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Abstract
We present a novel hollow-core anti-resonant fiber (HC-ARF) with a cladding ring, two nested resonant tubes and two nested silicon tubes. The cladding ring in the fiber contributes to decrease the fundamental mode (FM) loss of x-polarization and enlarge the polarization-extinction ratio (PER). In addition, the nested silicon tubes can improve birefringence greatly. The combination of cladding ring, nested resonant tubes and nested silicon tubes can make the fiber obtain low FM loss, single-polarization, and high birefringence. Specifically, the proposed HC-ARF exhibits total FM loss of x-polarization, PER, and birefringence of 0.89 dB/km, 4432, 3.07×10−4, respectively, at 1.55 µm. Moreover, the y-bend direction has a great influence on the propagation properties of the fiber. The fiber in the x-bend direction has low total bend-loss of 0.004 dB/m for a small bend radius of 5.8 cm.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The polarization effects play a significant role in many polarization-sensitive optical fiber systems, such as fiber lasers [1], fiber sensors [2], fiber-based gyroscopes [3], and polarization maintaining optical amplifier [4]. Environmental perturbations and fabrication imperfections for optical fibers will cause a random birefringence and result in an unpredictable output [5,6]. Polarization-maintaining fibers can be used to eliminate the unpredictable polarization evolution. For these fibers, the high birefringence is acquired and light propagates in only one polarization [7,8]. Over the past few years, the solid-core fibers with polarization maintaining property have been studied and fabricated. The two polarization states of the solid-core fiber have different propagation constants (β) [9,10]. By introducing either anisotropy [9,11] or stress [10] in the core of the fiber, high birefringence is achieved. However, for these high birefringence fibers, due to the solid-core material and the different β, the fundamental limitations are high non-linearity, low damage threshold and polarization mode dispersion which cannot be completely eliminated [12,13].
Hollow-core fibers (HCFs), guiding the light in the air-core, can solve the fundamental limitations mentioned above. In the past decade, researchers have studied two types of HCFs [14], namely hollow-core photonic bandgap fibers (HC-PBGFs) and hollow-core anti-resonant fibers (HC-ARFs). HC-PBGFs use photonic bandgap effect to guide light in the air-core [15], which can get birefringence by using asymmetric core shape [16–18]. Fini et al. reported a 19-cell HC-PBGF, which can obtain loss of ∼4.9 dB/km and birefringence of ∼3×10−4, but with limited bandwidth (<10 nm) [19]. In addition, the asymmetric cladding in the HC-PBGF helps the fiber to obtain single-mode, high birefringence, and single-polarization [20].
Compared with HC-PBGFs, HC-ARFs have outstanding optical properties, such as wide bandwidth and low loss. So, they have attracted massive interest from researchers in this field [21–23]. Due to the features of light guidance in the air-core and the low overlap between light and glass, it is challenging for HC-ARFs to obtain high birefringence (∼10−4) [12]. A HC-ARF with high birefringence was theoretically identified in a transmission band with hybrid resonance nature [24]. Mousavi et al. creatively used multiple nested resonators with different wall thicknesses to achieve PER of 1000 and high birefringence at 1.55 µm [12,25]. The 6-tube non-touching HC-ARF with nested resonant tubes numerically obtained PER of 850 and birefringence of 10−5 [26]. For the fiber, the coupling between the fundamental core modes and the glass modes of nested resonant tubes is used to cause differential loss of fundamental core modes in the x- and y- polarizations and increase the birefringence [26]. A single-mode birefringent anti-resonant hollow-core fiber was simulated, fabricated, and characterized by introducing capillary tubes of different thicknesses, which acquired a group birefringence of 4.4×10−5 and the loss of 0.46 dB/m at 1.55 µm [27].
Yan et al. achieved a single-polarization HC-ARF by coating a layer silicon with a suitable thickness on the inner surface of one vertical cladding tube [28]. A birefringence of 10−4 and a PER of 1732 can be obtained at 1.55 µm. Especially, Habib et al. proposed a HC-ARF design with hybrid silica/silicon cladding tubes [29]. By adding silicon layers in the HC-ARF, the mode coupling between x-polarization core mode and silicon layer modes provides high birefringence and single-polarization.
In this study, we add a cladding ring (CR) and two nested silicon tubes (NSTs) into the 6-tube non-touching nested HC-ARF structure with two nested resonant tubes (NRTs) to obtain low FM loss, single-polarization and high birefringence. By comparing four different optical fibers, our main purpose is to obtain a systematic understanding on how the components of these structures affect the characteristics of optical fibers. Moreover, we investigate the fiber properties by optimizing the structural parameters (e.g., the ratio of nested resonant tube diameter to cladding tube diameter, the thickness of nested resonant tubes, and the thickness of nested silicon tubes). Besides, we also explore the effect of different bend directions on the transmission properties of optical fiber at 1.55 µm and analyze surface scattering loss (SSL). Finally, we discuss the fabrication of optical fibers and the strength of connecting pipes.
2. Fiber geometry
In our numerical investigation, the 6-tube nested HC-ARFs with different cladding components are shown in Fig. 1. Figure 1(a) shows a 6-tube non-touching nested polarization-maintaining HC-ARF structure, in which there are two nested resonant tubes represented by orange rings in the y-direction. For polarization-maintaining fibers, the refractive index of the silica glass is 1.444 in our simulations at the wavelength of 1.55 μm [8,12,19]. As the glass thickness changes slightly, the effective index of the glass modes gets a large change. Therefore, the wall thickness of the two nested resonant tubes in the y-direction should be adjusted to the strong resonant condition, whereas other anti-resonant tubes are in the best anti-resonant status.
Fig. 1. In the simulations, four HC-ARF structures are considered. (a) polarization-maintaining HC-ARF with nested resonant tubes; (b) polarization-maintaining HC-ARF with nested resonant tubes and cladding ring; (c) HC-ARF with silicon tubes inserted in silica tubes; (d) proposed HC-ARF in which there are nested resonant tubes, cladding ring and nested silica tubes.
On the basis of Fig. 1(a), a cladding ring is added to the structure shown in Fig. 1(b), which is connected with the outer cladding layer (OCL) by two connecting pipes. As shown in Fig. 1(c), compared to Fig. 1(b), two nested resonant tubes are removed from cladding tubes in the y-direction and nested silicon tubes are placed in the silica tubes to obtain high birefringence which are represented by red rings. The proposed novel fiber design has a cladding ring, two nested resonant tubes, two nested silicon tubes which is shown in Fig. 1(d). Specifically, the fiber structure has core diameter Dcore, cladding tube diameter dtube, nested anti-resonant tube diameter d1, wall thickness of nested anti-resonant tubes, cladding tubes and cladding ring t1, nested resonant tube diameter d2, wall thickness of nested resonant tubes t2, wall thickness of nested silicon tubes t3, the minimum gap separation between the cladding tubes g, connecting pipe length m, and wall thickness of connecting pipes t4, which satisfy the functional relationship: Dcore = dtube + 2g + 2t.
3. Discussion on different fiber structures
The COMSOL software based on the finite-element modeling (FEM) was used to perform the numerical simulations. In order to accurately model the fiber modal properties, the outer cladding layer was set a perfectly-matched layer (PML) boundary [21,30]. In addition, in the air regions and silica/silicon tube walls, the extremely fine mesh sizes of λ/4 and λ/6 were used respectively to acquire fine agreement with the experimental results. In this work, the refractive index of silicon is chosen from Ref. [31]. The leakage loss is studied, and the loss mentioned in this paper is used to refer to leakage loss.
3.1 Effect of cladding ring
To get a better understanding of the influence of cladding ring on loss and effective refractive index neff, we research optical properties of the two fiber structures in Fig. 1(a) and (b). The relevant parameters are Dcore = 30 µm, dtube = 20.5 µm, d1/dtube = 0.45, t1 = 1.12 µm, d2/dtube = 0.74, t2 = 1.58 µm and t4 = 1.12 µm. According to the numerical simulation results, for the length of connecting pipes m, the FM loss of x-polarization decreases and the PER increases with the increase of m. So, when the wall thickness of CR satisfies the anti-resonance condition, enlarging the air layer between CR and OCL helps to reduce the FM loss and increase PER. For m = 5 µm, the fiber obtains excellent FM loss of x-polarization and PER. Considering the fiber manufacturing, in this paper, m = 5 µm is adopted. The diagrams (a), (b), (c) and (d) in Fig. 2 separately depict the FM loss for the x-polarization (x-pol.) and y-polarization (y-pol.), PER which is the ratio of the FM loss in y-polarization to the FM loss in x-polarization, effective refractive index for the x- and y- polarization, birefringence which is |nx− ny| as a function of wavelength.
Fig. 2. Numerical simulation results of two HC-ARFs with cladding ring and without cladding ring. (a) loss, (b) PER, (C) neff, (d) Birefringence.
It can be seen from Fig. 2(a) that when a cladding ring is added to the periphery of the cladding tubes, compared with the fiber without cladding ring (Fig. 1(a)), the FM loss of x-polarization and y-polarization is obviously reduced over a wide range of wavelength. In addition, the FM losses for x- and y- polarization are 0.47 dB/km and 9.803 dB/m respectively at 1.55 µm for the fiber with cladding ring. Figure 2(b) shows that the curves of PER for HC-ARFs without cladding ring and with cladding ring have two peaks at 1.545 µm and 1.55 µm, whose values are 8614 and 20745 respectively. The simulation results of loss and PER show that the cladding ring can effectively reduce the FM loss of x- and y- polarization and obtain larger PER. The cladding ring has no effect on effective refractive index and birefringence of fiber which can be seen in Fig. 2(c) and (d). A birefringence of 0.9×10−4 is achieved at 1.55 µm.
3.2 Effect of nested resonant tubes
In this work, we discuss the influence of nested resonant tubes on FM loss of x- and y- polarization, PER, effective refractive index and birefringence while keeping the core diameter Dcore = 30 µm, dtube = 20.5 µm, d1/dtube = 0.45, t1 = 1.12 µm, d2/dtube = 0.74, t2 = 1.58 µm, t3 = 214 nm and t4 = 1.12 µm for HC-ARFs in Fig. 1(c) and (d). As shown in Fig. 3(a), compared to the fiber only having nested silicon tubes, the fiber with nested silicon tubes and nested resonant tubes has lower FM loss for x-polarization in the range of 1.544 µm < λ < 1.556 µm and higher FM loss for y-polarization at 1.55 µm. It indicates that nested resonant tubes induce coupling between y-polarization core mode and the glass modes at 1.55 µm, which results in higher FM loss of y-polarization. So, a large PER of 13673 is achieved which is shown in Fig. 3(b). The FM loss of y-polarization for the fiber (Fig. 1(d)) is as high as 3.92 dB/m at 1.55 µm.
Fig. 3. Numerical simulation results of two HC-ARFs with nested resonant tubes (NRTs) and without nested resonant tubes. (a) loss, (b) PER, (C) neff, (d) Birefringence.
From the effective refractive index and birefringence curves in Fig. 3(c) and Fig. 3(d), it can be seen that the nested resonant tubes have no effect on the effective refractive index and birefringence. The effective refractive index of y-polarization and birefringence decrease sharply with the increase of wavelength. The birefringence is reduced from 5.5×10−4 to 2×10−4 in the wavelength range of 1.54–1.56 µm, which is 3.07×10−4 at 1.55 µm.
Moreover, the effective refractive index of y-polarization for the HC-ARFs with nested silicon tubes is increased significantly than that in Fig. 1(b), and the birefringence of the fiber in Fig. 1(c) is much larger than that in Fig. 1(b). These prove that nested silicon tubes can effectively improve effective refractive index of y-polarization and birefringence of optical fiber. Through the combination of cladding ring, nested resonant tubes and nested silicon tubes, the fiber can obtain low FM loss of x-polarization, large PER and high birefringence.
Figure 4 shows the mode fields for x- and y- polarization at the wavelength of 1.55 µm. The color and arrows of mode fields indicate the electric field intensity and the direction of the transverse electric field, respectively. And, the length of the arrow is directly proportional to the amplitude of the transverse electric field. It can be seen from Fig. 4(a) that the coupling between x-polarization core mode and the glass modes is suppressed. The core mode in the x-polarization is bound in the core. However, the y-polarization core mode couples with the nested silicon modes, as shown in Fig. 4(b), which leads to the increase of FM loss and neff in the y-polarization.
Fig. 4. (a) fundamental mode in the x-polarization, (b) fundamental mode in the y-polarization at the wavelength λ = 1.55 µm.
The proposed fiber has a bandwidth of ∼2 nm for PER >100, which can be used in polarization-filtering of fiber lasers [32–33].
4. Numerical results and discussions
From the above discussion, due to the function of cladding ring, nested resonant tubes and nested silicon tubes, the novel fiber shown in Fig. 1(d) has excellent properties in FM loss of x-polarization, PER and birefringence. To get better insights of the effect of d2/dtube, the thickness of nested resonant tubes and the thickness of nested silicon tubes on the FM loss of x- and y-polarization, PER, neff and birefringence, we investigate the fiber for a fixed wavelength, λ = 1.55 µm, Dcore = 30 µm, dtube = 20.5 µm, d1/dtube = 0.45, m = 5 µm.
4.1 Optimization of d2/dtube
To optimize the d2/dtube, we do research with t2 = 1.58 µm, t3 = 214 nm and t4 = 1.12 µm. For the newly designed fiber structure, it can be seen from Fig. 5(a) that there are two high FM loss peaks at d1/dtube of 0.56 and 0.67 for x-polarization whereas a high FM loss peak for y-polarization occurs at d2/dtube = 0.74. Here, a PER of 13672 is achieved and the FM loss of x-polarization is 0.28 dB/km. Hence, a fiber with an appropriate nested resonant tube diameter yields a larger PER. By tuning d2/dtube, excellent FM loss of x- and y- polarization and PER can be obtained. However, Fig. 5(b) depicts the effective refractive index for the x- and y- polarization has no obvious change in the range of d2/dtube = 0.45–0.75. The birefringence fluctuates slightly over a wide range of d2/dtube and the value is 3.07×10−4 at d2/dtube = 0.74.
Fig. 5. (a) FM loss of x-polarization and y-polarization, PER, and (b) effective refractive index of x-polarization and y-polarization, birefringence as a function of d2/dtube.
4.2 Optimization of t2
The effect of thickness of nested resonant tubes on FM loss of x- and y- polarization, PER, effective refractive index of x- and y- polarization and birefringence for a fixed nested silicon tube, t3 = 214 nm, t4 = 1.12 µm and d2/dtube = 0.74 is shown in Fig. 6. It can be seen from Fig. 6(a) that the FM loss of x-polarization remains < 0.42 dB/km in the range of 1.572 µm < t2 < 1.589 µm. In this range, the coupling between x-polarization core mode and the glass modes in the cladding and nested tubes is suppressed. Nevertheless, a strong coupling between y-polarization core mode and the glass modes in the nested resonant tubes leads to a larger FM loss of y-polarization at t2 = 1.58 µm. In addition, a PER of >10000 is achieved. As shown in Fig. 6(b), with the increase of t2, the birefringence has a large fluctuation in the range of t2 = 1.565–1.569 µm. t2 has great influence on birefringence for t2 < 1.57 µm.
Fig. 6. (a) FM loss of x- and y- polarization and PER, and (b) effective refractive index of x- and y- polarization and birefringence as a function of t2.
4.3 Optimization of t3
In this section, when d2/dtube = 0.74, t2 = 1.58 µm and t4 = 1.12 µm, we investigate the performance as a function of the thickness of nested silicon tubes which is presented in Fig. 7. Figure 7(a) shows that the FM loss in the x-polarization can be maintained less than 0.3 dB/km in the range of 205 nm < t3 < 224 nm. There is a FM loss peak in the y-polarization at t3 = 214 nm. It indicates that the modes of nested silicon tubes and the core mode in the y-polarization are resonantly coupled. So, the PER is large. It can be seen from Fig. 7(b) that t3 has no effect on effective refractive index for the x-polarization. However, with the increase of t3 from 217 to 225 nm, the effective refractive index in the y-polarization decreases slightly. Meanwhile, birefringence decreases sharply in the range of 216 nm < t3 < 225 nm. And the birefringence is 3.07×10−4 at t3 = 214 nm. The birefringence and PER properties can be improved by optimizing t3.
Fig. 7. (a) FM loss of x- and y- polarization and PER, and (b) effective refractive index of x- and y- polarization and birefringence as a function of t3.
4.4 Bend propagation property analysis
In this section, we investigate the effect of bend radius for x- and y- bend direction on FM bend loss of x- and y- polarization, PER, effective refractive index of x- and y- polarization, birefringence in the HC-ARF (Fig. 1(d)) while maintaining d2/dtube = 0.74, t2 = 1.58 µm, t3 = 214 nm and t4 = 1.12 µm. The bend loss can be calculated by the formula [34]: neq= n(x,y)e(x,y)/Rb, where neq is the equivalent refractive index of the bend fiber, n(x,y) is the equivalent refractive index of the straight fiber, (x,y) is the bend direction of x or y, Rb is the bend radius. In particular, for the straight fiber, the FM loss of x-polarization, the FM loss of y-polarization, PER, neff of x-polarization, neff of y-polarization and birefringence are 0.29 dB/km, 3.92 dB/m, 13673, 0.9993286, 0.9996361 and 3.075×10−4 respectively at 1.55 µm.
Figure 8 depicts the propagation properties for the bend fiber. In the x-bend direction, it can be seen from Fig. 8(a) that the FM bend loss of x-polarization remains < 0.001 dB/m for Rb > 5.6 cm. In addition, the FM bend loss of y-polarization gradually approaches to 4 dB/m with the increase of bend radius. However, in the y-bend direction, with the increase of bend radius, the FM bend loss of x-polarization decreases continuously whereas the FM bend loss of y-polarization is rising. Compared with x-bend direction, the y-bend direction has more influence on the FM bend loss of x- and y- polarization. Further, the PER in the x-bend direction is gradually close to that of the straight fiber, whereas the PER in the y-bend direction is small.
Fig. 8. Calculated (a) bend loss of x- and y- polarization, (b) PER, (c) effective refractive index of x- and y- polarization and (d) birefringence for both bend directions as a function of bend radius for the HC-ARF with a cladding ring, two nested resonant tubes and two nested silicon tubes (Fig. 1(d)).
Figure 8(c) shows that the effective refractive index of x- and y- polarization for y-bend direction is greatly changed. However, the x-bend direction has a slight effect on the effective refractive index. Figure 8(d) further illustrates the above statement. The birefringence in the x-bend direction can be maintained < 3.11×10−4 over a wide range of bend radius. But, the birefringence in the y-bend direction decreases from 4.82×10−4 to 3.33×10−4 in the range of 3 cm < bend radius <10 cm. Due to nested resonant tubes and nested silicon tubes in the y-polarization, for y-bend direction, the strong coupling between the fundamental core mode of y-polarization and modes existing in nested resonant tube or nested silicon tube regions increases the birefringence and leads to differential FM bend loss of x- and y- polarization compared with the loss in the x-bend direction.
4.5 Surface scattering loss analysis
The fiber has more complex surface structure, and more energy is distributed on the silicon tubes in the y-direction. Besides leakage loss, the surface scattering loss (SSL) also contributes to the propagation loss in hollow core fibers. The calculation details of the SSL can be obtained from Ref. [21,35]. Figure 9(a) shows each SSL generally decreases with the increase of wavelength.
At λ = 1.55 µm, the leakage loss, SSL in the x-polarization are 0.29 dB/km and 0.6 dB/km respectively. In addition, the SSL in the y-polarization is 18.74 dB/km at 1.55 µm, which plays a key role in FM propagation loss and PER. A PER of 31 is achieved for SSL. The total loss coming from SSL and leakage loss in the x-polarization, PER are 0.89 dB/km and 4432 respectively at λ = 1.55 µm. Moreover, total FM bend loss of x-polarization coming from SSL and leakage loss remains < 0.004 dB/m for Rb > 5.8 cm at λ = 1.55 µm.
4.6 Discussion on optical fiber fabrication
In this section, we discuss the fiber fabrication process and structural stability of the proposed optical fiber. For optical fiber fabrication, according to the designed optical fiber structure, capillary tubes of different diameters and connecting pipes are stacked together to form an optical fiber preform [36]. Both ends of the optical fiber preform are sintered and fixed by hydrogen-oxygen flame, or fixed tubes are inserted into the stack to avoid deformation of the desired structure. Then, by controlling the drawing temperature, speed, and air pressure, we can draw the fiber.
The silicon-coated HC-ARF has been fabricated successfully by using a high-pressure chemical vapor deposition (HPCVD) method [37]. The silicon layer can be manufactured in a silica tube by HPCVD method. We can directly assemble the capillary tube with a silicon layer into an optical fiber preform, and then draw the optical fiber. Silica fibers are usually drawn at approximately 1950 °C. These temperatures are higher than the melting point of silicon, and then the melt is adhered by the viscous silica cladding [38,39]. This method can be used in complex optical fiber structures and can manufacture long optical fibers. In another way, we also can use the HPCVD method to add a silicon layer to the inner wall of the cladding tube in the manufactured hollow-core fiber [40–42]. The thickness of silicon layer can be uniformly and accurately controlled.
In order to obtain better strength of the connecting pipe and fiber performance, we investigate the length and thickness of the connecting pipe. The relevant fiber parameters are Dcore = 30 µm, dtube = 20.5 µm, d1/dtube = 0.45, t1 = 1.12 µm, d2/dtube = 0.74, t2 = 1.58 µm and t3 = 214 nm. We discuss the effect of connecting pipe length m on FM loss of x- and y- polarization, PER, and birefringence while keeping the connecting pipe thickness, t4 = 1.12 µm. It can be seen from Fig. 10(a) that the FM loss of x-polarization decreases with the increase of m, but the FM loss of y-polarization changes slightly. Therefore, the PER increases with the increase of m. The neff of x- and y-polarization remains unchanged as a function of m and birefringence is in the range of 3.0747×10−4−3.0752×10−4 which can be seen in Fig. 10(b).
Fig. 10. (a) FM loss of x- and y- polarization and PER, and (b) effective refractive index of x- and y- polarization and birefringence as a function of m.
For the investigation of connecting pipe thickness, the FM loss of x-polarization remains unchanged in the range of 1.1 µm < t4 < 1.6 µm which is presented in Fig. 11(a). In addition, the FM loss of y-polarization and PER change little. There is no change in the effective refractive index for the x- and y- polarization and birefringence.
Fig. 11. (a) FM loss of x- and y- polarization and PER, and (b) effective refractive index of x- and y- polarization and birefringence as a function of t4.
Through the above research, it is found that the strength of the optical fiber structure can be increased by raising the thickness of the connecting pipes without much influence on the characteristics of the optical fiber. It can be seen from the manufactured HC-ARFs that the nested anti-resonant tube can be fixed in the cladding tube with a small contact area [43]. Here, the cladding ring can be fixed by two symmetrical connecting pipes. In addition, three or more connecting pipes can be used to make the optical fiber structure more stable.
4.7 Performance comparison of different HCF designs
Table 1 shows a summary of the loss, PER, birefringence and bend loss of different HCF designs and provides a direct performance comparison of the fibers. Compared with other designed fibers, it can be found that the designed fiber has lower loss, higher PER and greater birefringence. This shows that the cladding ring in the fiber helps to reduce FM loss. In addition, the combination of nested resonant tubes and nested silicon tubes can improve PER and birefringence greatly.
Table 1. Summary of the optical properties of different hollow-core fiber designs
5. Conclusion
In summary, we propose a novel 6-tube non-touching nested HC-ARF structure with a cladding ring, two nested resonant tubes and two nested silicon tubes, which has single-polarization, low FM loss and high birefringence. Through Numerical simulations, we found that cladding ring in the fiber can effectively reduce the FM loss of x-polarization and increase PER. In addition, the nested silicon tubes placed in optical fiber can improve birefringence greatly. Compared to the HC-ARF without nested resonant tubes, the HC-ARF (Fig. 1(d)) with two nested resonant tubes has large PER. The combination of cladding ring, nested resonant tubes and nested silicon tubes can make the fiber obtain low FM loss of x-polarization, single-polarization, and high birefringence. Numerical simulation results show the proposed HC-ARF design has total FM loss of x-polarization, PER, and birefringence of 0.89 dB/km, 4432, 3.07×10−4 respectively at 1.55 µm. The research results of bend fiber indicate that y-bend direction has a great influence on the bend loss of x- and y- polarization, PER, neff of x- and y-polarization and birefringence. The fiber has low total bend loss of 0.004 dB/m in the x-bend direction for a bend radius of 5.8 cm.
Funding
Local Science and Technology Development Fund Projects Guided by the Central Government, China (206Z0401G, 206Z1703G, F2018203346); Open Projects Foundation of Yangtze Optical Fibre and Cable Joint Stock Limited Company (SKLD2004).
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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