle of incidence to the lossy etalon model in Ref. 46. The etalon used here is estimated to have a free spectral range of 69.6 GHz (2.32 cm−1) and absorption losses α = 5 cm−1.

See the supplementary material for additional data and methods that support the main conclusions in this paper.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

This work was supported under the National Aeronautics and Space Agency’s (NASA) PICASSO program (Grant No. 106822/811073.02.24.01.85) and the Research and Technology Development Spontaneous Concept Fund. It was, in part, performed at the Jet Propulsion Laboratory (JPL), California Institute of Technology, under contract with the NASA. L. A. Sterczewski’s research was supported by an appointment to the NASA Postdoctoral Program at JPL, administered by the Universities Space Research Association under contract with the NASA.

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Supplementary Material