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Abstract
We have developed an ultra-low noise tunable Brillouin fiber laser exhibiting three orders of magnitude better frequency noise performance than the Neodymium-doped fiber laser pump and remarkable optical signal-to-noise ratio exceeding 80 dB suitable for immediate applications in coherent nonlinear conversion, quantum computing and underwater communications. In addition, we have implemented a custom optical phase-locked loop to ensure long-term stable operation and have investigated its impact on frequency noise. We demonstrate the power scalability of the single frequency (Hz-class) Brillouin laser, delivering over 500 mW with tunability across the 900 nm to 930 nm range in an all-fiber fully polarization-maintaining architecture.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fiber lasers have undeniably revolutionized the laser industry thanks to their exceptional robustness, versatility, and performance [1]. In particular, Ytterbium (Yb) and Erbium (Er)-doped fiber laser technology have reached maturity, affording a multitude of applications operating in the 1 µm and 1.5 µm emission window, respectively. However, the pursuit of shorter wavelengths for single frequency operation in the near infra-red and visible spectrum has sparked significant interest. This quest has been addressed innovatively through the development of novel rare-earth doped fibers [2,3] and nonlinear conversion techniques [4].
In this work, we use custom Neodymium (Nd)-doped fibers (NDF) operating on the three-level transition 4F3/2 → 4I9/2 for emission around 900 nm. While watt-class powers in continuous-wave (CW) operation are already demonstrated in NDFs [5–11] they are typically limited either by the laser architecture (fixed operating wavelength, free-space aligned) or fiber choice (fiber type or size affecting laser performance, beam quality and amplified spontaneous emission (ASE) content). Developing an ultra-low noise, CW, single-frequency (SF) fiber laser with tunability centered around 920 nm not only opens pathways to previously inaccessible wavelengths beyond the reach of Yb laser technology [12,13], but also unlocks the potential for generating deep blue and deep UV light through nonlinear conversion processes [14]. Such capabilities find practical applications in underwater communications and LIDAR systems [15], the first stage laser cooling of Strontium atoms (461 nm) [16,17] for their successive use in quantum computing [18,19] and metrology [20,21], as well as high-resolution spectroscopy and advanced lithography techniques [22,23].
SF lasers can be realized using various technologies. Solid state crystal lasers can deliver watt-class powers at narrow linewidths (< 100 kHz) but are bulky and complex. Fiber lasers with distributed-feedback (DFB) or distributed Bragg reflector (DBR) configurations can obtain kHz-class linewidth but lack tunability and are limited to a few mW of emitted power [12,13]. For semiconductor lasers, the linewidth commonly ranges from MHz-class for edge-emitting systems to tens of kHz-class for optically pumped vertical-cavity surface-emitting lasers (VCSELs) which is an emerging technology. Extended cavity diode lasers (ECDLs) widely used for their broad tuning range and low intensity noise characteristics can deliver few tens of mW at tens of kHz linewidths. While tapered amplifiers are available to power scale the ECDL seed, they require stringent free-space coupling and geometrical mode cleaning. It is therefore desirable to build a robust, fiber-based, high power (>100 mW), tunable (9xx nm), low-frequency noise (Hz-class) NDF laser. This development will enable subsequent power scaling in custom NDFs to surpass the watt-class Ti: sapphire and tapered amplifier systems with the added benefit of being a robust, all-fiber polarization-maintaining architecture with excellent beam quality and noise properties.
Stimulated Brillouin scattering (SBS) is the lowest threshold nonlinear effect in CW SF lasers and manifests through the generation of backward propagating Stokes wave that carries a significant fraction of the input power beyond a threshold level [24,25]. SBS can either be detrimental or advantageous depending on the system requirement. In an amplifier, SBS onset imposes limitations on power scalability and system stability. Conversely, in the case of a Brillouin laser, SBS determines the spectral narrowing of the Stokes wave potentially by several orders of magnitude, thereby resulting in ultra-narrow linewidth output [26–29].
In this work, we tackle SBS in both its manifestations and optimize the experimental parameters to mitigate SBS in the amplifier module while concurrently enhancing its occurrence within the Brillouin laser cavity. In optical fibers, SBS exhibits an efficient gain over a narrow homogeneous bandwidth of a few tens of MHz [24,25]. This distinctive feature empowers the use of fibers as a parametric gain medium for the realization of Brillouin fiber lasers (BFL) with intrinsic linewidths of the order of sub-kHz to Hz-class. A BFL cavity encompasses a closed fiber loop that resonates at the Stokes wave, resulting in an output with significantly improved phase (or frequency) noise characteristics. This improvement is attributed to the interplay of acoustic damping effects and cavity feedback mechanisms [29].
Depending on the pumping scheme adopted, BFLs can be broadly classified into two categories: resonant and non-resonant. Resonant pumping architectures typically have low SBS threshold, facilitating the attainment of sufficient Brillouin gain in short fiber lengths. However, they require servo-control mechanisms to frequency reference the pump laser to the cavity resonance [30] even in the presence of cavity length drifts and fluctuations. Without this servo-control, the output becomes unstable, making power scaling unfeasible. The Pound-Drever-Hall (PDH) technique can be used to stabilize the cavity [31,32], albeit requiring the introduction of a modulation signal on the pump laser which impacts the output.
In contrast, the use of a non-resonant pump [32–36], requires high pump powers and/or extended fiber lengths to counterbalance the heightened SBS threshold but is chosen for its simplicity, wavelength tunability and power scalability. Over 20 W of power has been recently demonstrated by Y. Tao et al., [37] in a non-resonantly pumped Brillouin/Yb fiber laser using passive and active large-mode-area (LMA) fibers within the cavity. However, NDF laser pumped BFL has yet to be explored within the existing literature and we aim to develop it with technical features that outshine the current SF sources operating around 920 nm.
In this pursuit, we present the development of an in-house built, tunable NDF laser and its subsequent use as a non-resonant Brillouin fiber laser pump. Our innovative approach yields a spectrally pure, ultra-low frequency noise, SF laser, which can be tuned from 900 nm to 930 nm. These features are obtained using a fully polarization maintaining architecture, while preserving the advantages of a fiber laser system.
2. Neodymium-doped fiber laser
The NDF laser employs a master-oscillator-power amplifier (MOPA) configuration with a Toptica DL Pro ECDL seed laser (tunable between 900 - 930 nm with 10 - 30 mW of fiber-coupled power respectively) and a co-propagating pump (over 20 W at 808 nm) as shown in Fig. 1. All the couplers and isolators use a standard PM980 fiber (5.5/125/250 µm core/clad/coating diameter and core numerical aperture (NA) of 0.12). The combiner input and output ports are made of custom 4/80/160 µm passive double-clad fiber to ensure compatibility with the active fiber.
Fig. 1. Schematic of the Neodymium-doped fiber (NDF) laser. SF: Single Frequency; SBS: Stimulated Brillouin Scattering; PM: Polarization Maintaining; CMS: Cladding Mode Stripper.
The amplifier consists of a polarization maintaining (PM) double-clad NDF with W-shaped core index profile, 4.7/80/160 µm core/clad/coating diameter, and core/clad NA of 0.16/0.46. Over repeated trials with custom PM NDFs of different fiber core/clad geometries (in collaboration with Exail), we observed that the 4.7/80 µm fiber offers the best performance: optimal bend-induced ASE suppression and moderate power scalability without compromising the polarization-extinction ratio (PER). The bend diameter was fine-tuned to 8 cm to achieve a PER exceeding 20 dB and total suppression of ASE at 1 µm. A coupler (2 × 1) is used at the input to monitor the backward propagating light for traces of ASE and SBS.
The custom NDF has a low clad absorption of 0.58 dB/m around 800 nm due to doping limitations posed by Nd3+ ion clustering effects [38]. For efficient pump absorption long gain fiber lengths are preferred. This presents an issue in the context of SF operation since long fiber lengths lower the SBS threshold and consequently limit power scaling. Therefore, our approach is to strongly pump a short fiber segment, optimized to 1.7 m through cut-back experiments. To cope with the high unabsorbed pump power (∼ 80% of the injected power), we designed a suitable cladding mode stripper (CMS) with efficient thermal management. As a result, we obtain an output signal of over 550 mW at 920 nm for a 14.5 W pump. This result translates to an overall conversion efficiency of approximately 4% and an absorbed pump to signal conversion efficiency of nearly 20% as quantified after the isolator. We obtain nearly 400 mW tunable between 900 nm to 930 nm as shown in Fig. 2(a). We remark that for a given injected pump power at 808 nm, there is a marginal reduction in output power at the edges of the tuning range. This deviation, as indicated in Fig. 2 (a), can be attributed to the degraded power of the ECDL seed (Toptica DLPro) around 900 nm. This wavelength falls below the specified operating wavelength window (> 915 nm) of the seed laser. We also observe a slightly lower NDF amplifier gain in the vicinity of the longer 930 nm wavelength. It is worth noting that the actual power of the NDF laser before the isolator is higher (∼ 750 mW at 920 nm), and the reduction (aside from the ∼10% insertion loss) is attributed to the splice loss occurring at the interface between the mismatched NDF and PM980 fiber at the CMS. Nonetheless, it is imperative to include an isolator to effectively prevent SBS seeding resulting from end-facet reflections.
Fig. 2. (a) Plot of output signal power of the tunable NDF laser vs. total pump power at 808 nm (b) Output spectrum of the tunable NDF laser normalized to the peak at 920 nm measured using an optical spectrum analyzer (Yokogawa AQ6374) with 0.1 nm resolution.
Tunability between 900 to 930 nm is also evident in the spectrum shown in Fig. 2(b), which was measured using a Yokogawa AQ6374 optical spectrum analyzer (OSA) with a 0.1 nm resolution. An optical signal to noise ratio (OSNR) ranging between 40 dB and 50 dB implies that more than 97% of all the output power is concentrated at the desired signal wavelength across the tuning range. This tunable NDF laser is subsequently used to pump a Brillouin laser.
3. Brillouin fiber laser
The schematic and experimental setup of the NDF laser pumped BFL is shown in Fig. 3(a) and 3(b) respectively. The Brillouin cavity consists of a circulator, 10 m of PM980 fiber spool, a 50/50 coupler and nearly 3 m of passive PM980 connecting fibers. The pump laser is injected into the cavity through the circulator (port 1). The pump, which is non-resonant, circulates once in the loop and ultimately terminates at the circulator port 3. Upon surpassing the threshold power, a Stokes wave is generated and travels counterclockwise within the cavity. The circulator permits the passage of the first order Stokes wave through the loop (port 2 to port 3) with 50% of the Stokes power out-coupled in each round-trip. An additional advantage of the circulator is its ability to suppress the growth of higher order Stokes waves, contributing to an efficient conversion and improved power scalability.
Fig. 3. (a) Schematic of the Brillouin fiber laser (BFL) non-resonantly pumped by an in-house built tunable Nd-doped fiber laser (NDFL) where arrows indicate the direction of pump (blue) and Stokes signal (red). (b) Picture of the in-house built compact NDF pump and the packaged BFL cavity.
Figure 4(a) shows the BFL output power vs. the injected NDF laser pump power inside the cavity at port 2. The insertion and coupling losses of the coupler and circulator reduce the overall power entering and circulating the cavity as evident in the plot. The threshold cavity input power for Stokes wave generation is ∼110 mW and the output is downshifted by about 18.5 GHz around 920 nm. Given the tunability of the pump laser and the transparency of the cavity to the input, the BFL output can also be finely tuned across the entire range from 900 nm to 930 nm. The measured output power is above 120 mW across the entire tuning range and over 200 mW between 910 nm and 920 nm with a PER of nearly 20 dB.
Fig. 4. (a) Plot of the output Brillouin Stokes power vs. cavity input pump power at various wavelengths; NDFL: Nd-doped fiber laser, BFL: Brillouin fiber laser. (b) Output spectrum of the tunable BFL normalized to the peak at 920 nm measured using an optical spectrum analyzer (Yokogawa AQ6374) with 0.1 nm resolution.
Fig. 5. Plot of Relative Intensity Noise Power Spectral Density (RIN PSD) vs. frequency for the Nd-doped fiber (NDF) laser pump at 920 nm (green curve) and Brillouin fiber laser (BFL) (blue curve). FSR: Free-spectral range.
The analysis of the BFL output spectrum as shown in Fig. 4(b) indicates a remarkable improvement in spectral content with the absence of ASE and high OSNR exceeding 80 dB. This result surpasses the OSNR measured in the NDFL pump (Fig. 2(b)) by 30 dB to 40 dB.
We use relative intensity noise (RIN) power spectral density (PSD) measurements to quantify the intensity noise of the NDF laser pump and BFL. RIN measurement is a highly sensitive and widely used technique to assess SF laser quality, given its ability to detect SBS and high levels of ASE [39,40]. Lower frequency measurements (up to 10 kHz) in RIN are primarily impacted by the pump characteristics; the properties of the seed and MOPA affect the higher frequencies (MHz) and the transition between these two regions is marked by a smooth decay, best described in terms of a first-order transfer function [40].
The NDF pump laser and BFL show low RIN level of nearly -155 dBc/Hz and -145 dBc/Hz respectively around 1 MHz as shown in Fig. 5. The shot-noise limit of the detector is -165 dBc/Hz and the detection noise floor is -170 dBc/Hz. The bandwidth of the detection system is nearly 10 MHz. RIN in the kHz frequency range is dominated by electronic noise and can be effectively reduced by using a low-noise driver for the high-power 808 nm diode. The RIN of the BFL is higher than that of the NDF laser pump. This can be attributed to several factors such as laser dynamics, feedback and fluctuations in pump and cavity reinjection rate. The two attenuated peaks observed in the BFL RIN correspond to frequencies of approximately 14.4 MHz and 28.7 MHz respectively. The spacing between the peaks corresponds to the cavity free-spectral range (FSR) between 14 to 15 MHz at 920 nm which matches the theoretical calculation for a ∼13 m long cavity.
Figure 6 represents the plot of wavelength stability of BFL with time. Although the main graph represents a stable output as measured by a relatively low-resolution instrument (like an OSA), the inset denotes the actual wavelength of the BFL characterized using a high-resolution wavelength meter (High Finesse: model WS7-60 with 60 MHz absolute accuracy and nominal 2 MHz wavelength deviation sensitivity). It is clear that the non-resonantly pumped BFL exhibits mode-hopping.
Fig. 6. Wavelength stability plot of BFL with time. Inset: Mode hopping captured with a high finesse wavelength meter WS7-60 with a sampling interval of 100 ms.
The origin of mode-hopping can be described as follows. The peak of the Brillouin gain spectrum (BGS) tracks the pump wavelength, whereas the output Stokes wavelength is set by the cavity resonant mode at (or near) the BGS maximum. Drifts in the pump wavelength cause BGS drifts. Whenever this shift is large enough to position the adjacent cavity resonant mode closer to the BGS maximum, the result is a mode hop of the Stokes wave observed on the output beam. These mod hops can also occur because of thermally induced cavity length fluctuations. In practice, both the pump laser and the resonator length fluctuate, resulting in multiple mode hops during operation.
The observed mode-hopping (inset of Fig. 6) is attributed to the BFL’s sensitivity to ambient factors, such as temperature/acoustic/mechanical fluctuations. The initial wavelength was 920.404734 nm, and several mode-hops were observed within a 5-minute interval, thanks to the high resolution of the wavelength meter. We recorded a wavelength shift of nearly 0.04 pm per mode hop, corresponding to 14 - 15 MHz at 920 nm. This closely matches with the calculated FSR for a cavity length of ∼13 m. It is worth remarking that the cavity was built inside a sturdy metal encased packaging and placed on an optical table. Nonetheless, we believe that in a practical setting, it would be impossible to guarantee long-term mode-hop free operation of a non-resonantly pumped free-running BFL cavity. As a result, non-resonantly pumped BFLs, convenient for their tunability and power scalability, require a servo-control system to guarantee long-term mode-hop free operation. For this reason, we propose the use of an optical phase locked loop (PLL) as previously demonstrated by G. Danion et. al. [41]. This solution is chosen for its simplicity of implementation and effectiveness in realizing a mode-hop free operation of a non-resonantly pumped BFL.
The schematic of the PLL is shown in Fig. 7. A small portion of the NDFL pump, operating at frequency νp, is combined with the BFL Stokes output, operating at frequency νs, via a 2 × 1 coupler. The combined signal is sent on a large bandwidth photodiode (PD), which detects the beat note (Δν = νp – νs). The beat note signal is then down-mixed using radiofrequency νLO from a local oscillator (LO) provided by an electrical synthesizer. The intermediate frequency (IF) output of the mixer (at Δν – νLO) is fed to a proportional-integrator (PI) filter. We monitor the signal entering the optical PLL using an RF spectrum analyzer (RFSA). In open loop condition, the system presents frequency instabilities due to the pump-Stokes detuning, primarily attributed to temperature and mechanical fluctuations. To stabilize the Stokes wave, the LO is matched to the peak of the Brillouin gain, which stands at 18.594 GHz for a pump operating at 920 nm. The closed-loop condition is obtained by feeding the filtered error signal to the laser source using both a fast actuator (the current modulation of the laser diode) and a slow one (the piezoelectric element setting the cavity length for the ECDL). When the PLL is active we observe a stable, single longitudinal mode operation of the laser, thanks to the 400 kHz bandwidth of the servo control.
Fig. 7. Schematic of the Nd-doped fiber laser (NDFL) pumped Brillouin fiber laser (BFL) with a phase locked loop (PLL). NDFA: Nd-doped fiber amplifier, PD: Photodiode, LO: Local oscillator, RF: Radio Frequency, IF: Intermediate frequency, RFSA: RF spectrum analyzer.
The wavelength stability of the locked BFL measured over 1 hour demonstrates the absence of mode hopping, as shown in Fig. 8. The sub-pm slow linear change in wavelength can be attributed to environmental disturbances, such as thermal drifts in the BFL cavity.
Fig. 8. Measurement of wavelength stability of the phase locked Brillouin fiber laser (BFL) using a high finesse wavelength meter (WS07-60) meter with a sampling interval of 100 ms indicating mode-hop free operation.
The nature of Brillouin gain mechanism results in improved noise properties of the Stokes shifted signal [42]. While the linewidth provides a simple assessment of the spectral quality of a laser, the characterization of high coherence SF lasers requires a more exhaustive measurement, in terms of its frequency or phase noise. To implement this approach, we measure the Power Spectral Density (PSD) of the laser’s optical spectrum, using a photodetection system coupled to low-noise electronics.
We built a Mach-Zehnder interferometer for homodyne detection where a signal interferes with a delayed replica of itself, after passing through an optical delay line. SF lasers, characterized by high coherence lengths, require long optical delay lines (over tens of kilometers) to reach complete signal decorrelation. This is not only impractical, but also unsuitable due to factors like the fiber attenuation (> 1 dB/km around 920 nm) and the onset of SBS in the interferometer, which increases the overall system noise floor. To avoid these issues, we use a shorter delay line [43], approximately 400 m, on one arm of the interferometer, and a fiber stretcher for frequency discrimination on the other arm, as shown in the schematic of Fig. 9(a). The disturbances on the delay line result in a varying relative phase between the two arms of the interferometer. We then measure the interference pattern of the decorrelated signals through a fast photodiode (PD), whose signal is fast-Fourier transformed using a vector spectrum analyzer.
Fig. 9. (a) Schematic of the in-house built interferometer used for frequency noise measurement; SF: Single frequency, PD: Photodiode, VSA: Vector Spectrum Analyzer. (b) Comparison of frequency noise of the pump and Brillouin fiber laser (BFL) with and without phase locked loop (PLL).
In Fig. 9(b) we present a comparative analysis of the frequency noise of the pump laser (green curve), the BFL without locking (blue curve) and the BFL with the PLL activated (red). Clearly, when compared to the pump the simple BFL already shows a remarkable improvement of nearly 3 orders of magnitude across the entire frequency range. Activating the PLL for the cavity stabilization in the BFL provides an additional improvement, resulting in an ultra-narrow Hz-class laser. By locking the pump-Stokes detuning to an RF reference, the frequency noise of the pump becomes correlated to the Stokes wave within the bandwidth of the servo-loop [42]. In our system, the PLL bandwidth surpasses the source laser linewidth, which results in the transfer of spectral purity from the BFL to the pump. In this way a narrower linewidth is obtained for the pump, which in turn improves the frequency noise of the generated BFL.
For the purpose of comparison, in Fig. 9(b) we indicate a dashed line (blue) corresponding to the 10 Hz linewidth of a white noise (Gaussian) source. The interferometer measurement is a full independent evaluation of the frequency noise, and it is possible to numerically estimate the linewidth of the laser using a beta-separation line as described by G. Di Domenico et al [44]. The linewidth of the pump laser, BFL without lock and BFL with lock is estimated to be approximately 115 kHz, 1.3 kHz and 600 Hz respectively. At frequencies below 1 kHz, the noise level of our system shows a high sensitivity to mechanical and acoustic vibrations. With improved isolation, these dominant peaks could be smoothened and the BFL linewidth will potentially be below 100 Hz. It is important to note that, for a SF BFL the frequency noise measurement is a better-defined indicator of laser spectral purity as opposed to a single value defined by the linewidth.
The high frequency dip observed in Fig. 9(b) at approximately 500 kHz corresponds to the first zero of the interferometer. A bump around 10 kHz frequency can be attributed to the vibration sensitivity of the fiber spool of the interferometer setup. As such, these features are not indicative of the test laser performance [45]. Therefore, we conclude that the BFL with an active PLL has an improved frequency noise below 10 Hz2/Hz beyond a few kHz. The use of PLL on a non-resonantly pumped BFL provides a simple, robust, and efficient way to achieve single longitudinal mode operation while also improving the frequency noise characteristics of the laser.
To verify the repeatability of our laser scheme, we built another NDF amplifier, closely resembling the one described in section 2. This amplifier was moderately seeded with the tunable BFL at ∼ 60 mW with improved spectral purity (high OSNR, ASE free, ultra narrow SF). This configuration achieved a signal output power of over 500 mW, with an OSNR exceeding 50 dB across the tuning range between 900 nm to 930 nm as shown in Fig. 10 (a) and (b) respectively. This compares favorably to the ECDL seeded MOPA stage in terms of power, ASE bandwidth and OSNR. The higher power and spectral purity of the BFL makes for an efficient seed to achieve power scaling in the amplifier. An interesting future direction would be to study the impact of seed characteristics (such as power, spectral width, and ASE content) on the NDF amplifier to further optimize the system for best performance.
Fig. 10. (a) Plot of output signal power of the booster NDF amplifier seeded by the Brillouin fiber laser vs. total pump power at 808 nm (b) Normalized output spectrum measured using an optical spectrum analyzer (Yokogawa AQ6374) with 0.1 nm resolution.
To test the robustness of the high-power system, we measure the output power around the 500 mW-level for over 4 hours as shown in Fig. 11. The peak-to-peak power fluctuation is less than 5% over the entire time period (from cold-start) and less than 2% after the first 3 hours of operation indicating steady state stable operation of the system.
4. Conclusion
In conclusion, we developed a high power, ultra-low noise, stable Brillouin fiber laser non-resonantly pumped by an in-house built Nd-doped fiber (NDF) amplifier tunable around 920 nm. The high spectral purity of the Brillouin laser represents an excellent optical source well-suited for a wide range of coherent and nonlinear applications, and in multi-stage amplification, particularly when used in combination with large mode area fibers. The BFL we have engineered delivers > 200 mW around 920 nm and >120 mW across the 900 nm to 930 nm tuning range. This achievement is further enhanced by a remarkable spectral purity, characterized by an OSNR > 80 dB, and ultra-low frequency noise, which reaches a level 3 orders of magnitude better than the pump laser. The BFL architecture, marked by its simplicity, tunability, and power scalability, represents a significant technological advancement. For improved robustness and long-term wavelength stability, we implement an optical phase locked loop (PLL) to actively lock the frequency detuning between the pump and Stokes waves to the SBS gain maximum. As an added advantage, the phase lock further improves the frequency noise of the BFL, yielding an ultra-stable, Hz-class fiber laser subsequently amplified to over 500 mW of power in a custom, polarization maintaining NDF. Our work opens exciting directions for future research and optimization. The dynamics of the NDF pumped BFL can be precisely characterized to surpass the existing single frequency lasers in the scarcely explored 900 nm region, in terms of power (watt-class), linewidth (kHz to Hz-class) and wavelength tunability (900 nm to 930 nm). These advances, coupled with the use of a fully fibered polarization maintaining architecture, will have an impact in a wide range of coherent and nonlinear applications in laser technology.
Funding
Agence Nationale de la Recherche (NEODUV-ANR-19-CE24-0029); Conseil Régional Aquitaine (AAPR2021-2021-12214510).
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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