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Abstract
We demonstrate the implementation of external cavity optical feedback to improve coherence and promote generation of harmonic states by a mid-infrared quantum cascade laser frequency comb. In particular, we present a Vernier-like scheme to realize harmonic comb states that increase the repetition rate of the comb by a factor of up to 6 and broaden spectral coverages from 46 cm-1 to 92 cm-1. Intermode beatnote and dual comb characterization indicate that the coherence of the comb has greatly improved for sub-optimal devices when the comb is operated in these harmonic states. This approach to control the generation of harmonic states and improve comb performance can be readily incorporated to various sensing systems and has great potential in spectroscopic measurements that require high repetition rates and/or broad optical bandwidth.
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1. Introduction
Mid-infrared quantum cascade laser (QCL) frequency combs (FCs) are becoming increasingly popular coherent light sources in many spectroscopic applications as they offer broadband coverage, room-temperature operations, as well as fast spectral measurement capabilities if used in dual-comb spectroscopy (DCS) configurations [1–9]. Their self-starting comb generation requires only direct electrical pumping that obviates sizeable equipment and enables chip-scale systems [1,10]. However, QCL-FCs are generated via nonlinear self-frequency-modulation with linear chirp rather than forming optical pulses [11–13] and still face great challenges regarding reliable and repeatable comb formation with high coherence [11,14].
Many efforts have thus been made to stabilize comb operations, achieve control of comb generation, and broaden their spectral coverages in order to improve the suitability of QCL-FCs for spectroscopic systems. For instance, optimized comb design of active regions and waveguides achieves sub-kHz intermode beatnotes (IBNs) that manifests itself in an improved comb stability [10,15]. Proper dispersion management of the comb via gain and waveguide design has been shown to produce spectral coverages of more than 100 cm-1 [16]. Gires–Tournois interferometer (GTI) dispersion compensation is also shown to increase spectral coverage to gain-limited bandwidth and mitigate high phase-noise regime [17]. Furthermore, a piezo-actuated GTI planar micro-mirror behind the back laser facet has been demonstrated to control dispersion with the ability of carrier envelope offset frequency (fceo) tuning with minimal effect on the comb’s repetition frequency (frep) [18,19]. However, most of these device-level dispersion compensation efforts require customized device design or sophisticated on-chip integration. On the other hand, many studies have observed that external system solutions can also be used for optimization of QCL-FC generation. For example, radio frequency (RF) injection to the QCL-FCs at frep allows coherent control and stabilization of comb operations [13,20,21] as well as spectral broadening [22,23] without the need for sophisticated device engineering, although it requires RF-optimization [15,20]. Double-locking techniques consisting of frep stabilization by RF injection as well as fceo control by phase-locking to a metrological-grade mode-locked FC [13], molecular transition line-locking via a distributed-feedback (DFB) QCL [24], or optical injection locking by a DFB QCL [25] have all been used to achieve full stabilization of QCL-FCs. Similarly, optical systems such as external cavities (EC) [26–28] and modulation with external light sources such as light-emitting diodes [29] or near infrared laser diodes [30] have also been employed to stabilize QCL-FC generation.
One interesting aspect of QCL-FC is its ability to produce harmonic comb states with significantly larger repetition rates. In conventional mode-locked optical fiber combs, filter Fabry-Perot cavities have been used to increase repetition rates to achieve higher acquisition speeds in DCS systems [31]. In QCLs, harmonic comb generation can be achieved internally, which has been modeled theoretically and experimentally acquired through a number of techniques [32–34] including optical seeding by a single-mode QCL [35], RF injection [36–38], and device-level design [38–43].
In this work, we present the scheme to generate different harmonic states in QCL-FCs by EC optical feedback injection (OFI) to achieve higher repetition rates as well as to improve comb coherence and spectral coverage. The optical feedback is provided by a macroscopic EC that is an upgraded version of the configuration presented in Ref. [28] and allows the optical length of the EC (LEC) to be varied by multiple QCL chip cavity optical lengths (LQCL) with sub-micrometer precision. Note that as optical lengths, the terms LEC and LQCL are determined by taking into account the respective indices of refraction. Although uncontrolled optical feedback is generally considered detrimental to harmonic comb formation [32], with this system we are able to fully control EC-OFI to achieve low phase-noise harmonic comb states with improved coherence, broadened spectral coverage, and higher comb repetition rate, attributes that are greatly desirable for high-precision spectroscopic systems. While various aforementioned methods of harmonic comb generations in QCLs have been studied both theoretically and experimentally, to the best of our knowledge this is the first experimental demonstration of harmonic comb states obtained via EC-controlled OFI.
2. Overview of EC-OFI on QCL-FC
2.1 System setup
The system implemented in this study is shown in Fig. 1. Two EC-QCL-FCs operating at 9.6 µm are arranged in DCS configuration. The EC-QCL-FCs use folded cavity configuration with a beamsplitter (BS, Thorlabs BSW710) as an output coupler and a flat gold mirror that provides optical feedback mounted on a translation stage (Thorlabs PT1 with manual or Z825B motorized actuator). The amount of OFI coupled to the waveguides of QCL-FCs is ∼11-18% as estimated using characterization of the change in threshold current [44] with the reflectivities of laser chip facets (92% for the back facet and 27% for the output facet) and waveguide loss (3-7 cm-1) provided by the laser manufacturer. Note that the reflectance of the BS is characterized to be 65%, so the amount of OFI before coupling back to the QCL-FC’s collimator is close to 42%. Additional losses including coupling loss and diffraction contribute to the further reduction of OFI to the estimated levels. The flat mirror as well as the QCL front and back facets form a coupled cavity system whose length can be finely tuned by the translation stage. The amount of OFI has been adjusted through misalignment of the flat mirror, thereby altering the re-injection efficiency to achieve different harmonic comb states, as indicated in Table 1. For each harmonic state, the best QCL-FC performance is achieved with the OFI level indicated in Table 1. The optical length of the EC is ∼165 mm, which is about 11 times the optical length of the QCL-FC chip cavity with a fundamental frep of 9.82 GHz. The electrically measured IBNs of the QCL-FCs are extracted via bias tees and analyzed with an RF spectrum analyzer (Rohde & Schwarz FSW43). IBN provides reliable measurement of the comb frep, and its linewidth can be used as an approximate indicator (although not deterministic) of the comb’s coherence [2,21]. To enable verification of the actual comb coherence, a DCS measurement is realized by combining the outputs from two QCL-FCs on another BS followed by a multiheterodyne measurement on a fast photodetector (Vigo PV-4TE-10.6). The secondary beam after the BS is additionally directed to an optical spectrum analyzer (Bristol Instruments 771B-MIR) to measure the optical spectra of the combs.
Fig. 1. System schematic of two QCL-FCs coupled with optical feedback from EC (blue box) in DCS configuration. The optical lengths, LEC and LQCL, are indicated with dashed arrows. Inset shows a photograph of the EC consisting of a BS and a mirror mounted on a computer-controlled micrometer translation stage.
Table 1. OFI Ratio for Different Harmonic States
2.2 IBN characterization with coarse LEC scan
To perform qualitative evaluation of the effects of EC-OFI on comb generation, a coarse LEC scan is first performed while observing the full width at half maximum (FWHM) of generated IBNs, a proxy of the degree of comb coherence. For free-running QCL-FCs without EC, the FWHM of the IBN occurring at frep is at ∼100 kHz level, which indicates relatively poor comb coherence. It is clearly noticeable from Fig. 2(a) that the FWHM of the IBNs varies during the coarse scan of LEC. For the majority of different LEC positions, the IBN is observed at frequency that is close to the free-running frep and appears quite broad with FWHM of ∼1 MHz, which is even greater than the free-running case. This indicates that if the phase of the OFI is not matched with the QCL chip cavity, it will cause further deterioration of comb coherence. Such high phase-noise behavior is generally similar to comb disruption due to an unwanted optical feedback [45]. However, a significant drop in IBN’s FWHM to the level of a few kHz is observed when LEC is tuned to mLQCL (where m is an integer) indicated as the ‘0’ position on the x-axis in Fig. 2(a). The IBN frequency at this mLQCL position remains close to the fundamental frep observed for free-running QCL-FCs. When LEC is tuned to (m ± 1/2)LQCL or (m ± 1/3)LQCL, we have also noticed distinct comb states with the following observations: 1) the fundamental IBN is suppressed and higher harmonic IBNs at 2× or 3×frep can still be observed, and 2) the spacing of comb lines in the optical spectrum is increased by a factor of 2 and 3, respectively. These have been denoted as the second and third harmonic states in Fig. 2(b) where LEC is detuned from mLQCL by 1/2 and 1/3 of LQCL, and in these regions the FWHM of the IBN shown in Fig. 2(a) is measured at 2× or 3×frep, respectively. Note that a third order harmonic state can also be accessed when LEC is tuned to (m ± 2/3)LQCL since this position is degenerate with [(m + 1) ± 1/3]LQCL, as indicated in Fig. 2(b). To explain the generation of EC-induced harmonic states, in the following section we provide a simplified Vernier-like scheme to analyze mode structures supported by the coupled cavity system.
Fig. 2. (a) The FWHM of IBN of an EC-QCL-FC as LEC detunes from an integer multiple of LQCL. (b) A summary of comb behaviors as LEC detunes from an integer multiple of LQCL. Both figures are in units relative to LQCL.
3. Scheme of harmonic state generation with OFI
As illustrated in Fig. 1, the QCL-FCs are coupled to two cavities, the QCL chip cavity and the EC defined by an external mirror, both of which affect the comb formation. The free spectral range (FSR) of the chip cavity and of the EC are respectively, ${FS}{{R}_{{QCL}}} = \frac{c}{{2{L_{{QCL}}}}}$ and ${FS}{{R}_{{EC}}} = \frac{c}{{2{L_{{EC}}}}}$, where c is the speed of light. Let us first consider a special case when ${L_{{EC}}}$ is set to an integer multiple of ${L_{{QCL}}}$, namely, ${L_{{EC}}} = m{L_{{QCL}}}$. FSRQCL is thus m times as large as FSREC, which is schematically shown in Fig. 3(a) and (b). In this EC configuration, the ratio of FSRs is an integer FSRQCL/FSREC = m, and each chip cavity mode corresponds to every m-th mode supported by the EC. As a result of QCL gain dynamics and mode selection mechanisms (i.e. spatial hole burning), the QCL-FC in this configuration is generated with a frequency spacing determined by ${FS}{{R}_{{QCL}}}$, a state denoted as fundamental EC state in Fig. 2(b). However, when ${L_{{EC}}}$ detunes from $m{L_{{QCL}}}$ by millimeter scale, this direct synchronization of mode structures is not supported any longer, which results in noisy operation of the QCL-FC with broad IBN as shown in Fig. 2(a). Once ${L_{{EC}}}$ detunes from $m{L_{{QCL}}}$ by ${L_{{QCL}}}/N$, where N is an arbitrary positive integer $\ge 2$ (N = 1 corresponds to the next fundamental EC state), the external cavity optical length becomes $L_{{EC}}^{\prime} = ({m + 1/N} ){L_{{QCL}}}$, which results in a new free spectral range of:
The ratio of FSRs becomes then:As a result, we observe Vernier-like mode selection with every Nth QCL chip cavity mode to coincide with the (Nm + 1)th mode of the EC, as shown in Fig. 3(c). This causes the generation of a harmonic comb state with a frequency spacing of $N \cdot FS{R_{{QCL}}}$. Thus, detuning ${L_{{EC}}}$ by ${L_{{QCL}}}/N$ promotes the generation of a harmonic comb state with comb repetition rate increased by a factor of N. Notice that since m is always assumed to be an integer, per Eq. (3), the generation of harmonic comb states can be achieved by detuning LEC from any integer multiple of LQCL. In theory, any high harmonic comb state should be realizable with this method, but in our experiments, we observe that harmonic comb states only up to N = 6 can be generated before the QCL-FC switches back to generating a mode structure resembling the fundamental EC state with modes separated by frep. Harmonic states of N > 6 require optical feedback levels that are too low to maintain stable harmonic comb operations, as experimental observations in Table 1 indicate that higher-order harmonic states generally need weaker feedback for stable operation. Note that high-order harmonic comb states are omitted in Fig. 2(b) because they are unobservable due to coarse LEC scan, but they can be observed with sufficiently precise control of LEC as shown in the following sections.
Fig. 3. The Vernier-like scheme to generate a harmonic comb state. The case of m = 4 and N = 3 is shown here for demonstration. (a) The comb modes in the frequency domain supported by the chip cavity with optical length ${L_{{QCL}}}$. (b) The comb modes supported by the EC with optical length ${L_{{EC}}} = m{L_{{QCL}}}$. (c) The comb modes supported by the EC tuned to $L_{{EC}}^{\prime} = ({m + 1/N} ){L_{{QCL}}}$.
4. Experimental results
The generation of different comb states using the scheme outlined above is confirmed and characterized using a combination of measurement techniques including: the RF spectrum of the IBN, the optical spectrum, and the multiheterodyne spectrum in a DCS configuration to evaluate the comb coherence [46].
4.1 Verification of harmonic state generation
First, to verify the generation of harmonic comb states we collect the electrical IBN data and optical spectra when LEC is detuned by ${L_{{QCL}}}/N$ for different N values while maintaining the drive current and temperature at approximately 1200 mA and 25 °C, respectively. Our RF spectrum analyzer can perform IBN measurements up to 43.5 GHz, which allows accessing IBNs for up to the fourth harmonic comb state. As a reference, the IBN at ${f_{rep}} \approx $9.82 GHz shown in Fig. 4(A1), is acquired in the free-running state without EC, and it exhibits a significant pedestral, a feature that is typically observed for QCL-FCs with relatively high phase noise. Similar low-quality IBNs are observed for the second, third, and fourth harmonics (shown in Fig. 4 (A2-A4)), which also points to the low coherence of the free-running comb as later confirmed by the DCS measurements. The optical spectrum in Fig. 5 confirms that the comb spacing of 0.33 cm-1 extracted from it is consistent with frep measured as the IBN frequency. Note that the optical spectra are measured with a resolution of 0.06 cm-1.
Fig. 4. Electrical IBNs for free-running (A1-A4), second- (B1-B4), third- (C1-C4), and fourth-order (D1-D4) harmonic comb states. Columns illustrate the frequency ranges anticipated for the first to fourth harmonics of the IBN, respectively. Where no IBN is expected, data is examined over a larger frequency span to confirm the absence of IBN.
Fig. 5. Optical spectra acquired for free-running, second-, third-, and fourth-order harmonic comb states. The increase in optical mode spacing, denoted on the right, agrees well with the expected multiple of the FSR of QCL chip.
To generate harmonic states, we set the integer multiple m to 11 in our experiments for ease of setup and for demonstration, but m can theoretically be any arbitrary integer >1 as explained in Section 3. The IBNs measured for the second harmonic state where LEC detunes from $m{L_{{QCL}}}$ by ${L_{{QCL}}}/2$ are shown in Fig. 4(B1-B4). The odd harmonics of IBN disappear while the even harmonics of IBN remain, which suggests that the comb repetition rate and the comb spacing are indeed doubled. This is confirmed with the optical spectrum in Fig. 5 indicating that the comb spacing becomes 0.66 cm-1, which is twice as large as the free-running mode spacing. Similar increases of comb spacing by integer-multiple times are observed when LEC is detuned by 1/3, 1/4, 1/5, and 1/6 from $m{L_{{QCL}}}$.
A fine-resolution sweep of LEC, with a step size of ∼0.5 µm, is conducted around the third-harmonic state to demonstrate the evolution of IBN (Fig. 6) and optical spectra (Fig. 7) with small LEC tuning. Sharp third-harmonic beatnotes with corresponding comb spacing are consistently recovered over a range of ∼80 µm, which are indicated by the red boxes in Fig. 6 and Fig. 7. While optical spectra with third harmonic comb spacing may still be recovered outside of this locking range, these states are typically paired with broad IBNs indicating a lack of coherence, which are shown in the green and light-blue states ($\mathrm{\Delta }{L_{EC}} = 104$ µm and $134$ µm, respectively) in Fig. 6 and Fig. 7. As LEC continues to tune away from the locking range of coherent third-harmonic state, a contribution of modes with fundamental comb spacing eventually reemerges, which are indicated in the dark-blue and red states ($\mathrm{\Delta }{L_{EC}} ={-} 16$ µm and $164$ µm, respectively). Note that within the ∼80 µm locking range of coherent harmonic state the frequency of the IBN is LEC dependent (similar to Ref. [28]), and optical spectra change slightly as well. We have also confirmed that the actual detuning of the EC mirror position (measured as the translation stage displacement) for the second- (∼7.823 mm), third- (∼5.186 mm), and fourth-harmonic (∼3.883 mm) states presented in Fig. 5 are within ∼80 µm of the position predicted as a fraction of LQCL, which fall within the locking range of coherent harmonic states and validate the Vernier-like mode selection scheme.
Fig. 6. Evolution of the third harmonic IBN for small changes in LEC around the expected third-harmonic-state position with a ∼0.5 µm step size as a waterfall plot (A) and selected RF traces (B). The red box indicates an estimated range where coherent third harmonic states with narrow IBN are observed. The colored arrows to the left of (A) indicate the approximate positions where the traces of (B) are located within the waterfall plot.
Fig. 7. (A) Waterfall and (B) stacked optical spectra of the third harmonic state for the same LEC sweep as Fig. 6. The red box indicates the same region as in Fig. 6(A), and optical spectra corresponding to the same EC detuning lengths shown with the colored arrows to the left of (A) are extracted in (B) for direct comparison.
4.2 Improvement of QCL-FC performance
4.2.1 Comb coherence
Most notably, we observe improved QCL-FC performance when operating in harmonic states. Previous studies have analytically [47] and experimentally [48] demonstrated an increase in the coherence of single-mode QCLs with OFI, and a similar trend can be observed in QCL-FCs. A significant improvement of comb coherence is anticipated in the case of second harmonic state shown in Fig. 4(B), because the second harmonic IBN becomes very narrow with a FWHM of 1.6 kHz. This is typically observed in highly coherent QCL-FCs and the coherence improvement has been confirmed with DCS measurements discussed later in this paper. This significant narrowing of IBN is also observed in higher order harmonic states (with FWHMs of 2.5 kHz and 4.6 kHz for the third and fourth harmonic states respectively), while the low order IBN harmonics are clearly suppressed as well (shown in Fig. 4(C-D)). We expect similar trends for IBNs associated with harmonic states of order 5 and 6, but the IBN measurements for these states could not be provided since they exceed the frequency range of our spectrum analyzer (43.5 GHz).
To further study the improvement of comb performance in the harmonic states, we test two similar EC-coupled QCL-FCs in a DCS configuration, which provides a more conclusive confirmation of comb coherence [46]. Both QCL-FCs exhibit similar free-running phase-noise pedestal (shown in Fig. 4(A1)), indicating noisy comb operations without the EC. We set one of the two combs to the fundamental EC comb state with OFI by setting ${L_{{EC}}} = m{L_{{QCL}}}$, which allows for improved coherence of this comb manifested by the narrow IBN with FWHM of 25 kHz (shown in Fig. 8(A)) while keeping the comb mode spacing at ${f_{rep}} \approx \; $9.80 GHz, which is similar to the observations in Ref. [28]. We employ a similar configuration to Ref. [40], where one EC-QCL-FC is kept in the same fundamental EC state throughout all DCS measurements and is utilized as the “local oscillator” (LO) to sample multiheterodyne spectra of different comb states observed in the other “test” QCL-FC. Although in this study we focus on the impact of EC-OFI on harmonic states, we notice that the fundamental comb state with EC-OFI has also shown an increased dynamic range of comb formation and improved comb coherence (the IBN’s FWHM of the test QCL-FC also narrows from 170 kHz to 22 kHz). However, since the fundamental EC state has been extensively discussed in Ref. [26,28], we present here only the data related to harmonic states.
Fig. 8. Coherence verifications of selected harmonic comb states. Column (A) shows the IBN of LO EC-QCL-FC operating in a fundamental EC state which is used for all DCS measurements. Column (B) shows IBNs of the test QCL-FC in free-running as well as in the EC-induced second-order and fourth-order harmonic states. The IBN for the sixth-order harmonic state could not be measured as it exceeds the bandwidth of the RF spectrum analyzer. Column (C) shows multiheterodyne spectra and column (D) shows self-mixing spectra acquired with the LO and the test comb in DCS configuration. The legend shows different states of the test QCL-FC.
The first multiheterodyne spectrum collected with the dual comb system shown in Fig. 8(C) corresponds to the LO EC-QCL-FC beating with the test QCL-FC in the free-running state without EC. As expected, the IBN with a pedestal observed for the free-running comb indicates poor comb coherence, and the resulting multiheterodyne spectrum shows non-resolvable down-converted RF comb lines. We also perform digital difference frequency generation (DDFG) step that extracts self-mixing harmonics of the comb repetition rate difference, and those down-converted RF comb lines are highly equidistant for coherent combs (this step is often used in coherent DCS averaging to correct fluctuations in the difference of DCS comb repetition rates [49]). Well-resolved harmonics spanning broad RF-frequency range in the Fast Fourier Transform (FFT) of the photodetector signal after DDFG, referred to as a self-mixing spectrum, indicate high comb coherence. As clearly visible in Fig. 8(D), the self-mixing spectrum for the free-running comb state does not contain any resolvable harmonics of the difference in frep of both lasers (or Δfrep), which further confirms that the free-running QCL-FC state is not coherent.
The situation is significantly improved in the case of harmonic comb states. When the test QCL-FC is operated with EC-OFI, the high-order comb-state IBNs collapse to FWHMs < 5kHz (shown in Fig. 8(B)), and the DCS test produces distinctly separated RF comb lines in multiheterodyne spectra with high SNR (shown in Fig. 8(C)). Similarly, the self-mixing spectra are broadband with multiple harmonics of Δfrep (shown in Fig. 8(D)), which indicates great improvement of comb coherence. While a FWHM of IBN at low-kHz level or better is standard for high-quality QCL-FC [1,2], the improvement of comb coherence with EC-OFI is the most significant for sub-optimal devices that exhibit poor coherence when free running, and the data presented here clearly demonstrates this trend.
4.2.2 Spectral bandwidth
In addition to an improved coherence, we have also observed an increase in spectral bandwidth of the combs operating in EC-induced high-order harmonic states, which is demonstrated in Fig. 9. The optical spectrum of the free-running comb has a spectral bandwidth of ∼46 cm-1. The spectral bandwidth gradually increases as the comb is driven to higher-order harmonic states via LEC tuning, and the spectral bandwidth nearly doubles with respect to the free-running case and reaches 92 cm-1 for the sixth harmonic state. This amount of broadening is comparable to the method of device-level dispersion management [16,17] and microwave injection [23]. Notice that optical modes that are at least 3 dB above noise floor and with expected spacing are counted when determining the spectral bandwidth. The emission power of QCL-FC is almost constant for different harmonic states, which indicates higher power per comb mode for higher-order harmonic states since the number of comb modes decreases.
Fig. 9. Optical spectra of the free-running QCL-FC in comparison with the harmonic states in EC-QCL-FC. The spectral bandwidth of each state is highlighted. As the comb is significantly broadened in the fifth and sixth harmonic states, the range of the exported spectra is increased to capture all modes.
5. Conclusion
In conclusion, we provide a method to control the generation of harmonic comb states in QCLs by coupling them to an EC consisting of a position-tunable mirror and a beamsplitter that produces controlled optical feedback injection. High-order harmonic comb states with different repetition rates can be achieved by adjusting the length of the EC enforcing Vernier-like mode selection scheme, whose simple setup can be readily accommodated to different combs without the need for gain chip modifications. Most notably, the EC supports harmonic states with an improved comb coherence manifested by the narrowing of IBN linewidth as well as fully resolvable, high SNR multiheterodyne spectra and broadband, fully resolved self-mixing spectra. During the peer-review process of this work an independent theoretical paper on a similar topic was published [50]. However, its findings do not entirely agree with our experimental observations (for instance, we observe reliable harmonic comb formations in our experiment instead of irregular dynamics predicted by Ref. [50] at similar operating conditions). We are optimistic that further work in the community will obtain a unifying theory on the mechanisms of EC-OFI in QCL-FCs.
The ability to access harmonic combs with tunable spacing could allow generation of microwave and THz radiation with adjustable frequency directly inside the chip due to ultrafast gain recovery of QCL-FCs, which has potential applications in wireless communications [34]. In addition, the large mode spacing provided by high-order harmonic QCL comb states could potentially enable mode-locked pulse formation in the mid-infrared region as postulated by Piccardo et al. [32]. In spectroscopic chemical sensing aimed at dynamic processes, frequency combs with high repetition rates are desired for applications that require high-speed DCS acquisitions, which in conventional combs is usually achieved through spectral filtering [31]. The controlled generation of harmonic states in EC-QCL-FCs offers integer-multiple repetition rate increase and significant spectral broadening, which, together with low phase-noise operations, further promote the application of QCL frequency combs in spectroscopy systems that can take advantage of these added functionality and improved parameters of the combs.
Funding
Defense Advanced Research Projects Agency (HR00111920006); National Aeronautics and Space Administration (80NSSC19K0806, 80NSSC21K1253).
Acknowledgments
This work was supported by NASA Space Technology Graduate Research Opportunity. The authors acknowledge Thorlabs for generously providing the lasers used in this investigation, and Southwest Research Institute for loan of the Bristol 771 spectrum analyzer.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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