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Abstract
Hollow-core negative curvature fibers can confine light within air core and have small nonlinearity and dispersion and high damage threshold, thereby attracting a great deal of interest in the field of hollow core fibers. However, reducing the loss of hollow-core negative curvature fibers is a serious problem. On this basis, three new types of fibers with different nested tube structures are proposed in the near-infrared spectral regions and compared in detail with a previously proposed hollow-core negative curvature fiber. We used finite-element method for numerical simulation studies of their transmission loss, bending loss, and single-mode performance, and then the transmission performance of various structural fibers is compared. We found that the nested elliptical antiresonant fiber 1 has better transmission performance than that of the three other types of fibers in the spectral range of 0.72–1.6 µm. Results show that the confinement loss of the LP01 mode is as low as 6.45×10−6 dB/km at λ = 1.06 µm. To the best of our knowledge, the record low level of confinement loss of hollow-core antiresonant fibers with nested tube structures was created. In addition, the nested elliptical antiresonant fiber 1 has better bending resistance, and its bending loss was below 2.99×10−2 dB/km at 5 cm bending radius.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Hollow-core fibers (HCFs) [1] are special fibers whose unique ability to confine light in air has attracted a great deal of interest among the researchers over the past decades. These fibers are used in many areas for high power delivery [2], high-speed data communication [3], ultra-short pulse delivery [4], pulse compression [5], terahertz applications [6], and supercontinuum [7]. The first type of HCFs includes hollow-core photonic bandgap fibers (HC-PBGFs), which are divided into OmniGuide HC-PBGFs [8] and 2D HC-PBGFs [9]. Since the laser beam propagates in air in HCFs, the optical nonlinearities are significantly lower comparing to the solid-core counterparts [3]. However, the surface scattering loss (SSL) has become the bottleneck limiting the loss reduction of the HC-PBGFs. Only the improvement of the manufacturing process can reduce the loss caused by the rough surface to break through the loss bottleneck. However, the fabrication process of HC-PBGFs can still be remarkably improved. Therefore, continuous research is insignificant. As a result, the researchers preferred hollow-core negative curvature fibers (HC-NCFs) [10].
The HC-NCFs are obtained by simplifying the cladding structure of the HC-PBGFs into a cladding structure. Its guiding mechanism is the antiresonant reflection optical waveguide [11,12], which is also called hollow-core antiresonant fibers. Various properties of HC-NCFs are mainly realized by designing the cladding component. The different cladding components are reported in the current literature including single-ring, double-ring, nested-ring, elliptical tubes, conjoined tubes, and nested elliptical [3,4,13–20]. As an example, in 2011, Pryamikov et al. from the Russian Academy of Sciences designed and fabricated an HC-NCF for laser transmission in the 3.5 µm band [16]. However, due to the very thick quartz wall of the fiber cladding, the transmission spectrum is very narrow. In 2012, Yu F from the University of Bath improved the drawing process of the HC-NCF designed by Pryamikov, and fabricated an HC-NCF similar to an ice-cream structure. The minimum loss of the fiber is 34 dB/km at 3.05 µm, which is 3 orders of magnitude lower than the absorption loss of quartz material in this band [21]. However, only when the bending loss (BL) was low for bending diameter greater than 40 cm. The researchers noticed that HC-NCFs with nodes in the cladding can cause a “Fano resonance” leakage effect, leading to severe BL in such fibers. So research has focused on how to eliminate these points of contact.
In 2013, Kolyadin et al. from the Russian Academy of Sciences designed and fabricated a cladding nodeless HC-NCF. The measured loss of the fiber at λ = 3.39 µm is 50 dB/km, and the loss curve became smoother [22]. In 2014, Belardi and Knight from the University of Bath conducted theoretical analysis and research on the BL characteristics of HC-NCFs with and without nodes [23]. They fabricated an HC-NCF which presents a BL as low as 0.25 dB/turn for a bend radius of 2.5 cm at 3.35 µm. It was found that the BL of the HCFs can be effectively reduced when the nodes of the HC-NCFs cladding are removed. In 2015, Belardi further fabricated a cladding nodeless HC-NCF has a transmission loss of 175 dB/km at 480 nm [24]. However, since the wall thickness of the small quartz tube on the inner side of the cladding is much larger than that of the outer quartz tube, the transmission loss is large. In 2017, Gao et al. from Beijing University of Technology fabricated nodeless HC-NCF with a cladding structure of 6 thin-walled capillary tubes, with a transmission loss of 100 dB/km at 1 µm and a low BL value of 0.2 dB/m for a bend radius of 5 cm at 1.55 µm [25]. In the same year, Debord et al. from the University of Limoges reported the advantages of nodeless HC-NCF in transmission, obtaining a transmission loss of 7.7 dB/km at 750 nm, and a BL of 0.03 dB/turn for a 30 cm bend diameter at 750 nm [4]. In 2018, Gao et al. from Beijing University of Technology proposed a new structural design of HC-NCF, and its lowest transmission loss of 2.0 dB/km at 1512 nm was reduced to below 10 dB/km. The BL was measured as low as 0.7 dB/km for bending radius of 10 cm at 1512 nm [3]. In 2020, Jasion et. al. from the University of Southampton reduced the loss of HC-NCF to 0.28 dB/km from 1510 to 1600 nm by adding a circular nested tube; the loss was reduced to below 1 dB/km. The measured bend loss is less than 0.1 dB/m for bend diameters ≥ 8 cm at 1550 nm [26].
In recent years, several research groups have simulated and analyzed HC-NCFs with transmission loss below 0.1 dB/km [13,18,27,28], indicating that the theoretical loss limit of HC-NCFs potentially can be lower than that of HC-PBGFs and silica fibers (0.14 dB/km). In 2014, Poletti from the University of Southampton proposed and simulated an HC-NCF with the cladding geometry of six node-free nested tubes, which has better performance than the photonic bandgap fiber. The simulation results show that the fiber has ultralow confinement loss (CL), which is lower than the SSL of the fiber, and the fiber also exhibits ultralow BL [13]. In 2015, Habib et al. from the Technical University of Denmark simulated and designed an HC-NCF with three adjacent nested antiresonant tubes, and the CL as low as 0.0015 dB/km and the BL of 0.006 dB/km at 5 cm bending radius is predicted at 1.06 µm [28]. In 2016, Chaudhuri et al. from Pennsylvania State University designed a regular and nested HC-NCF with elliptical capillary tubes. Simulation results show that the HC-NCF has lower loss and much broader transmission bandwidth than the photonic bandgap fiber [18]. In 2017, Hasan proposed an HC-NCF that has an elliptical nested element in the antiresonant tubes. Numerical simulation shows that despite using only a single elliptical nested tube, ultralow loss is achievable over λ = 0.9 µm to 1.8 µm [27]. In 2021, Yang et al. proposed a connecting circle HC-NCF with a low CL of ∼0.004 dB/km and BL of ∼0.4405 dB/km with a bending radius of 5 cm at λ = 1.06 µm [29]. Recently, Shaha et al. reported an anisotropic nested antiresonant fiber that provided a CL of 0.0007 dB/km at λ = 1.06 µm, which is currently the lowest loss achieved by simulation methods among HC-NCFs. It also achieved better bend insensitiveness, and the BL is decreased to 0.007 dB/km for bending radius of 12 cm at λ = 1.4 µm [30]. Although the loss of HC-NCFs has been significantly decreased and commercial HC-NCF have already exist, there is still a gap between the laboratory demonstration and mass production of proposed HC-NCFs, mainly due to the optimization of fiber fabrication procedures. Hence, further research is highly expected to solve this problem.
This article presents a nested elliptical antiresonant fiber 1 (NEARF1) with two elliptical tubes nested within the circular tubes (small elliptical tube away from fiber core) arranged in such a way that form nodeless hollow-core fiber structure. To the best of our knowledge, the proposed NEARF1 can, therefore, offer record low LP01 loss in the near-IR spectral regions. In addition, considering the low BL, effective dual-mode performance, and relatively simple fiber structure, we believe that the proposed NEARF1 is most likely to be fabricated and applied for transmission applications in the near-IR spectral regions.
2. Fiber design
We designed three types of new structures and combined one structure reported in the previous literature to study the influence of HC-NCFs with different structures on the beam transmission loss. We also systematically studied the loss performance of HC-NCFs with different ellipse nested tube structures. The cross-sectional views of the four types of HC-NCFs are shown in Fig. 1, where the black area is silica material and the white area is full of air. The nodes between the cladding tubes cause additional resonance of the transmission bands [22]. Thus, we adopt node-free cladding structures. Our main motivation is to find an HC-NCF design capable of broadband low transmission loss near-IR transmission. The outer circular cladding tubes are used to confine light in the fiber core, preventing light from entering the interior of the cladding elements as well as the gap between cladding tubes. The elliptical nested elements in the circular tubes has two functions: first, by introducing an additional antiresonant layer, light passing through the cladding tube wall can be reflected back to the fiber core by the anti-resonance effect; Second, the core boundary curvature can be optimized to the best to reduce the CL for a given core radius [31,32].
Fig. 1. Geometry includes four quarter structures, namely, (a) nested elliptical antiresonant fiber 1 (NEARF1) with two elliptical tubes (small elliptical tube away from fiber core), (b) nested elliptical antiresonant fiber 2 (NEARF2) with two elliptical tubes (small elliptical tube is near fiber core), (c) nested elliptical antiresonant fiber 3 (NEARF3) with one elliptical tube, and (d) nested elliptical antiresonant fiber 4 (NEARF4) with three elliptical tubes. HC-NCFs have six cladding elements, where the outer circular tube diameter of Dt and the semi-major and semi-minor axis of larger and smaller tubes are Ra, Rb, Rm, and Rn. All fibers have the same core radius Dc = 25 µm and uniform silica strut thickness t = 0.35 µm.
The four types of HC-NCFs contain six node-free circular cladding tubes, and the cladding tube has 2, 2, 1, and 3 elliptical nested tubes. The core diameter and cladding tube diameter of the four types of fibers are the same, that is, 2Dc = 50 µm and Dt = 40 µm, respectively. The so-called core diameter is the maximum diameter of the circle that can be inscribed in the fiber core, as shown in the dotted circle in Fig. 1. The silica strut thickness of the cladding tube and the nested tube are the same, t = 0.35 µm. The semi-major axis and semi-minor axis of the large ellipse nested tube are Ra = 19.65 µm and Rb = 5 µm, respectively. The semi-major axis and semi-minor axis of the small ellipse nested tube are Rm = 7 µm and Rn = 4 µm, respectively. In the full text, the number and position of small elliptical nested tubes are used as variables, and four types of optical fiber structures are simulated to explore their transmission loss, bending loss, and single-mode performance.
3. Results and discussion
The full vector finite element method is used to calculate the fiber loss. In Fig. 1, the effective refractive index of air is nair = 1, and the effective refractive index of silica material is determined by the Sellmeier equation [33].
3.1 Loss
The simulation results of the four fiber structures in Fig. 1 are shown in Fig. 2(a). The CL of cladding tubes with different structures are distinguished by different curve colors, and the corresponding mode profile of the core fundamental mode (FM) is shown in Fig. 2(b). The color of the border line of the mode profile corresponds to the color of the loss curve.
Fig. 2. The confinement loss spectra as a function of wavelength for different fiber structures. (a) Loss of NEARF and (b) mode profiles with four cladding structures. The line color of curve relates with the color of the frame of geometry.
The CL spectrum in Fig. 2(a) shows that the loss of NEARF1 is lower than that of the three other fibers in the spectral range of 0.72–1.6 µm. Figure 2(b) shows that the LP01 modes of the four types of fibers are concentrated in the fiber core. As a representative example, we prefer to explore the NEARF performance at λ = 1.06 µm. Among the four different structures, the loss of NEARF1 at λ = 1.06 µm is the lowest at 6.45×10−6 dB/km. The trend of the loss curve of NEARF1 and NEARF3 is the same, and the loss remains unchanged after a rapid decrease with the increase in wavelength. The minimum losses at λ = 1.01 µm are 4.66×10−6 and 2.44×10−5 dB/km. The loss curves of NEARF2 and NEARF4 fiber almost overlap. The loss decreases rapidly to the lowest point, and then increases sharply with the increase in wavelength; the minimum loss is 2.8×10−5 dB/km at λ = 0.96 µm. Due to the increased thickness of the antiresonant wall at the core-cladding boundary of NEARF2 and NEARF4, their loss curves form a high-loss resonance region beyond 1.1 µm, resulting in a sharp increase in CL. The loss changes of the four structures satisfy the antiresonance law [34]. The lowest loss of NEARF1 is one order of magnitude lower than that of the three other fibers with different structures. The four types of fibers with different nested tube structures are optimized at λ = 1.06 µm, but the lowest loss is not obtained, and the lowest loss point occurs at a shorter wavelength. This finding shows that for the nested design of the fiber structure, to obtain the minimum loss at the predicted wavelength, considering a larger silica strut thickness may be possible to move this minimum toward the selected target wavelength.
From the CL spectrum shown in Fig. 2(a) we see that the loss performances of NEARF1 (red line) and NEARF3 (green line) are close to each other with different structures. We infer that the low CL of the proposed fiber seems to be gained by the ellipse nested tube, indicating that NEARF1 has the best performance among those structures. Since both ends of the large elliptical tube are always tangent to the circular cladding tube, its semi-major axis (Ra) does not change. Here we further investigate the effect of the semi-minor axis (Rb) of the larger elliptical tube of NEARF1 on CL. Figure 3 represents the low CL as a function of the wavelength for several different values of Rb while keeping the semi-major axis fixed at Ra = 19.65 µm. As can be seen from the comparison results in Fig. 3, when the CL of NEARF1 is below 10−3 dB/km, the loss does not decrease significantly by changing the value of Rb. This plot reveals that NEARF1 still has the best CL performance at the interesting wavelength of 1.06 µm and the lowest CL at 1.01 µm when Rb = 5 µm.
Fig. 3. Simulated CL versus wavelength for several different values of Rb when Ra = 19.65 µm. Figure 3 is a part of the full spectral range (wavelength range: 0.9–1.1 µm). The purpose is to compare the CL at the wavelength of 1.01 µm (the lowest CL wavelength) and 1.06 µm for different values of Rb, respectively.
The SSL is also an important issue and it is calculated by following the expression as [13]
where η is the normalized factor [13], F is the overlap integral between the core mode and the cladding [35], and λ0 is the target central wavelength [13].The plots in Fig. 4 confirm that SSL dominates the loss for NEARF1 in the spectral range of 0.76–1.6 µm. The SSL is 1.67×10−2 dB/km at 1.06 µm and it provides the lowest SSL of 4.88×10−3 dB/km at 1.6 µm. The total loss is less than 5.54×10−2 dB/km at 0.76 µm in the spectral range of 0.76–1.6 µm.
Fig. 4. The loss performances of NEARF1. Total loss (purple) is the sum of CL (red) and SSL (green). The LP01 mode field profile is displayed in the inset.
3.2 Bending Loss
Bending loss is another important characteristic of fiber. Therefore, simulating the BL of different optical fiber structures is necessary. The results are shown in Fig. 5. We used the conformal transformation method [36] to calculate the BL. The BL is solved by formula (1), as follows:
where $n\mathrm{^{\prime}}(x,\textrm{y})$ is the effective refractive index of the fiber after bending, $n(x,y)$ is the refractive index profile of the straight fiber, Rb is the bending radius, and x is the transverse distance from the center of the fiber.Fig. 5. Bending loss as a function of wavelength for different fiber structures. (a) Bending loss curves of NEARF and (b) mode field with four cladding structures at a bending radius of 5 cm. The line color of the curve relates with the color of frame of geometry.
The BL was calculated at λ = 1.06 µm, and the bending direction was selected as the x-axis giving the bend-loss curve shown in Fig. 5(a). The BL of the four types of fibers with nested elements are almost constant for reasonable bend radii. It should be noted that the BL of NEARF3 has a local peak at 6 cm bend radius. The extra loss due to the resonances between the core mode and cladding modes appear when the modes are phase matched [27,37,38]. Within the bending radius of 5–40 cm, the BL of NEARF1 is lower than that of the three other fibers. The loss of NEARF1 is as low as 2.99×10−2 dB/km at a bending radius of 5 cm. Figure 5(a) also confirms that the NEARF1 has a bend loss below 1.01×10−5 dB/km at 40 cm bending radius, which is approximately four orders of magnitude lower than that of the NEARF2 and NEARF4. The BL curves of NEARF2 and NEARF4 also almost overlap, it is therefore confirmed again that the loss performance of NEARF2 and NEARF4 is very similar. The trend of the BL curve of NEARF1 and NEARF3 is the same, and the loss remains basically unchanged after a rapid decrease with the increase in bending radius. This finding is caused by the offset of the bending mode field that decreases, and the influence on the transmission loss of the fiber is also reduced. Figure 5(b) shows the mode field of the bent four types of fibers with nested elements at a bending radius of 5 cm. The spot position in the figure indicates that the mode field of the curved NEARF fibers shift in the bending direction, but the mode field is completely confined in the fiber core.
3.3 Single-mode performance
The higher-order-mode (HOM) extinction ratio (HOMER) can be used to evaluate the single-mode performance of HC-NCFs. The so-called HOMER is the ratio between the transmission loss of the HOM having the lowest transmission loss and the transmission loss of the FM under the same structure parameters. The HOMER simulation results of four types of fibers with nested elements are shown in Fig. 6.
Fig. 6. HOMER as function of wavelength for all different fiber structures. The inset shows the mode fields of the LP01 mode and the LP11 mode.
The HOMER curves in Fig. 6 show that NEARF1 has the best single-mode performance at 1.06 µm, and its HOMER value (9.12) is higher than that of the other three fibers. In the range 0.72–1.6 µm, four types of fibers with nested elements have been optimized to provide the highest HOMER value in the state of straight fiber. Among them, the highest HOMER of NEARF4 fiber is 40.78 at λ = 1.45 µm. NEARF1, NEARF2, and NEARF3 have the largest HOMER at λ = 1.45, 1.45, and 1.37 µm, respectively, and the corresponding HOMER values are 23.30, 38.27, and 12.17. The inset of Fig. 6 shows that the mode fields of the LP01 mode and the LP11 mode are concentrated in the HC-NCF fiber core, indicating that the LP01 mode and the LP11 mode are hardly coupled with the HOM supported by the cladding tube.
It is found that the four types of fibers are not single-mode at λ = 1.06 µm in the straightened state. Compared with the other three types of fibers, NEARF1 has the best performance in CL, BL, and single-mode performance at λ = 1.06 µm. Therefore, we further optimize the single-mode performance of ultralow loss NEARF1 (the optimization method used is from [39]). When the fiber is in a bent state, the single-mode performance is further improved. The single-mode performance of our optimized NEARF1 is shown in Fig. 7.
Fig. 7. (a) The CL spectrum at different bending radii R, and (b) the fundamental mode profile at λ = 1.06 µm for several different values of R. The inset in (a) shows the mode field of the LP01 mode at R = 10 cm. (c) HOMER as a function of wavelength at different bending radii R.
As can be seen from Fig. 7(a) and 7(b), as the bending radius decreases (R from 25 cm to 5 cm), the CL gradually increases, and the corresponding FM field is further from the fiber core. It can be seen from Fig. 7(c) that the HOMER of the fiber is well improved when the fiber is bent, and the maximum value is increased to 105.08. In addition, the HOMER value of the NEARF1 at 1.06 µm is increased from 9.12 (Fig. 6(a)) to 45.98 (bending radius R = 10 cm), achieving effective mode stripping. It is well known that the HOMER value of greater than 10 provides a standard for a single-mode fiber [14]. As can be seen from Fig. 7(a), when the bending radius is 10 cm, the CL at 1.06 µm is 4.12×10−4 dB/km. Considering that the main source of NEARF1 transmission loss is the SSL (the SSL is 1.67×10−2 dB/km at 1.06 µm). Therefore, the CL value is still very low when the bending radius is 10 cm, which has little effect on the transmission loss of NEARF1. It can be seen that a lower CL value can get a higher HOMER, that is, an effective single-mode behavior of the fiber can be obtained.
Even though none of the four types of fibers are single-mode in the state of straight fibers, properties of HOMs are also interested (such as LP11 mode) to the community. Specifically, the LP11 mode among the HOMs can be converted into cylindrical vector light by adjusting its polarization state, which is useful for laser processing. The processing speed can be increased by 1.5-2 times in laser welding or cutting [40,41], the straight hole with aspect ratio can be obtained in laser drilling [42] and with a engineered bionic surface structure [43]. In addition, cylindrical vector light is also useful for high-resolution optical imaging systems [44,45]. The spatial resolution can be significantly improved. The LP11 mode with ultra-short pulse and high peak power can generate high optical gradient force and scattering force under strong focusing conditions, which can be used for particle capture and guidance [46], and even directly used for particle acceleration [47,48], thereby breaking through the classical diffraction limit of traditional coherent light field.
NEARF may support ultralow transmission loss of the LP11 mode and become a dual-mode fiber with excellent performance. To this end, we further study the loss performance of the LP11 mode in the state of straight fiber, and the loss spectrum is shown in Fig. 8.
Fig. 8. The loss spectrum of LP11 mode of NEARF1. Total loss (purple) is the sum of the CL (red) and SSL (green). The LP11 mode field profile is displayed in the inset.
The loss spectrum in Fig. 8 shows that the trend of the CL curve of LP11 mode remains unchanged after a rapid decrease with the increase in wavelength. The CL of LP11 mode at 1.06 µm is 5.89×10−5 dB/km and its lowest loss is 3.51×10−5 dB/km at 1.25 µm. The plots in Fig. 8 confirm that SSL dominates the loss for the LP11 mode of NEARF1 in the spectral range of 0.76–1.6 µm. The total loss is 1.68×10−2 dB/km at 1.06 µm and it provides the lowest total loss of 6.48×10−3 dB/km at 1.6 µm in the spectral range of 0.76–1.6 µm.
In addition, we also calculated HOMER between another lowest loss HOM (LP02) and the LP11 mode of NEARF1, as shown in Fig. 9. It shows that the HOMER between LP02 and LP11 modes is relatively high in the range of 0.72–1.6 µm, and the HOMER value can be over 106.41. The highest HOMER of approximately 2386.54 is obtained at 0.79 µm, and the HOMER of NEARF1 can be over 715.65 at λ = 1.06 µm. The mode field shows that the LP11 mode only exists inside the fiber core, indicating that the introduced nested tubes ensure the low loss of the core mode and greatly increase the HOMER.
Fig. 9. HOMER between LP02 mode and LP11 mode (left). The mode field diagram (right) for two HOMs (LP02 and LP11).
4. Conclusion
Finite element modelling has been used to simulate and calculate the transmission loss, BL, and single-mode performance of the four types of fibers with different nested tube structures. The results show that the transmission loss of NEARF1 has better transmission performance than that of the three other fibers with different nested structures in the range of λ = 0.72–1.6 µm. The transmission loss as low as 6.45×10−6 dB/km is predicted at λ = 1.06 µm. To the best of our knowledge, the record low level of transmission loss of HC-NCFs with nested tube structures was created. In addition, NEARF1 has been confirmed to have better bending resistance. Within a bending radius of 5–40 cm, NEARF1 has a bend loss below 2.99×10−2 dB/km at 5 cm bending radius; the bend loss is below 1.01×10−5 dB/km at 40 cm bending radius.
Subsequently, we have studied the single-mode performance of four types of fibers with different nested tube structures. The NEARF1 has the best single-mode performance compared with the three other fibers at the designed λ = 1.06 µm, and the HOMER between LP11 mode and LP01 mode is higher than 9.12 in the state of straight fiber. After optimization of its single-mode performance, the HOMER value increases from 9.12 to 45.98 at 1.06 µm when the bending radius of NEARF is R = 10 cm.
Finally, we further study the loss performance of the LP11 mode in the state of straight fiber. The result shows that the LP11 mode of NEARF1 still has very good transmission loss performance at 1.06 µm. In addition, we also calculate HOMER between another lowest loss HOM (LP02) and the LP11 mode, and the HOMER of NEARF1 can be over 106.41 in the range 0.72–1.6 µm. Therefore, NEARF1 may support ultralow transmission loss of the LP11 mode and become a dual-mode fiber with excellent performance in the state of straight fiber. NEARF1 can maintain good single-mode performance, that is, only the LP01 mode is retained when NEARF1 is in a bent state. We believe that the proposed NEARF1 design offers significant advantages and improvements over the designs reported in the current literature, promising excellent performance for transmission applications in the near-IR spectral regions.
Funding
National Natural Science Foundation of China (61871031, 61875012, 61905014); Beijing Municipal Natural Science Foundation (4222017).
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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