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Abstract
Chalcogenide hollow-core anti-resonant fibers (HC-ARFs) are a promising propagation medium for high-power mid-infrared (3-5 µm) laser delivery, while their properties have not been well understood and their fabrications remain challenging. In this paper, we design a seven-hole chalcogenide HC-ARF with touching cladding capillaries, which was then fabricated from purified As40S60 glass by combining the “stack-and-draw” method with a dual gas path pressure control technique. In particular, we predict theoretically and confirm experimentally that such medium exhibits higher-order mode suppression properties and several low-loss transmission bands in the mid-infrared spectrum, with the measured fiber loss being as low as 1.29 dB/m at 4.79 µm. Our results pave the way for the fabrication and implication of various chalcogenide HC-ARFs in mid-infrared laser delivery systems.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The 3-5 µm mid-infrared (MIR) region is a key atmospheric window, within which there are strong characteristic absorptions for many chemical and biological molecules [1]. To this, MIR lasers are crucial for many applications including environmental monitoring, homeland security, and laser surgery, to name just a few of them [2]. In most of these applications, optical fibers, as a transmission medium, are necessary for MIR laser power delivery from its source to the required place, making the system more compact and efficient compared to that for space transmission.
Owing to having the advantageous features of low phonon energy and wide infrared transmission band in various glasses, relatively stable physical and chemical properties, as well as good fiber formation ability [3], chalcogenide glasses (ChGs) have become one of the key infrared materials for manufacturing the MIR laser power delivery fiber. The ChG solid-core fibers, like the most commonly used As40S60 ones, are limited by a low laser damage threshold (a maximum incident power density of 12 MW/cm2 under a 2 µm CW thulium-doped silica fiber laser [4], which is lower than that of silica glass fibers by 2-3 orders of magnitude), high nonlinearity (a nonlinear refractive index n2 of 1.96 × 10−18 m2/W, which is higher than that of silica glass fibers by two orders of magnitude [5]), and thermal induced modal degradation as increasing the MIR laser transmission power, make it hard to enhance the corresponding power-handling capacity [6].
Recently, hollow-core anti-resonant fibers (HC-ARFs) were found to be a good solution for improving the fiber’s mode field area and achieving high-power laser delivery [7]. The core of such HC-ARFs is air, and the cladding consists of several capillaries attached to a jacket tube, with the negative curvature of the core-cladding boundary. Silica HC-ARFs have the best performance in all the reported silica hollow-core fibers, such advantages include broad transmission band [8], high laser damage threshold [9], high mode purity [10], and low bending loss [11], emphasizing the importance of the development of ChG HC-ARFs for mid-infrared applications. In contrast to silica, ChGs have inferior mechanical strength and steeper viscosity-temperature curves [12,13]. The fabrication of preforms and ChG HC-ARFs with uniform structure is, accordingly, quite challenging. Experimentally, Shiryaev et al. in 2014 reported two types of As40S60 HC-ARF with either eight touching cladding capillaries [14] or ten ones [15] for MIR laser applications, having the minimum loss of 3 dB/m at 4.8 µm and 1.2 dB/m at 2.7-3.4 µm, respectively; both fibers were fabricated by a “stack-and-draw” method in which several capillaries were firstly assembled with a jacket tube, and then drawn into the fiber. However, such fabrication method faces a challenge of obtaining tubes with high manufacturing tolerances. Two years later, Gattass et al. prepared a ChG HC-ARF preform with eight non-touching capillaries by using a different way called the “extrude-and-draw” method to improve the performance [16], achieving a low measured fiber loss of 1.7 dB/m at 4.7 µm. The reported ChG HC-ARFs with truncated cladding capillaries were, however, not the most optimized structure due to the limitation of the extrusion die in the method [17]. In 2021, Carcreff et al. demonstrated the fabrication of the HC-ARF drawn from a Te20As30Se50 glass 3D printed preform [18,19], and this method could obtain new geometries that the two previous methods cannot realize. For all the fabrication methods, addressing the increased loss induced by imperfect fiber structure is necessary. Despite the ChG HC-ARF exhibits extremely low absorption on the theoretical side, its measured loss could still be significantly higher because of capillary inhomogeneity, displacement, and deformation, as well as other imperfections [20–22].
In this paper, we design a seven-hole ChG HC-ARF with touching cladding capillaries, which can radically suppress higher-order modes that degrade the lasers’ beam quality. Theoretically, we address the confinement loss, bending loss, material loss and higher-order mode suppression of such ChG HC-ARF by means of the finite element method. Based on the “stack-and-draw” method, the ChG HC-ARF was fabricated in the form of seven touching cladding capillaries according to the theoretical designed fiber structure, obtaining several low-loss transmission bands in the mid-infrared spectrum, and the low measured fiber loss being 1.29 dB/m at 4.79 µm, providing a new avenue in fabricating and implying for high-power mid-infrared laser delivery using diverse ChG HC-ARFs.
2. Fiber design and modeling
2.1 Fiber design
High-purity ChG of As40S60 composition with good thermal stability and fiber drawing performance was selected as the fiber material. The corresponding refractive indices were measured using an infrared variable angle spectroscopic ellipsometer (J.A. Woollam, IR VASE Mark II) and the resultsare shown in Fig. 1. The refractive index dispersion curve can be well fitted with the conventional Sellmeier formula, yielding:
Table 1. Summary of Sellmeier coefficients for the As40S60 glass and fiber geometry for As40S60 HC-ARF
HC-ARF with an air core and seven touching cladding capillaries was firstly designed with high-purity As40S60 glass, and its structure schematic diagram is shown in Fig. 2(a), in which the gray parts are glass, and the white regions represent air, and the diameter of the fiber core is adjusted to 138 µm in order to achieve the low-loss transmission at 3-5 µm. Figure 2(b) shows the amplitude of the normalized electric field for the fundamental mode, which can be effectively confined in the air core, whose effective mode field area is larger than 7000 µm2. Besides, the designed values of the physical parameters: the number of capillaries N, the air core’s diameter Dcore, the inner diameter of cladding capillary dtube, the wall thickness of cladding capillary t, and the wall thickness of jacket tube T, are all listed in Table 1.
Fig. 2. (a) Structure schematic diagram of As40S60 ChG HC-ARF with an air core and seven touching cladding capillaries. (b) Amplitude of the normalized electric field for the fundamental mode. The dimensional parameters (N, dtube, t, and T) are described in the text.
2.2 Confinement, bending and material loss
According to the above fiber geometry, the confinement loss, bending loss, and material loss of the fiber were calculated using the Comsol Multiphysics which relies on the finite element method. The fiber confinement loss ($CL$) is given by the expression:
where Im(neff) is the imaginary part of effective refractive index, with λ being the light wavelength [23]. By constructing the fiber model as shown in Fig. 2(a), filling with air and As40S60 glass, meshing the grid, setting the optical module, and performing mode analysis, the associated CL is then accumulated in Fig. 3, from which one can see that the fiber has several low-loss transmission windows in the 3-5 µm band.We then investigate the bending loss in two core fundamental modes with polarization directions either parallel or perpendicular to the bend direction (which is assumed to be along the x-axis). Such bending loss at different bend radii is shown in Fig. 4(a), displaying four high-loss peaks dependent on mode coupling for both the parallel-polarized and perpendicular-polarized modes. In Fig. 4(b), we have also shown the simulated normalized electric fields of parallel-polarized core modes at two bend radii of 27.5 cm and 35 cm. It is seen that the parallel-polarized mode’s coupling exhibits a loss up to 4 times higher than that for the perpendicular-polarized mode for the former, while the modes are well-confined in the air core with a bending loss of 0.1 dB/m for the latter. Therefore, we can conclude that the mode coupling between the core and tube modes accounts for the bending loss peaks. To prevent these loss peaks, the bending radius of the fiber should be larger (> 35 cm) for MIR laser delivery systems.
Fig. 4. (a) The calculated bending loss as a function of bend radius for parallel-polarized and perpendicular-polarized modes. (b) Amplitudes of the normalized electric fields for parallel-polarized modes at bend radii of 27.5 cm and 35 cm. The black arrows indicate the direction of the transverse electric field.
In the HC-ARF, the fiber material impacts slightly the core mode properties, including the total fiber loss. Such loss may be measured by:
where the confinement loss αCL can be obtained numerically, and the absorption of material αabs can be measured experimentally, η denotes the modal overlap factor between the propagating core mode and surrounding glass cladding structure [24]. In our ChG HC-ARF, an enlarged core diameter could lead to a low η down to 10−5 at 4.79 µm. The total fiber loss as a function of the material absorption loss for As40S60 glass is depicted in Fig. 5, showing a little change in total fiber loss in red regions as an increase of the glass absorption loss from 0.1 to 100 dB/m, which demonstrates that the fiber loss is most ascribed to the confinement loss and the glass absorption loss is ignorable; when such absorption loss exceeds 100 dB/m, the total fiber loss increases greatly. In comparison, the measured material absorption loss of As40S60 glass is 0.36 dB/m at 4.6-4.8 µm, which can be neglected for the total fiber loss accordingly. In addition, this curve also allows evaluation of the contribution of the loss peaks from glass impurity absorption (e.g., S-H absorption feature at 4 µm) on material loss.2.3 Higher-order mode suppression
Resonant coupling between core higher-order modes and cladding tube modes could be the underlying mechanism for suppressing core higher-order modes. The higher-order mode suppression characteristic depends on the ratio dtube/Dcore between the inner diameter of the cladding capillary and the core diameter [25], and such ratio can be adjusted by changing either the number of capillaries or the wall thickness in HC-ARF with touching cladding capillaries. The former way is preferred owing to the range of wall thickness adjustment being relatively small due to fabrication feasibility. According to the literature [26], N ≤ 7 is necessary to obtain the suppression of the higher-order modes through resonant coupling, and particularly, such fibers with N = 7 exhibit the best tradeoff between higher-order mode suppression properties and low fundamental modes’ losses. The real parts of the effective refractive index for both the core modes and cladding tube ones are displayed in Fig. 6(a), showing that their values for two degenerated fundamental modes (HE11 modes), higher-order modes (TE01, HE21, and TM01 modes), and cladding tube modes exhibit a decreased tendency. Particularly, the case for the TE01 mode (in the middle one) is closer to that of the latter (cladding tube modes), and they can accordingly be easier to resonantly couple which results in a further increase of the confinement loss. Figure 6(b) shows the confinement loss of core modes, where the TE01 mode has the lowest loss among higher-order modes. The higher-order mode extinction ratio (HOMER) is calculated as:
where LossHOM is the higher order mode with the lowest loss and LossFM is the loss of the core fundamental mode. Standard TIA-455-80-C specifies that the effective single-mode transmission condition for a HOMER should be larger than 19.3 dB [27]. The TE01 mode’s HOMER is shown in Fig. 6(c). It is observed that, when t = 6 µm and dtube/Dcore = 0.679, the confinement loss is 0.316 dB/m for the TE01 mode and 0.008 dB/m for the HE11 mode, and the calculated HOMER is 15.96 dB which is large enough and meets the requirement of a quasi-single-mode transmission for this HC-ARF.Fig. 6. (a) Real part of the effective index of HE11 modes, TE01 mode, TM01 mode, HE21 modes and tube modes; (b) CL of HE11 modes, TE01 mode, TM01 mode, HE21 modes; (c) HOMER of the TE01 mode to the HE11 mode.
2.4 Manufacturing tolerance
Figure 7 shows the anti-resonant curve of confinement loss as a function of cladding capillary wall thickness at an anti-resonant wavelength of 4.6 µm, showing a periodicity with alternating resonant and anti-resonant effects. The confinement loss of 0.5 dB/m represents the dividing line between the resonant and anti-resonant regions. In the resonant regions, core modes are partially coupled with cladding modes, and a substantial confinement loss is induced by such coupling. In the anti-resonant regions, however, the core modes are well-confined in the fiber core with a lower confinement loss. The rapid change of ChG’s sensitive temperature-viscosity profile makes it more difficult to fabricate the microstructured fiber geometry precisely than that for silica. With a high manufacturing tolerance of 0.25 µm, the fiber loss is less than 0.5 dB/m. Such manufacturing tolerance ensures an acceptable confinement loss in the anti-resonant regions. The thickness t and the manufacturing tolerance of thickness were selected as 6 µm and ± 0.25 µm, respectively, to ensure acceptable confinement loss and fabrication feasibility in the anti-resonant regions.
Fig. 7. The anti-resonant curve of calculated confinement loss as a function of cladding capillary wall thickness.
3. Fiber fabrication and characterization
3.1 Fiber fabrication process
Using the “stack-and-draw” method, the HC-ARF with seven touching cladding capillaries was fabricated according to the designed fiber structure. Figure 8 shows the schematic diagram of the preform and fiber fabrication process. First, As40S60 glass tubes with an outer diameter of 14 mm were drawn into capillaries whose outer diameter was 3.3 mm. Next, seven capillaries were positioned in a tight circle along the inner wall of the jacket As40S60 glass tube with an inner diameter of 11.2 mm, and 1 cm-long supporting tubes were inserted into each end to support and prevent the capillaries from moving. The stacked preform was heated to 210 °C in a vacuum furnace to fuse the capillaries to the jacket glass tube. The fabricated ChG tubes and preform are shown in Fig. 9. The preform was fixed in a fixture connected with a dual gas path pressure control system. One path was for the air core (applied pressure was recorded as pcore), and the other was for the capillaries (applied pressure was recorded as pcapillary). During the drawing process, the pcore represents atmospheric pressure and the pcapillary was maintained above atmospheric pressure. The pressure difference Δp = pcapillary – pcore was kept as a positive value. By regulating the drawing temperature, Δp, and drawing process parameters, the fabricated fiber was drawn to one with the expected structure.
3.2 Influence of drawing process parameters on fiber structure
Figure 10 shows the cross-sections of the fabricated fibers at different fiber drawing temperatures and Δp. At a fiber drawing temperature of 333 °C and Δp = 0, all capillaries contract significantly and move transversely due to surface tension, according to Fig. 10(a). There is no additional pressure within the capillary to counteract the surface tension, and the combined effect of both, as well as the resistance at the glass node, results in severe deformation of the capillaries. In Fig. 10(b), when the fiber drawing temperature was down to 329 °C and Δp = 400 Pa, the deformation of capillaries was significantly reduced. However, the capillaries continue to exhibit excessive touch, and the core-cladding boundary curvature equates to nearly zero, indicating that the fiber drawing temperature is still excessively high. In Figs. 10(c), (d), as Δp increases at a lower fiber drawing temperature of 325 °C, the cross-sectional geometries of the capillaries keep round while the curvature of the core-cladding boundary remains negative. The viscosity of glass increases as decreasing the fiber drawing temperature, and a relatively large viscosity is advantageous for reducing the surface tension-induced deformation. Increasing the Δp can obtain a core-cladding boundary with negative curvature, as shown in Fig. 10(e). The prepared HC-ARF has an outer diameter of about 400 ± 4 µm, an effective core diameter of 130 ± 1 µm, a capillary inner diameter of 96 ± 1 µm, and an average capillary wall thickness of 5.95 µm (the maximum wall thickness is 6.05 µm, the minimum wall thickness is 5.83 µm, and the error of the wall thickness is less than 0.17 µm).
Fig. 10. The cross sections of prepared As40S60 HC-ARFs under various fiber drawing temperatures and Δp: (a) 333 °C, 0 Pa; (b) 329 °C, 400 Pa; (c) 325 °C, 200 Pa; (d) 325 °C, 400 Pa; (e) 325 °C, 1000 Pa.
Compared to the designed fiber geometry, the core diameter decreases slightly while the inner diameter of the cladding capillary increases a little due to the capillary's expansion, and the average wall thickness of the cladding capillary is in excellent agreement with the designed value. It is hard to manage the multiple dimensional parameters in the process of fiber drawing simultaneously, and the wall thickness of the cladding capillary is given priority because it can affect both the transmission bandwidth and confinement loss. The relative error between the inner diameter of the cladding capillary and the core diameter has a negligible effect on transmission performance, thus the fabricated fiber can reserve its intended optical properties.
3.3 Fiber characterization
To compare the measured loss of the fiber in the anti-resonant and resonant regions, as shown in Fig. 11, a 4.22-4.33 µm tunable quantum cascade laser (QCL) (DAYLIGHT, TLS-SK-41043-MHF) and a 4.79 µm semiconductor laser (Institute of Semiconductors, Beijing, China) were used as the laser sources, and the fiber loss was measured using the cut-back method. Both lasers were coupled into fiber through a ZnSe lens with a focal length of 4 mm which implies that the spot size is suitable. For the 4.22-4.33 µm measurement, a cut-back was performed by measuring the fiber loss 4 times (3 cuts) from 70 cm to 40 cm. At 4.79 µm, the output power was measured 3 times by the power meter from 40 cm to 20 cm (2 cuts). It should be noted that the theoretical loss was re-simulated according to the actual prepared fiber’s structural parameters, and the measured results (with a measured loss of 1.29 dB/m at 4.79 µm) match well with the theoretical loss curve (see Fig. 12). In addition, a lower fiber loss might be obtained by measuring the fiber at 4.5-4.6 µm band.
To evaluate the higher-order mode suppression properties of the ChG HC-ARF, the characteristic output beam profiles were measured at the output of a 20 cm long fiber at 4.79 µm, replacing the power meter with a beam profiler (DataRay, WinCamD-IR-BB). Figure 13 depicts a Gaussian-like output beam profile, indicating that such fiber supports nearly single mode. We also note a slight deformation of the beam profile and a part of off-centered energy, likely due to the glass nodes (which act as waveguides), a small bend of the fiber, or poor coupling.
4. Discussion
The measured fiber loss is slightly larger than the theoretical prediction, which may be explained by the fact that the glass nodes between the capillaries are larger than their theoretical counterparts. To this end, using the numerical modeling of ChG HC-ARF fiber with the same core size and capillary wall thickness but different glass node lengths L whose influence on the fiber’s performance was investigated, according to Fig. 14, where the lowest loss and low-loss bandwidth of the fiber significantly degrade as L changes from 0 to 30 µm, with the average confinement loss of 0.67 dB/m, 0.79 dB/m, 0.99 dB/m, 1.19 dB/m, 2.48 dB/m, 3.64 dB/m, and 4.14 dB/m, respectively. The corresponding bandwidths with confinement loss less than 0.5 dB/m are listed as 0.6 µm, 0.55 µm, 0.5 µm, 0.5 µm, 0.45µm, 0.4 µm, and 0.35 µm, respectively. These theoretical findings account for the occurrence of resonances between the core and cladding modes, induced by glass nodes, and consequently, such resonances lead to a degradation in fiber’s performance. In our numerical simulations, the L should be taken at a small value (< 20 µm) to obtain the lowest loss smaller than 0.1 dB/m in this ChG HC-ARF fiber for high-power MIR laser delivery.
Fig. 14. The calculated confinement loss as a function of the wavelength with different glass node lengths.
Although the glass nodes are practically unavoidable, their lengths (L) can be regulated by adjusting the manufacturing parameters during the process of fiber drawing, wherein the capillaries experience two phases, i.e., the “expansion phase” and the “contraction phase” [28]. The former is driven by applied pressure, and the surface tension results in the latter. When such expansion for the former is excessive, it is difficult to balance it and the contraction in the latter, resulting in the excessive touch of the capillaries and glass nodes. The expansion in the former can be reduced by determining the balanced pressure difference, and the deformation in both phases can be reduced by lowering the drawing temperature. It is, thus, anticipated that the ChG HC-ARFs with non-collapsed cladding structure, negative core-cladding boundary curvature, and smooth surface could be realized in experiments.
Thanks to a very low modal overlap factor (down to 10−5) [29] and a larger core diameter (a ChG step-index single-mode fiber designed for MIR bands typically has a core diameter of around 10 µm), the ChG HC-ARFs, compared to that of the ChG step-index single-mode fibers, have exceptionally high laser damage thresholds and almost negligible nonlinear impairments. Besides, a special cladding structure can improve the thermal stability during high-power laser delivery through such fibers [30]. In particular, silica HC-ARFs can achieve an improvement of two orders of magnitude in power or distance over that of large effective area silica glass-core fibers [7], stressing the possibility of the development of ChG HC-ARFs. In a word, the ChG HC-ARF combines the unique advantages of low loss, negligible nonlinearity, and high laser damage threshold, providing a potential route to deliver high-power MIR laser over long distances.
5. Conclusion
A seven-hole MIR ChG HC-ARF (novel structure) with touching cladding capillaries was designed and fabricated from purified As40S60 glass by combining the “stack-and-draw” method with a dual gas path pressure control technique. We find, from numerical modeling and experimental characterizations, that such novel fiber has higher-order mode suppression properties and several low-loss transmission bands in the MIR spectrum (with the measured loss of 1.29 dB/m at 4.79 µm). Significantly, further optimization of the drawing process and manufacturing parameters could reduce the experimental loss. Such fabrication methods, combined with the ChG HC-ARFs, open up a new possibility to implement flexible and reliable microstructured fibers with low loss for high-power MIR laser delivery.
Funding
National Natural Science Foundation of China (61935006, 62090065); Natural Science Foundation of Shaanxi Province (2023-JC-JQ-31); Open Fund of the Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications (Jinan University).
Acknowledgments
We thank Prof. Jianhua Zeng for improving the writing of the manuscript.
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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