Abstract
We demonstrate an eight-wavelength-switchable single-frequency (SF) ultra-narrow linewidth erbium-doped fiber laser (EDFL). A switchable polarization-dependent eight-channel filter (S-PDECF), fabricated using femtosecond laser direct-writing technology, determines the eight wavelengths of the laser output, with four channels concentrated near 1530 nm and the other four near 1550 nm. A dual-coupler ring-based compound-cavity filter is utilized to achieve single-longitudinal-mode selection for the EDFL. The introduction of a femtosecond laser direct-written scattering-enhanced fiber (SEF) effectively narrows the laser linewidth, enabling ultra-narrow linewidth outputs lasing at all eight wavelengths, and the wavelength self-adaptive linewidth compression of the SEF is verified for the first time. Furthermore, the incorporation of SEF significantly enhances the overall performance of the EDFL. The eight switchable single-wavelength laser outputs all exhibit exceptional characteristics, including spectral wavelength fluctuations of ≤0.011 nm, spectral peak power fluctuations of ≤0.54 dB, optical signal-to-noise ratios of ≥71 dB, linewidths of ≤248 Hz, output power fluctuations of ≤0.252 dB over a 10-min measurement period, and relative intensity noise of ≤−150.17 dB/Hz @≥ 3 MHz.
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1. Introduction
Single-frequency (SF) narrow-linewidth fiber lasers possess unique attributes such as high coherence, low noise, and excellent compatibility with fiber-optic systems. These features make them suitable for applications such as large-capacity ultra-long-haul coherent optical communication, high-resolution optical metrology and spectroscopy, long-distance high-resolution distributed-fiber sensing, coherent Doppler lidar, gravitational-wave measurement, and other applications related to optical atomic clocks, fundamental-constant measurements, and physics [1–7]. As the performance demands of these applications continue to increase, SF narrow-linewidth fiber lasers are required to have wavelength-tuning/scanning/switching capabilities and dual/multi-wavelength operation [8–13]. Additionally, they must maintain ultra-narrow linewidth output across various modes, which imposes stringent requirements on linewidth compression technologies.
Ultra-short laser cavity structures provide the simplest and most mature technology for fabricating SF fiber lasers, such as distributed feedback (DFB) and distributed Bragg reflection (DBR) types [14–16]. However, these lasers generally suffer from low output power, high noise, and poor functional scalability, making it challenging to meet the high-performance requirements of advanced applications. Long ring laser cavity configurations allow the integration of various functional devices into the laser system, enabling multifunctional output and performance enhancement [9,17–20]. To achieve multi-wavelength switchable laser output, the optimal approach is to incorporate multi-channel fiber Bragg grating (FBG) filters for wavelength selection and filtering within the laser system. Numerous devices have been proposed for this purpose, including superimposed FBGs, high-birefringence FBGs, FBG Fabry-Perot (F-P) filters, chirped moiré FBGs, sampled FBGs, and chirped phase-shifted FBGs [9,19,21–26]. These are fabricated in single-mode fibers (SMFs) or polarization-maintaining fibers (PMFs) using the phase mask method. Among these, devices with polarization-dependent characteristics combined with polarization controllers (PCs) are the most effective for realizing wavelength switching [9,19,23]. In recent years, femtosecond laser direct-writing technology has been widely applied in FBG fabrication [27–30], significantly enhancing the flexibility of creating new FBG based multi-channel filters. This technology allows for the fabrication of functional filter devices that are unattainable with the phase-mask method. For instance, our research group has utilized the femtosecond laser to fabricate a parallel FBG (P-FBG)-based four-channel filter with high polarization-dependent characteristic in an SMF, and has then utilized that to achieve high-performance four-wavelength-switchable laser output. Building on this foundation, this paper describes the fabrication of a novel eight-channel polarization-dependent FBG filter achieved by combining an optical switch to achieve higher performance in fiber lasers.
Linewidth compression is a core technology for ultra-narrow-linewidth fiber lasers. Several methods have been proposed, including the slow-light effect [31], self-injection locking [32], saturable absorbers (SAs) [9], and Pound-Drever-Hall (PDH) frequency stabilization [6,33]. The first three methods have limited linewidth compression effects, especially for long ring cavity fiber lasers, where it is challenging to compress the linewidth to as little as hundreds of Hz. The PDH technique can reduce laser frequency instability to a state-of-the-art level of <10−16, compressing the fiber laser linewidth to the mHz level [33]. However, this technology requires locking the laser to an ultra-stable cavity, involving a complex photo-electric auxiliary servo system that is expensive and has stringent operating conditions, making it unsuitable for widespread application. In addition to the above methods, in recent years, linewidth compression methods based on fiber Rayleigh-scattering randomly distributed feedback have been widely studied theoretically and experimentally [34–36]. Randomly distributed scattering feedback in lasers can effectively reduce the impact of spontaneous emission on stimulated emission by continuously converting spontaneous-emission noise photons into stimulated-emission photons, thereby effectively narrowing the laser linewidth [35]. Linewidth compression using fiber randomly distributed feedback has been demonstrated both inside [37,38] and outside [36] the laser cavity. However, utilizing Rayleigh-scattering randomly distributed feedback from SMFs requires hundreds of or even more than a thousand meters of fiber to achieve sufficient feedback accumulation. This not only reduces the fiber laser's resistance to environmental disturbances but also hinders system miniaturization and integration. Although high numerical-aperture fibers with stronger scattering have been used to replace SMFs, they still require lengths greater than 50 m [36], and their cost is higher. More importantly, the inherent Rayleigh scattering in fibers is uncontrollable, allowing control only over the length of the fiber used, which limits the optimization of fiber-laser systems. To address this issue, our research group has utilized advanced femtosecond laser direct-writing technology to induce high-scattering centers in SMFs, creating scattering-enhanced fiber (SEF) with random distributed feedback. We have introduced the SEF into an single-longitudinal-mode (SLM) fiber laser for linewidth compression, achieving a linewidth of less than 150 Hz using only 20 m of SEF, and the overall laser output performance is excellent. However, the wavelength-dependent characteristics of SEF for linewidth compression have not been fully verified, and its potential for application in broadband wavelength-tunable fiber lasers remains to be further explored.
In this work, we first utilized femtosecond laser direct-writing technology to fabricate two polarization-dependent P-FBG-based four-channel filters on SMFs, with reflection center wavelengths around 1530 nm and 1550 nm. By combining these with an electrically controlled optical switch (EC-OS), we obtained a switchable polarization-dependent eight-channel filter (S-PDECF). Next, a femtosecond laser was employed to introduce randomly distributed high scatters in an SMF to create an SEF. We incorporated the S-PDECF and the SEF into a ring-cavity erbium-doped fiber laser (EDFL) and used a dual-coupler ring-based compound-cavity (DCR-CC) filter for SLM selection. This setup enabled us to achieve eight-wavelength-switchable SF ultra-narrow linewidth laser output, with all eight lasers having a linewidth of less than 250 Hz. This confirmed the feasibility of using SEF for broadband tunable laser linewidth compression and demonstrated the wavelength self-adaptive linewidth compression of SEF. In addition to small linewidth, the fiber laser exhibited excellent performance in terms of spectral stability, optical signal-to-noise ratio (OSNR), longitudinal-mode purity, power stability, and relative-intensity noise (RIN). Furthermore, we explored the relationship between laser linewidth at different wavelengths and the length and high-scatter density of the SEF, laying the groundwork for future research.
2. Experimental setup, principle, and theory
The proposed laser system configuration is shown in Fig. 1. A 980-nm laser diode (LD) with a maximum output power of 550 mW is used to provide the pump energy. The pump light is coupled into a 3-m erbium-doped fiber (EDF, Fibercore Cor., M12-980-125) via a 980/1550 nm wavelength-division multiplexer (WDM). The EDF, coiled around the plates of a three-loop polarization controller (TL-PC), provides laser gain with an absorption rate of 16.0 − 20.0 dB/m at 1531 nm. A fiber in-line polarizer (ILP) converts the passing laser light into linearly polarized light. The DCR-CC is composed of four 90:10 optical couplers (OCs). Two sub-rings, composed of OC-1, OC-2 and OC-3, OC-4, have lengths of ∼60 cm and ∼61 cm, respectively. Based on the theoretical research methods previously proposed by our group [23,39], the free spectral range (FSR) of the DCR-CC is approximately 20.46 GHz, and the full-width at half-maximum (FWHM) is about 8.75 MHz. The DCR-CC may exhibit slight polarization dependence due to the random polarization characteristics of the four couplers used. A three-port optical circulator (CIR) is used to introduce the wavelength-selective device S-PDECF into the laser cavity while also serving as an isolator to ensure unidirectional laser oscillation. The S-PDECF consists of two P-FBGs and an EC-OS. A direct current (DC) power supply provides voltage signals to the EC-OS, enabling it to switch transmission from Port 1 to Port 2 (insertion loss: 0.6 dB) and Port 1 to Port 3 (insertion loss: 0.8 dB). This operation toggles the use of either P-FBG-1 or P-FBG-2 in the laser cavity. A drop-in polarization controller (DI-PC) works in conjunction with the DCR-CC to achieve an optimized SLM filtering and with the S-PDECF to achieve different wavelength lasing outputs. A 22.3-m SEF is introduced between the S-PDECF and port 2 of the CIR for laser linewidth compression. The total cavity length of the laser is ∼52 m, corresponding to a longitudinal-mode spacing (LMS) of ∼5.77 MHz. Theoretically, the DCR-CC ensures SLM oscillation in the laser system [23,39]. The laser output is extracted from the 30% port of OC-5, with the remaining 70% retained in the cavity to maintain laser oscillation. The entire laser system is arranged on a rigid optical platform without additional temperature control or encapsulation.
Both the S-PDECF and SEF used in this study were fabricated using a femtosecond laser direct-writing system, which was placed on a vibration-isolated air flotation platform. The light source was a mode-locked femtosecond ytterbium-doped fiber laser (YSL Photonics Corp., FemtoYL-20) with a central wavelength of 1030 nm, a pulse width of 382 fs, and a repetition rate of 200 kHz. The output parameters of the femtosecond laser, such as repetition rate and pulse energy, were controlled by computer software.
The relationship between the central reflection wavelength of the FBG and its period is given by [19]
where k is the diffraction order of the grating, and is the effective refractive index. By adjusting the writing period, the central reflection wavelength of the FBG can be flexibly changed. Using the point-by-point method to fabricate the FBG in a standard SMF (Corning SMF-28e) requires that the speed v of the moving displacement stage matches the modulated laser pulse repetition frequency of the signal generator, which is related to the FBG period by
Previous studies have found that symmetrically writing two FBGs with different periods on the two sides of the fiber core center using the point-by-point method results in a P-FBG [19]. Due to the inherent non-uniformity of the femtosecond laser spot and the spatial asymmetry of the written FBGs in the fiber core, local high birefringence is induced in the grating area. This leads to reflection channels with different central wavelengths for two orthogonal polarization states within the same FBG, with the wavelength spacing given by
where is the difference in the effective refractive indexes between the x-polarized (X-Pol) and y-polarized (Y-Pol) directions of the fiber. The magnitude of is mainly related to the femtosecond laser pulse energy and the grating inscription length.
A schematic diagram of the P-FBG writing process is shown in Fig. 2. The SMF was fixed on a 3D translation stage with a moving speed of 50?µm/s, and the femtosecond laser was focused on the fiber core. The fiber coating of SMF was stripped to achieve a more precision index modulation. A series of laser pulses sequentially reached different positions in the fiber core, inducing periodic refractive index modulation. The modulation period corresponds to the FBG period Λ in Eq. (1), where k is set to 2. Note that, to prevent the overlapping of adjacent femtosecond laser spots, each approximately 1?µm in size, and thereby reduce period-ambiguity-related chirping, writing gratings with higher diffraction orders can enhance grating performance. However, as the diffraction order increases, the number of inscribed points decreases, which leads to a reduction in grating’s reflectivity. After careful consideration, we opted to fabricate gratings with a diffraction order of 2. First, the focal point of the laser spot was placed on the fiber core with an offset of 1?µm from the centerline along the y-axis. The modulation laser pulse repetition frequency was set to 48.04 Hz, and an FBG-1 with a length of 9 mm, a period = 1.0409?µm, and a central wavelength of ∼1528 nm was written in the SMF. Subsequently, the SMF was moved up 2?µm horizontally along the y-axis, and was adjusted to 47.97 Hz. An FBG-2 with a length of 9 mm, a period of 1.0422?µm, and a central wavelength of ∼1530 nm was written. Through this process, P-FBG-1 was obtained. The optical micrograph of P-FBG-1 captured at a local position is shown in the inset of Fig. 2. Using the same method, adjusting modulated laser pulse repetition frequencies and to 47.42 Hz and 47.36 Hz, respectively, FBG-3 with a period =1.0555?µm and a central wavelength of ∼1548 nm, and FBG-4 with a period =1.0559?µm and a central wavelength of ∼1550 nm were inscribed on another SMF, resulting in P-FBG-2.
A testing system consists of an erbium-doped fiber amplifier, an ILP, a PC, a CIR, and an optical spectrum analyzer (OSA, Yokogawa AQ6375D) with a spectral resolution of 0.02 nm and a data sampling rate of 0.001 nm. This setup was used to evaluate the filtering performance of the two P-FBGs. By adjusting the PC to control the state of polarization (SOP) of the linearly polarized light entering the P-FBGs, we measured the transmission and reflection spectra of P-FBG-1 and P-FBG-2, as shown in Figs. 3(a) and 3(b). In these figures, the red dashed curves represent measurements using X-Pol light, and the blue solid curves represent measurements using Y-Pol light. The insertion loss (IL) for each FBG is indicated in the figure and is <0.9 dB. Typical parameters for each channel of the P-FBGs are listed in Table 1. Channels C1, C2, C3, and C4 belong to P-FBG-1, while channels C5, C6, C7, and C8 belong to P-FBG-2. The data show that the eight wavelengths reflected by the two P-FBGs exhibit a high reflectivity, > 90%. and a narrow bandwidth of ≤0.280 nm. Note that, the reflection bandwidth can be further induced by decreasing the femtosecond laser pulse energy and increasing the grating writing length; The spacing between the polarization-dependent channels of each P-FBG can be adjusted by changing the femtosecond laser pulse energy and the grating writing length.
The fabrication method for SEF is as in our previous report [21], with further optimization of the manufacturing process. In the experiment, the average output power of the femtosecond laser was controlled to randomly vary within the range of 1.233 − 1.468 W. Single laser pulses were used to induce high scatters in the core of the SMF, with the spatial positions of these high scatters being randomly controlled. The fiber coating of SMF does not need to be stripped off. The spacing between adjacent high scatters was randomly controlled within 8 − 10 cm, resulting in a 22.3 m SEF. The backscattering distribution of the SEF was measured using an optical frequency domain reflectometry (OFDR) system, as shown in Fig. 4. It can be seen that in the SEF region, the scattering intensity of the high scatter induced by the femtosecond laser increased by approximately 45 dB relative to the intrinsic scattering of the SMF, and the scattering characteristics exhibited strong randomness. Additionally, the IL of the SEF was tested using a broadband light source (NKT Photonics Cor., SuperK EVO) and an OSA. The IL of the fabricated SEF in the range of 1500 − 1600 nm is <0.4 dB.
3. Experimental results and discussion
3.1 Laser output performance measurements
The pump threshold of the laser was tested to be about 80 mW, and a typical pump power value of 180 mW was selected for experimental demonstration and performance demonstration. By switching the working channels of the EC-OS and carefully adjusting the PC, laser outputs at eight different wavelengths were successfully obtained.
The output spectra of the laser at all wavelengths were measured using the OSA, as shown in Figs. 5(a) and 5(b). These figures correspond to the four wavelengths reflected from the P-FBG-1 behind EC-OS Port 2 and the four wavelength lasers reflected from the P-FBG-2 behind Port 3, respectively. As marked, the minimum polarization extinction ratio (PER) among the eight switchable lasers is 60 dB. To evaluate the spectral stability of the laser output, the spectra of each laser repeatedly scanned using the OSA with a time interval of 6 min over ∼60 min were measured. The typical spectra are shown in Figs. 5(c) and 5(d), corresponding to the measurements of the lasers at λ1 and λ8, respectively. The typical spectral parameters for all wavelength lasers, including spectral wavelength fluctuation fλ, spectral peak power fluctuation fP, and OSNR, are listed in Table 2. It can be seen that under all wavelength output modes, the EDFL exhibited an fλ ≤ 0.011 nm, fP ≤0.54 dB, and OSNR ≥71 dB, demonstrating excellent stability and beam quality.
A scanning F-P interferometer (FPI, Thorlabs, SA200-18B) with an FSR of 1.5 GHz and a resolution of 7.5 MHz was used to investigate the longitudinal-mode characteristics of the laser at each operating wavelength, as shown in Fig. 6(a). The pink sawtooth wave represents the FPI's driving voltage signal, while the other curves display the interferometer scanning results for the laser modes at each wavelength. It is evident that within a given voltage scanning period, only two longitudinal modes were detected for each laser output, indicating that the lasers at each wavelength were stably operating in SLM. To further verify this, a self-homodyne system composed of a 400-MHz photodetector (PD, Thorlabs, PDB470C) and a radio-frequency (RF) electrical spectrum analyzer (ESA, Keysight N9010A) was used to test each laser. Each laser was measured continuously over 10 min using the maximum hold (MH) mode of the ESA; the results are shown in Fig. 6(b). No beat frequency signals were captured in any of the operations. The combination of these two methods confirms that the laser outputs are stable SF lasers at all operating wavelengths.
A delayed self-heterodyne measurement system (DSHMS) was used to measure the laser output linewidths at various wavelengths. The system comprised a Mach-Zehnder interferometer (MZI) with a 200-MHz acousto-optic modulator (AOM) and 100-km SMF in two arms, a 400 MHz PD, and an RF ESA. For demonstration, the measurement result for laser λ1 is shown in Fig. 7(a). The beat frequency signal was fitted with a Lorentzian profile, achieving a high Adj. R-Square parameter of 0.99. The linewidth was obtained from the bandwidth 20 dB down from the maximum of the fitted curve, yielding a measured linewidth of 248 Hz. It should be noted that, theoretically, such a narrow linewidth measurement requires using thousands of kilometers of delay fiber to fully decorrelate the laser arms, which would introduce significant 1/f frequency noise and substantial power attenuation. Thus, the measured result includes the Gaussian broadening introduced by the 100-km delay fiber, implying that the intrinsic linewidth of the laser should be less than the measured value. To evaluate the linewidth compression effect of the SEF, the SEF was removed from the cavity and the linewidth was remeasured. As shown in Fig. 7(b), the linewidth increased to 1248 Hz. According to the Schawlow-Townes principle [40], extending the photon lifetime by increasing the cavity length can improve the laser linewidth characteristics.
To further validate that the linewidth compression is due to the SEF, a comparison experiment was conducted using 17 m of SMF in place of the SEF. The measurement result for laser λ1 is shown in Fig. 7(c), yielding a linewidth of 1193 Hz. The slight reduction in linewidth after adding 17 m SMF is attributed to the minor increase in photon lifetime and the weak Rayleigh feedback provided by the short SMF, which is insufficient to effectively narrow the laser linewidth. Notably, the reason for not using an equivalent 22.3-m length of SMF as a replacement for the SEF is that beyond 17 m of SMF, the laser could no longer achieve stable SLM output, demonstrating that the SEF also contributes to stable SLM operation. A comparison of the laser output linewidths at eight wavelengths with and without the SEF is shown in Fig. 7(d). The SEF narrows the linewidths of all lasers to similar levels of <250 Hz, with slight discrepancy between each other, indicating weak wavelength dependence in the linewidth compression effect. This demonstrates that the SEF can achieve wavelength self-adaptive linewidth compression over a broad wavelength tuning range and offers higher stability and greater potential for compact integration than the SMF.
A power meter with a data sampling rate of 10 Hz was used to measure the output power fluctuations fo_λi (i = 1, …, 8) of the laser at each wavelength. Each laser was measured for 10 min. The results are shown in Figs. 8(a) to 8(h). Analysis shows that the average power of the laser output at each wavelength surpasses −3.239 dBm, and the output power fluctuations remain below 0.252 dB, indicating that the laser exhibits good output stability over prolonged periods of operation.
To evaluate the instantaneous power stability of the EDFL, the RIN was measured using a 400-MHz PD, an oscilloscope (Tektronix, TDS2024C), and an ESA. Taking the lasers at wavelengths λ1 and λ8 as examples, the results are shown in Figs. 9(a) and 9(b). The RIN measurements for all lasers are summarized in Table 3. It can be observed that for all operating wavelengths, the RIN is ≤−150.17 dB/Hz @≥3 MHz (the shot noise level is calculated to be −151.87 dB/Hz at 1530 nm or −151.93 dB/Hz at 1550 nm), and that the relaxation oscillation peak (ROP) is ≤−93.38 dB/Hz. The variation in the ROP positions for different lasers can be attributed mainly to the differences in cavity lengths and net gains for each lasing wavelength.
3.2 SEF performance parameters on the laser linewidth
To investigate the effect of different lengths of SEF on the laser output linewidth, the length of the 22.3 m SEF in the laser cavity was gradually shortened. Using lasers at wavelengths λ1 and λ8 as examples, the DSHMS was conducted, with the results shown in Figs. 10(a) and 10(b). The extracted and calculated linewidths are depicted in Figs. 10(c) and 10(d). As shown, the laser linewidth increases rapidly as the SEF length is reduced. Furthermore, for the two lasers with a wavelength difference greater than 20 nm, the linewidth compression effect exhibits a similar trend with changes in SEF length, thereby reaffirming the wavelength self-adaptive linewidth compression of SEF. Note that, based on our experiments, when the SEF is longer than 22.3 m, the SLM operation cannot be sustained for a long running period due to the excessive cavity length.
The stability of the fiber laser output is inversely proportional to the overall cavity length. Longer cavity lengths result in weaker resistance to environmental disturbances, making it preferable to use shorter SEFs to achieve the same linewidth compression effect. To explore whether a shorter SEF can achieve as much linewidth compression as a longer SEF, we kept the number of high scatters in the SEF constant but reduced the spacing between adjacent points to 5 − 6 cm, creating an SEF with a length of ∼11.5 m. The Rayleigh scattering distribution of this SEF is shown in Fig. 11(a), indicating that its overall scattering enhancement is similar to that of the previously used SEF. We then incorporated this shorter SEF into the proposed laser and measured the laser output linewidth using the DSHMS, again taking the λ1 and λ8 lasers as examples. The test results are shown in Figs. 11(b) and 11(c). The results demonstrate a significant linewidth compression effect, with linewidths of 239 Hz and 225 Hz, respectively. More importantly, the narrowed linewidths are comparable to those obtained with the 22.3-m SEF, indicating almost identical linewidth compression effects. This result lays an important foundation for further performance regulation and continuous optimization of SEF for laser linewidth compression and its miniaturization and integration in future research and application.
4. Conclusion
This study introduces and demonstrates an eight-wavelength tunable SF ultra-narrow linewidth EDFL. By combining two femtosecond laser direct-written polarization-dependent P-FBGs, with reflection centers at wavelengths near 1530 nm and 1550 nm, with an EC-OS, a novel S-PDECF was developed to determine laser oscillation wavelengths in the EDFL. Coupled with a DCR-CC for SLM selection, this setup enables the output of SF lasers at eight different wavelengths. To achieve ultra-narrow linewidths, we introduce an SEF fabricated by a femtosecond-laser direct writing technique, which possesses controllable random distribution feedback characteristics. This SEF effectively compresses the laser linewidth, resulting in outputs with <250 Hz linewidth across all eight wavelengths, spanning over 20 nm. The wavelength self-adaptive linewidth compression of SEF in fiber lasers was verified for the first time. Performance testing of the laser revealed that the eight switchable single-wavelength outputs exhibit spectral wavelength fluctuations of ≤0.011 nm, spectral peak power fluctuations of ≤0.54 dB, OSNRs of ≥71 dB, output power fluctuations of ≤0.252 dB over a 10-min measurement period, and RINs of ≤−150.17 dB/Hz @≥3 MHz. With proper packaging, temperature control, and vibration isolation, further performance improvements are anticipated. Additionally, we explored the effect of SEF scatter distribution control on fiber laser linewidth compression. Our findings indicate that a shorter SEF with a higher scatter point density can achieve linewidth compression effects similar to those of a longer SEF. This study demonstrates the potential of SEF for achieving wavelength self-adaptive linewidth compression in broadband tunable fiber lasers and dynamic linewidth compression in scanning fiber lasers. Furthermore, it provides new insights into the miniaturized design of SEF for ultra-narrow linewidth laser applications.
Funding
National Key Research and Development Program of China (2021YFB2800900); National Natural Science Foundation of China (61827818); Natural Science Foundation of Hebei Province for Distinguished Young Scholars (F2023201024).
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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