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Abstract
We investigate the influence of various optical fiber fabrication processes on the fluorescence decay of RE ions commonly used in fiber lasers and amplifiers, i.e. Yb3+, Tm3+ and Ho3+. Optical fiber preforms were prepared using the MCVD method combined with Al2O3 nanoparticle doping and subjected to subsequent heat treatment processes such as preform elongation and fiber drawing. The fluorescence decay of RE ions was measured in multiple stages of optical fiber preparation: in an original preform, in an elongated preform (cane), in a standard fiber, and in an overcladded fiber. It was found that heat treatment processing of the preforms generally leads to a faster fluorescence decay, which can be explained by the diffusion of dopants and clustering of RE ions. The fiber drawing exhibited a greater effect compared to preform elongation, which was ascribed to a faster cooling rate of the process. In general, the heat treatment of RE-doped silica glass preforms leads to the decline of fluorescence decay.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Rare-earth (RE) doped fiber lasers represent one of the major scientific breakthroughs that has shaped the modern world. Thanks to their high-quality beam, highly efficient operation, alignment-free configuration, and practicality of use, they have rapidly found applications in many areas of human activity, including materials processing, research, sensors, telecommunications, defense and medicine [1]. Fiber lasers based on several RE ions, specifically Yb3+, Tm3+ and Ho3+, remain at the forefront of interest thanks to their unique spectroscopic properties that find use in various applications [2]. Yb3+ ions exhibit emission around 1 µm, and ytterbium-doped fiber lasers (YDFL), capable of reaching tens of kilowatts of output power, are used e.g. in materials processing [3–5]. Tm3+ and Ho3+ have emission around 2 µm, and thulium- and holmium-doped fiber lasers (TDFL and HDFL) are used in “eye-safe” applications such as medicine and defense, as well as in atmospheric sensing or materials processing [6–9].
Silica glass remains a prospective option as a host matrix for RE ions thanks to its unmatched material properties such as transparency, thermal stability, and chemical durability, as well as its low cost and compatibility with common fiber components. However, silica glass suffers from several drawbacks, including high phonon energy and low RE ion solubility, both of which drastically limit photoluminescence properties [10]. To overcome these deficiencies, pure silica glass needs to be co-doped with a suitable modifier, such as Al2O3, which locally acts to increase RE ion solubility and form a beneficial low-phonon environment [11–13]. Nevertheless, photoluminescence quenching remains a significant concern, and great efforts are currently being undertaken to optimize matrix compositions to achieve higher photoluminescence efficiency and better lasing performance [14–17].
The fluorescence lifetime of the lowest excited level is one of the most important parameters to determine the quality and suitability of RE-doped silica fibers for laser applications; the important transitions for laser emissions in the NIR range include 2F5/2 in Yb3+ ions, 3F4 in Tm3+ ions, and 5I7 in Ho3+ ions. The fluorescence lifetime strongly correlates with quantum efficiency, where optical fibers with higher fluorescence lifetimes exhibit longer energy storage times and lower laser thresholds [18]. One potential process that may significantly influence the fluorescence lifetime is the diffusion of both Al2O3 and RE ions at high temperatures during the fiber fabrication process [19]. Changes in the host matrix structure (and local RE ion environment) may lead to a deterioration of photoluminescence properties via several means, including non-radiative processes, such as multiphonon relaxation by interaction with vibrational phonons of the surrounding matrix, as well as inter-ionic energy transfer processes, such as energy transfer up-conversion (ETU) and pair-induced quenching (PIQ) due to the clustering of RE ions [20–22].
These effects present a significant challenge in the fabrication of advanced fiber designs, including nanostructured fibers or single-mode fibers with small core diameters, both of which require the use of unconventional heat treatment processes during fiber preparation (e.g., the preform elongation) [5,23]. A shortening of the fluorescence lifetime during fiber drawing has been previously reported for some of the higher excited Tm3+ ion transitions (3H4 and 1G4) [24], which suggests a significant local change in the RE ion environment during fiber drawing. There are currently no detailed studies on how the main NIR transitions of various RE ions are affected by both fiber drawing and other fabrication processes (e.g., preform elongation). A thorough understanding of the effect of heat treatment processes on the fluorescence lifetime of RE-doped silica fibers is necessary for the advancement of optical fiber laser technologies.
In this paper, we present a thorough investigation of the effect of heat treatment processes on the fluorescence lifetime of the lowest excited levels for three RE ions commonly used in the NIR range: Yb3+, Tm3+ and Ho3+. We measured fluorescence lifetimes for fibers prepared with each RE ion in multiple stages of the fabrication process: in the original preform, the elongated preform (cane), the fiber, and the overcladded fiber. The dependency of the fluorescence lifetime on these fabrication processes is discussed in detail.
2. Experimental
2.1 Preparation of the preforms and fibers
The sample preparation process used herein is depicted schematically in Fig. 1. Optical fiber preforms doped with RE ions and co-doped with Al2O3 were prepared using the Modified Chemical Vapor Deposition (MCVD) method combined with a nanoparticle doping technique [18,25,26]. A porous silica layer was deposited onto the inner wall of a pure silica tube (F300, Heraeus), soaked with an ethanolic solution of RE chlorides (TmCl3·6H2O, YbCl3·6H2O or HoCl3·6H2O, Sigma Aldrich, 99.99%) and Al2O3 nanoparticles (particle size <50 nm, Sigma Aldrich, 99.9%) and dried. The doped tubes were sintered and collapsed into preforms above 2000 °C. After a measurement of the refractive index profiles (RIPs) of the preforms, samples with approx. 2 mm thickness and 9 mm diameter were cut for further analysis. The optical fiber preform was subjected to several subsequent heat treatments. One half of the preform was drawn in a fiber drawing tower, equipped with a graphite resistance furnace (Centorr, USA) at temperature of 1950 °C into a fiber with a diameter of approx. 125 µm and a core diameter of approx. 17.5 µm. The other half of the preform was elongated in the fiber drawing tower to a diameter of approx. 3 mm, and a sample of the elongated preform (designated as “cane”) was cut for fluorescence lifetime analysis. The cane was overcladded with a pure silica tube and drawn in the same manner into a fiber with a diameter of approx. 125 µm and core diameter 5 µm. Selected cane samples were further subjected to a heat treatment of both 1900 and 2000 °C for 5 minutes in the graphite resistance furnace.
2.2 Characterization of the preform, cane and fiber samples
Dopant concentrations in the original preform were measured by a Cameca SX-100 electron probe microanalyzer (EPMA) in mol. % for Al2O3 and ppm for RE ions, with the accuracy of RE content determination 2 rel. %. The refractive index profiles of the preforms were measured using a Photon Kinetics A2600 refractive index profiler, and the refractive index profiles of the optical fibers were measured using an IFA-100 refractive index profiler. The fibers were characterized regarding their absorption, background losses, and OH- group content. A tungsten halogen lamp was used as a broadband source of radiation. The absorption and background losses were measured using both an ANDO AQ6317 optical spectrum analyzer and a Nicolet 8700 FTIR spectrometer that was adopted in-house for fiber-optic measurements. Background losses were evaluated from absorption spectra minima. RE contents were calculated from the absorption peaks of Yb3+, Tm3+ and Ho3+ at 976 nm, 1640 nm and 1950 nm, respectively, as described in [18,27]. The OH content was determined from the OH related peak at 1383 nm [7].
Figure 2 shows a schematic of the measurement setup for the fluorescence decay analysis of both fibers and bulk samples (preform and cane); further details for measurements of optical fibers can be found in [28]. Fluorescence decay curves were measured using a Lumics LU793M250 diode emitting at 792 nm as excitation source for Tm3+ ions, EM4 P161-600-976 diode emitting at 976 nm as excitation source for Yb3+ ions, and Innolume FBF-1150-PM-300 diode emitting at 1150 nm as excitation source for Ho3+ ions. We used a Hamamatsu G8371-01 InGaAs PIN photodiode as a detector. The measured fibers were approximately 1 mm long, and emission was detected from the side in order to suppress the influence of amplified spontaneous emission (ASE). We measured decay curves for multiple excitation powers; decay times for each respective excitation power were obtained from the 1/e value of the maximum fluorescence intensity (taken from normalized data). The fluorescence lifetime, i.e. the decay time extrapolated to zero pump power, was obtained using multiple methods. If decay curves were single-exponential across all excitation powers and the decay times remained constant, the fluorescence lifetime was calculated by averaging the decay times at different excitation powers. If the decay characteristics varied with excitation power, indicating the presence of inter-ionic energy transfer processes, values of decay time vs. excitation power were fit to Eq. (1):
3. Results
3.1 Basic characterization of prepared preforms and fibers
We characterized all preforms and fibers with respect to their optical and spectroscopic properties; these data are summarized in Table 1. The content of Al2O3 was approx. 9 mol. % in all prepared preforms. RE ion concentrations were measured in the range 4,000-5,000 ppm, with the exception of Ho-doped preform, which contained Ho3+ ions at approx. 10,000 ppm. The distribution of Al2O3 and RE ions in all preforms was plateau-shaped with a flat maximum in the center. A representative example of the concentration profile is shown in Fig. 3(a) (for the Ho-doped preform).
Fig. 3. a) concentration profiles of the dopants in the Ho-doped preform, b) refractive index profiles of the Ho-doped preform and fiber, c) absorption spectra of the fibers (absorption of Yb3+ ions divided by factor of 3 for better comparison)
Table 1. Summarized properties of the RE-doped preforms and fibers.
The refractive index difference of the original preforms was between 23·10−3 and 25·10−3, which corresponds to the content of dopants [28]. The refractive index difference of the fibers was comparable to that measured in the preforms, where the small differences of ±1·10−3 can be explained by the measurement error of both the IFA and A2600 refractive index profilers [30,31]. Figure 3(b) shows the typical shapes of the refractive index profiles for the Ho-doped samples. Due to their specific dimensions, it was not possible to measure the refractive index differences of both the cane and overcladded fiber samples with reasonable accuracy. The absorption spectra of the optical fibers are shown in Fig. 3(c), absorption of Yb3+ ions is divided by factor of 3 for better comparison; the concentrations of RE ions obtained from spectral absorption are in a reasonable agreement with EPMA values. Measured values of both basic attenuation (below 0.050 dB/m) and OH content (below 2 ppm) suggest a good quality of the prepared fibers in terms of drying and a low loss operation around 2 µm.
3.2 Yb-doped preforms and fibers
Figure 4 (a) shows the fluorescence decay curves of the Yb-doped preforms and fibers, measured for the 2F7/2→2F5/2 transition after in-band excitation at 978 nm. These results highlight the significance of both the preform elongation and fiber drawing processes: there is a clear decrease in the fluorescence lifetime after each step in the fiber preparation process. Figure 4(b) summarizes the measured decay times as a function of pump power. All fluorescence decay curves were single-exponential with the exception of the overcladded (OC) fiber, which showed slight deviations from single-exponentiality with increasing pump power. The decay times of the preform, cane, and fiber were independent on the pump power, where variations (±4 µs) were within the error of the measurement.
Fig. 4. a) measured decay curves of Yb-doped preform, cane, fiber and overcladded fiber, b) decay times for multiple diode pump powers, dashed curves represent either a calculated average of decay times (preform, cane and fiber) or a fit according to Eq. (1) (fiber OC), c) detail of the lifetime-power dependency of the OC fibers, d) simplified scheme of the Yb3+ ion energy levels, including the energy transfer process in Yb3+ dimers and trimers.
The measured fluorescence lifetime values τ0 are summarized in Table 2. Only the decay time of the OC fiber showed an observable decline with increasing pump power, and the decay time-excitation power dependency was fitted by Eq. (1). The saturated lifetime extrapolated to infinite power was approx. 20 µs shorter than the fluorescence lifetime (3% decrease). The shortening of fluorescence lifetime with increasing excitation power can be explained by the presence of an energy transfer (ET) processes between clustered Yb3+ ions as described by Qin et al. [32]. The excited 2F5/2 level can be depopulated by an ETU process into virtual levels of Yb3+ dimers and trimers, as depicted in Fig. 4(d), which leads to a faster fluorescence decay. The rate of this ETU process is proportional to the population of the 2F5/2 level, which increases with power density. The difference between the standard and the OC fiber suggests that the Yb3+ clusters are more prevalent in the OC fiber, but the higher power density in OC fiber due to smaller core diameter must be considered as well.
Table 2. Fluorescence lifetimes of Yb-doped samples, obtained from an average of decay times for multiple input excitation powers (preform, cane, fiber) or from fitted parameters of Eq. (1) (fiber OC)
3.3 Tm-doped preforms and fibers
Figure 5(a) shows the fluorescence decay curves of the Tm-doped fibers and preforms, measured at the 3F4 level upon excitation at 792 nm (3H6→3H4 transition). The Tm-doped preforms and fibers exhibited similar behavior as the Yb-doped samples: fluorescence decay deteriorated as a result of the preform elongation step and further decreased during fiber drawing. As shown in Fig. 5(b), the decay curves of the preform samples (i.e., the original preform and cane) exhibited single exponential behavior and decay times were independent on the pump power. The values of fluorescence lifetime τ0 and other parameters are listed in Table 3. Unlike the Yb-doped fibers, however, Tm-doped optical fibers manifested significant deviations from single exponentiality and the decline of decay time with increasing pump power was much more apparent; the saturated lifetimes τSAT of fiber and OC fiber were 27% and 33% shorter than fluorescence lifetimes, respectively. This effect stems from the different electronic structure of the Tm3+ ion and a different nature of the inter-ionic processes that were involved.
Fig. 5. a) measured decay curves of Tm-doped preform, cane, fiber and overclad fiber, b decay times for multiple diode pump powers, dashed curves represent the calculated average of decay times (preform, cane) or a fit to Eq. (1) (fiber and fiber OC)
Table 3. Fluorescence lifetimes of Tm-doped samples, obtained as an average of decay times for multiple input excitation powers (preform, cane) or fitted parameters of Eq. (1) (fiber, fiber OC)
Figure 6 depicts the inter-ionic processes that lead to a depopulation of the 3F4 level and thus induce deviations from single-exponentiality and shortening of the decay time. The main processes are ETU between the 3H6←3F4→3H4 levels (determined by k1130 energy-transfer coefficient) and between the 3H6←3F4→3H5 levels (k1120) of closely coupled ions, with the k1120 process being dominant [28,33]. These processes contribute to the faster depopulation of the 3F4 level with increasing power, as demonstrated in our previous study [28], as well as Jackson [33]. In order for the ETU processes to take place, Tm3+ ions must be sufficiently close to each other, but the formation of dimers or trimers is not necessarily required (unlike the case of Yb3+ ions). The ETU effect is therefore significantly stronger compared to the Yb-doped fibers, and the decline of decay time with increasing excitation power is more pronounced in both fiber samples. The general trend of declining decay time with additional heat treatment is preserved even in the case of fluorescence lifetime extrapolated to zero pump power, which eliminates the influence of ETU processes.
Fig. 6. Generalized scheme of the energy levels of the Tm3+ and Ho3+ ions (energy levels are not in scale), and inter-ionic processes depopulating the lowest excited level, ETU = energy-transfer up-conversion.
3.4 Ho-doped preforms and fibers
Figure 7 summarizes the time-resolved photoluminescence properties of the Ho-doped preforms and optical fibers. The fluorescence decay of the 5I7→5I8 transition of the Ho3+ ions upon excitation at 1150 nm (5I8→5I6 transition) differed from the behavior of the Yb- and Tm-doped samples. In particular, we observed no significant decrease of the fluorescence lifetime after the preform elongation step, where fluorescence lifetimes remained within the margins of error. A decline of the time-resolved photoluminescence properties was observed only as a result of the fiber drawing process. The fluorescence decay curves of the optical fibers exhibited increased deviations from single-exponentiality, which is a result of similar inter-ionic mechanisms as those observed in Tm-doped fibers. As listed in Table 4, the fluorescence lifetime extrapolated to zero pump yielded nearly identical results for both fibers, but the decay time of the OC fiber fell off faster compared to the standard fiber, and the saturated lifetime was significantly shorter, which can be ascribed to higher degree of Ho3+ ions clustering and higher rate of ETU processes. The saturation lifetimes τSAT of fiber and OC fiber were 19.7% and 22.1% shorter than the fluorescence lifetimes, respectively.
Fig. 7. a) measured decay curves of Ho-doped preform, cane, fiber and overclad fiber, b) decay times for multiple diode pump powers, the dashed curves represent calculated average of decay times (preform, cane) or a fit to Eq. (1) (fiber and fiber OC).
Table 4. Fluorescence lifetimes of Ho-doped samples obtained as an average of decay times for multiple input excitation powers (preform, cane) or fitted parameters of Eq. (1) (fiber, fiber OC)
To clarify the effect of heat treatment on the Ho-doped bulk samples, which differed from the phenomena observed in the case of Yb- and Tm-doped preforms and canes, the Ho-doped cane was subjected to additional heat treatments up to 2000 °C; fluorescence decay measurements are summarized in Fig. 8. The additional heat treatment led to a fluorescence lifetime of 1.40 ms in the case of 1900 °C and 1.36 ms in the case of 2000 °C.
Fig. 8. a) measured decay curves of Ho-doped cane, as well canes heat treated to 1900 and 2000 °C, b) decay times for multiple diode pump powers, dashed curves represent the calculated average of decay times.
4. Discussion
We have investigated the fluorescence decay of the main NIR transitions of several RE ions (Yb3+, Tm3+ and Ho3+) in various stages of the fiber preparation process. The fluorescence lifetime was evaluated in four different samples – the original preform (0 heat treatment steps subsequent to preform preparation), the cane (1 subsequent heat treatment step: preform elongation), the fiber (1 subsequent heat treatment step: fiber drawing) and the OC fiber (2 subsequent heat treatment steps: preform elongation and fiber drawing).
Two different types of heat treatment can be distinguished in the fiber fabrication process: preform elongation and fiber drawing. Both processes were carried out under identical conditions at a temperature of 1950 °C in a graphite-resistance furnace, where the only difference was the cooling rate. Compared to preform elongation, fiber drawing involves a significantly faster cooling rate due to more effective heat transport stemming from the smaller diameter of the fibers with respect to the cane.
The following observations can be made based on the results of the fluorescence decay measurements from all RE-doped samples: 1) preform elongation leads to a decline of fluorescence lifetime in the case of Yb- and Tm-doped samples, while no negative effect can be observed in the case of Ho3+ ions. The fluorescence lifetime of the Ho-doped cane declined only after additional heat treatment above 1900 °C; 2) fiber drawing always leads to a deterioration of the time-resolved photoluminescence properties, i.e., lower values of both fluorescence and saturated lifetimes for Yb3+, Tm3+ and Ho3+ ions; 3) when considering both heat treatment processes, the fiber drawing results in a greater decline of fluorescence decay characteristics, which can be ascribed to the faster cooling rate.
The general trend of the decay decrease with heat treatment can be explained by the diffusion of dopants (and resulting changes in the RE ion environment) that occurs during heat treatment above the glass transition temperature [19]. In the nanoparticle-doping technique, Al2O3 is doped into the preforms in the form of alumina nanoparticles. Temperatures can reach over 2000 °C during preform collapse and sintering, which leads to the dissolution of the original alumina nanoparticles [15]. The formation of mullite 3Al2O3·2SiO2 nanocrystals or Al2O3-enriched amorphous nanoparticles may occur as a result of the relatively low rate of cooling [15,34]. Due to their low solubility in mullite, RE ions will primarily occupy Al2O3-enriched shells around the nanoparticles created by the diffusion process [12,15]. Additional heat treatment steps may cause i) the dissolution of the beneficial Al2O3-enriched nanoparticles and their low-phonon shells, which would enhance the multiphonon relaxation of RE ions in these environments, as well as ii) the diffusion of RE ions into the unfavorable Si-rich regions with lower solubility, which would increase clustering. The greater effect of fiber drawing compared to preform elongation can be explained by the faster cooling rate. It has been previously shown that the faster cooling rate and extreme mechanical stresses during fiber drawing may exacerbate the break-up of the Al2O3-rich nanoparticles, which can result in the placement of RE ions in less favorable environment [35].
As a result of these processes, the fluorescence decay is shortened by two different mechanisms: multiphonon relaxation due to an unfavorable RE environment, and inter-ionic energy-transfer processes due to RE ions clustering. The decay time-pump power dependency, i.e. the decline of decay time with increasing pump power, is caused solely by inter-ionic energy transfer processes such as ETU. The rate of these processes depends on several factors. We first note that the inversion population of the involved excited state [20,21] is proportional to the power density in the optically active core. The decay times of both preform and cane samples, which have large (≈mm) diameters, are therefore mostly independent on pump power, while the fluorescence decay of fibers with smaller (≈µm) diameters is strongly affected by the ETU process and rapidly falls off with increasing pump power. The size of the core diameter affects the critical power parameter PCRIT in Eq. (1), which may explain the universally lower values of PCRIT in OC fibers. However, values of fluorescence and saturation lifetimes are independent of power density, as they represent decay times extrapolated to zero and infinite power, respectively. The shortening of fluorescence and saturation lifetimes can therefore be ascribed mainly to higher rates of multiphonon relaxation due to the diffusion of RE ions into less favorable environments, and higher content of RE ion clusters.
Comparing the three RE ions, the preform elongation process led to a clear deterioration of fluorescence decay in the case of Yb3+ and Tm3+ ions, whereas the fluorescence decay of Ho3+ remained nearly unchanged. A possible explanation for this phenomenon lies in the lower diffusion rate of Ho3+ ions due to the larger ionic radius compared to Tm3+ and Yb3+ ions (0.901, 0.880 and 0.868 Å, resp., in 6-fold coordination [36]). It was previously shown that even small differences in ionic radii of RE ions may have a significant impact on the diffusion rates in various materials, with smaller ions exhibiting higher diffusion coefficients [37,38]. Another factor to consider is the different energy level structure of the three RE ions under study, and thus different kinetics of the inter-ionic ET processes, which may have an impact on the fluorescence decay, even at low power density in the bulk samples. However, the ET kinetics in Ho3+ ions are far less researched compared to Tm3+ and a detailed study is yet to be performed.
Several measures may be taken in order to mitigate these negative effects and improve the fluorescence decay of nanostructured optical fibers. The first possible solution is to decrease the temperature of the preform elongation and fiber drawing to a necessary minimum, i.e. 1900 °C, in order to limit the break-up of nanoparticles and the diffusion of dopants [5]. However, the conditions needed for a complete eradication of the diffusion processes are incompatible with temperature requirements for optical fiber fabrication, since the preform must be sufficiently softened in order to be elongated into a cane or drawn into an optical fiber [19]. Another approach would be to use novel materials with increased fluorescence lifetimes, which can potentially result in optical fibers maintaining high fluorescence lifetimes despite the diffusion and clustering processes – i.e. silica glass with higher concentration of Al2O3 up to mullite 3Al2O3.2SiO2 composition – which have been shown to possess very high lifetimes in the case of Ho3+ and Tm3+ ions [15], or using nanostructured-core designs with nanoparticles of ZrO2 [39–41], YAG [42,43], LaF3 [44] or BaF2 [45].
5. Conclusion
We investigated the influence of the optical fiber fabrication process on the fluorescence decay of RE ions commonly used in fiber lasers and amplifiers, specifically Yb3+, Tm3+, and Ho3+. Optical fiber preforms were prepared using the MCVD method combined with Al2O3 nanoparticle doping and subjected to various heat treatment processes (preform elongation and fiber drawing). The fluorescence decay of RE ions was measured in multiple stages of optical fiber preparation: in an original preform, in an elongated preform (cane), in a standard fiber, and in an overcladded fiber. It was found that these heat treatment processes generally leads to an increased decay of fluorescence lifetimes, which can be explained by both the diffusion of dopants and clustering of RE ions. The fluorescence lifetime of Yb3+ and Tm3+ significantly decreased in all stages of optical fiber fabrication, whereas Ho3+ ions were more affected by fiber drawing rather than the preform elongation. The greater effect of the fiber drawing was ascribed to a faster cooling rate with respect to that in preform elongation. In general, the heat treatment processing of RE-doped silica glass preforms leads to the decline of fluorescence decay properties, which may be partially mitigated by decreasing the temperature of the heat treatment to a necessary minimum.
Funding
Narodowe Centrum Nauki (OPUS LAP 020/39/I/ST7/02143); Grantová Agentura České Republiky (GAP21-45431L).
Acknowledgement
Authors thank Dr. Nicolas S. Lynn for critical reading and language correction of the manuscript. Authors also acknowledge valuable comments to the work from our colleagues within the research task group NATO SET-294 “Advanced Mid-Infrared Laser Technology”.
Disclosures
The authors declare no known conflict of interest. Portions of this work were presented at Advanced Solid State Lasers 2021, virtual event, paper JTu1A.38.
Data availability
Data underlying the results presented in this paper are available from the corresponding author upon reasonable request.
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