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Abstract
A large mode-area chalcogenide all-solid anti-resonant fiber has been designed and successfully prepared for the first time. The numerical results show that the high-order mode extinction ratio of the designed fiber can reach 6000, and the maximum mode-area is 1500 um2. The fiber possesses a calculated low bending loss of less than 10−2 dB/m as the bending radius is larger than 15 cm. In addition, there is a low normal dispersion of -3 ps/nm/km at 5 μm, which is beneficial for the transmission of high power mid-infrared laser. Finally, a completely structured all-solid fiber was prepared by the precision drilling and two-stage rod-in-tube methods. The fabricated fibers transmit in the mid-infrared spectral range from 4.5 to 7.5 μm with the lowest loss of 7 dB/m @ 4.8 μm. Modeling suggests that the theoretical loss of the optimized structure is consistent with that of the prepared structure in the long wavelength band.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-power fiber lasers have wide applications in scientific research, medical diagnosis and treatment, manufacturing, and the military [1–3]. Many types of fibers for mid-infrared transmission have been developed in the past. However, these fibers have a low damage threshold and therefore are unsuitable for high-power transmission [4,5]. The use of large-mode-area fibers can effectively increase their power thresholds [6,7]. In general, increasing the core size increases the mode field area of the fiber. However, for traditional step fibers, the increase in core size leads to the multimode transmission of fibers. Therefore, it is urgent to develop a new fiber structure to achieve higher power transmission.
To date, different fiber designs have been proposed to achieve single-mode operation with large mode areas, including leakage channel fibers (LCFs) [8,9], large-pitch fibers (LPFs) [10–12], all-solid photonic bandgap fibers (AS-PBGFs) [13–15], and chirally coupled core fibers (CCCFs) [16,17]. The fibers with these structures all achieved large-mode-area characteristics, but the complex fabrication process hinders the further development of infrared chalcogenide fibers. In recent years, anti-resonant fiber (ARF) has attracted much interest thanks to its wide transmission bandwidth, low transmission loss, and high mode purity. Unlike traditional step fibers, the ARF is transmitted by an anti-resonant ring [18]. In addition, it can be designed with a large core size and can realize a single-mode operation [19–21]. At present, a variety of hollow ARFs based on chalcogenide glass have been successfully fabricated [22–24]. However, due to the brittleness of its material, the preparation of chalcogenide-based preforms with a uniform structure is challenging. The viscosity-temperature characteristics of chalcogenide glass cause certain deformation of the prepared fibers, making them unable to achieve the desired performance. In addition, due to the large refractive index difference between chalcogenide glass and air, the cladding tube thickness of the hollow core ARF is designed smaller, which further increases the difficulty of preparing. The all-solid structure can not only solve the problem of large refractive index difference of air-core ARF but also form a stable support structure, which is convenient for improving the accuracy of preparing fiber structures.
This paper proposed an all-solid anti-resonant fiber (AS-ARF) based on chalcogenide glass, in which the high refractive index ring is used as an anti-resonant element to achieve light conduction. The dependence of the normalized tube diameter d/Dcore, the tube thickness t, and the core diameter Dcore on fiber structure parameters was discussed. Theoretically, when d/Dcore = 0.68, the high-order mode extinction ratio (HOMER) is more than 6000. When the Dcore reaches 100 μm, the ARF has a mode field area greater than 5000 μm2 with a HOMER of 17000. The fiber possesses a caculated low bending loss less than 10−2 dB/m when the bending radius excceds 15 cm, as well as a low dispersion less than ±20 ps/nm/km at 5–6.9 μm wavelength. Finally, we successfully prepared an AS-ARF based on the drilling and two-stage rod-in-tube methods.
2. Model and theory
2.1 Fiber structure and analysis method
We designed a chalcogenide AS-ARF with a hexagonal arrangement of the anti-resonant rings, as shown in Fig. 1(a). The core is As2S3 material, and the cladding tubes are Ge10As22Se68 with a high refractive index ring. Differs from the traditional step-index fiber, the proposed structure conducts light according to the mechanism of anti-resonant. The structural parameters are defined as follows, the core diameter is Dcore, the cladding tube diameter is d, and the cladding tube thickness is t. Figure 1(b) shows the refractive index of the core and the cladding tubes in 2–14 μm measured by an infrared ellipsometer (IR-VASE MARKII, J. A. Woolllam Co.). Numerical simulations were carried out using the commercial software Comsol Multiphysics based on the finite element method (FEM). The well-optimized perfectly matched layer (PML) thickness and meshing were defined during the simulation. We calculate the convergence diagram of the simulation results, and the relative tolerance decreases with the number of iterations. When the number of iterations is 6, the relative tolerance is as low as 10−6, which indicates the convergence of the simulation calculation. The Sellmeier coefficient can be calculated by the Sellmeier equation based on the measured refractive indices [25]:
Fig. 1. (a) The schematic of the AS-ARF; (b) Measured refractive indices of the core and cladding materials.
Table 1. Refractive coefficient of glasses
According to the anti-resonant reflection theory, the design of the capillary thickness needs to satisfy the anti-resonant condition. The resonant thickness and anti-resonant thickness are calculated from the equations [28]:
where λ is the wavelength, ni (i = 1,2) are the refractive indexes of two different materials, and m is an integer, representing the order of the resonance.Loss is an important indicator in evaluating the performance of optical fibers. In general, the loss of ARF is dominated by the confinement loss [28], which can be expressed as:
where λ is the operating wavelength, Im(neff) represents the imaginary part of the effective refractive index. The effective mode area (Aeff) is given by the following Eq. (5) [7]:3. Results and discussion
3.1 Optimization of the fiber structure
The FEM is adopted to optimize the parameters and performance of AS-ARF. There are some differences in the energy distribution of the ARF at the resonant thickness and the anti-resonant thickness. In this section, we calculate the light field distribution at the anti-resonant wavelength and resonant wavelength of the fiber with the parameters of Dcore = 60 μm, d = 36 μm, and t = 5 μm. According to Eq. (3), the third anti-resonant wavelength is 3.64 μm and the second resonant wavelength is 4.56 μm. As can be seen from Fig. 2(a) and (b), the energy intensity of the fundamental mode under resonant conditions is much less than that of the anti-resonant conditions. Furthermore, a part of the light in the core under resonant conditions is leaked into the cladding, corresponding to Fig. 2(c). In this circumstance, the ability of fibers to confine light is greatly weakened. On the contrary, the light is well bound in the core under anti-resonant conditions. Figure 2(d) shows a small amount of energy exisiting in the cladding, which is relatively negligible.
Fig. 2. The fundamental mode under resonant conditions (a) and anti-resonant conditions (b). Energy intensity distribution for resonant conditions (c) and anti-resonant conditions (d).
In addition, we calculated the effect of different thicknesses (t) on the effective refractive index and confinement loss. As shown in Fig. 3, the two spectra of the fundamental mode exhibit significant resonant characteristics, which is consistent with the trend of hollow-core anti-resonant fibers. At a wavelength of 3.64 μm, the resonant thickness is calculated by Eq. (2) to be 2 μm, 4 μm, and 6 μm, respectively. When resonant coupling occurs, the loss is large at the corresponding wavelength, and the effective refractive index changes abruptly. When the wavelength at 1 μm, 3 μm, and 5 μm, the loss reaches the minimum, corresponding to the anti-resonant wavelength calculated by Eq. (3). These results indicate that the light-guiding mechanism of all-solid anti-resonant fibers is still the same as that of hollow anti-resonant fibers. Based on the feasibility of the preparation, we selected the third anti-resonant thickness (t = 5 μm) for subsequent manufacture.
Fig. 3. Effective refractive index (a) and confinement loss (b) of the fundamental mode as a function of capillary thickness t. The structural parameters are set as Dcore = 60 μm, d/Dcore = 0.6, λ= 3.64 μm.
3.2 Single mode characteristics of the AS-ARF
In the transmission process, the large mode-area and single mode operation of the fiber are indispensable. We studied the influence of fiber structure parameters on single-mode performance. In general, the fundamental mode loss of the fiber is less than 0.1 dB/m, and the minimum high-order mode loss is higher than 1 dB/m. The fiber can be considered a single-mode operation.
The thickness of the anti-resonant elements is set to 5 μm, corresponding to the third anti-resonant thickness. Figure 4 shows the four mode field distributions that may occur in different d/Dcore. In Fig. 5(a), we calculated the loss and the ratio of the fundamental mode and the LP11 mode with different d/Dcore. Under the condition of 0.5 < d/Dcore < 0.75, the loss of LP01 mode increases slowly. However, when d/Dcore > 0.78, the LP01 loss increases rapidly, because the gap between tubes is smaller, which leads to the deepening of coupling with tube mode [22]. The loss of LP11 increases first and then decreases due to the couplings with the cladding mode (CM). It is worth noting that the loss of LP11 reaches the maximum when d/Dcore = 0.68, and the corresponding mode field distribution was shown in Fig. 4(d). The violent couplings between LP11 and CM in the region between adjacent capillaries can explain this phenomenon.
Fig. 5. The loss spectra of LP01 mode (solid yellow) and LP11 mode (solid green), as well as the HOMER (solid red line on the right axis) with a variation of the normalized tube-diameter ratio d/Dcore (a), and the core diameter Dcore (b). The parameters of (a) are Dcore = 60 μm, t = 5 μm, λ = 3.64 μm. The parameters of (b) are d/Dcore = 0.68, t = 5 μm, λ = 3.64 μm.
Based on the optimal parameters of d/Dcore, the confinement loss and HOMER curves with respect to the core diameter were presented in Fig. 5(b). It can be observed that the loss of LP01 and LP11 reduce gradually as Dcore increases. When 40 μm < Dcore < 100 μm, the loss has unstable fluctuations, caused by the Fano resonances generated by different core diameters [30]. In addition, the proposed fiber has a HOMER of more than 3000 (solid red line) over the Dcore range from 40 μm to 100 μm. In current technology, the glass tubes with a thickness limit of 1.2 mm can be prepared. After drawing into a thin rod, the ratio of the thickness of the high refractive index ring to the outer diameter of the thin rod is certain. In order to approach the optimal normalized tube-diameter ratio (d/Dcore = 0.68), the core diameter can be prepared up to 60 μm.
3.3 Mode area and dispersion characteristics
Moreover, we investigated how the core diameter scaling affect on mode field area. It can be seen from Fig. 6(a), the Aeff of LP01 modes increase with increasing Dcore, and when Dcore reaches 100 μm, the Aeff exceed 5000 μm2 at the wavelength of 3.64 μm. Then the dispersion characteristics of the designed ARF has been investigated by the Eq. (6). In order to avoid the resonant band with the wavelength of 4–5 um, the dispersion of 3.1–3.9 μm and 4.7–6.9 μm were calculated, respectively. As is shown in Fig. 6(b), the AS-ARF has a zero dispersion wavelength of 5.09 μm, and the fiber has a low dispersion between −8.5 and 16.5 ps/nm/km in 4.9–6.9 μm. From the illustration of Fig. 6(b), it is obvious that the fiber possesses normal dispersion in the 3.1–3.9 μm wavelength range.
Fig. 6. (a) Calculated Aeff of the LP01 mode at 3.64 μm when Dcore increases from 40 μm to 100 μm. The parameters are d/Dcore = 0.68, t = 5 μm, λ = 3.64 μm. (b) Variation of dispersion (D) with wavelength for the designed ARF.
3.4 Bend characteristics
The large mode-area fiber is sensitive to the change of bending condition, so it is meaningful to conside the bending loss of the designed fiber. When the fiber was bent along the positive direction of the x-axis, the equivalent refractive index distribution was calculated as follows [26]:
where nR and n are the equivalent refractive index after bending of the fiber and the initial refractive index of the straight fiber, respectively, x is the coordinate along the x-axis positive direction, R is the bending radius, Reff is bending radius after introducing elastooptic correction factor and Reff=1.28R.In this section, the structural parameters are fixed at Dcore = 60 μm, d = 36 μm, t = 5 μm, and λ = 4 μm. We calculated the bending loss of the LP01 mode under different bending radius, as shown in Fig. 7(a). $LP_{01}^x$ and $LP_{01}^y$ represent the two different polarization states of the FM. The bending loss of x-polarized mode is higher than that of y-polarized mode. When the bending radius exceeds 15 cm, the loss gradually decreases as the bending radius increases and tends to be flat. There are two high loss peaks in the bending loss curves for both the x-polarized and y-polarized modes. From the Fig. 7(b)–(e), it can be seen that at the bending radius of 5.5 cm and 11.5 cm, the core mode and the tube mode are coupled, corresponding to the loss peak in Fig. 7(a).
Fig. 7. (a) Relationship between bending loss and bend radius of FM. (b) – (e) The x-polarized and y-polarized modes at bend radius of 5.5 cm and 11.5 cm. The arrows represent the direction of the transverse electric field.
4. Fiber fabrication and optical measurements
4.1 Preparation of glass and perform
High-purity glasses including matrix glass As2S3 and anti-resonant elements Ge10As22Se68 were prepared through the conventional melt-quenching method [31]. The metal Mg is added to the high-purity raw material (Ge, As, S, and Se with a purity of 5 N) to remove oxide impurities for distillation purification. Finally, As2S3 glasses with a diameter of 10 mm and Ge10As22Se68 glasses with a diameter of 20 mm were prepared. The glass samples was cut with a thickness of 2 mm and polished on both sides to prepare for measuring their thermal and optical properties.
The transmission spectra of As2S3 and Ge10As22Se68 glasses were measured by Fourier transform infrared spectrometer (Nicolet 380), which was shown in Fig. 8(a). There are only a slight impurity such as S-H peak at 4.01 μm and Se-H peak at 4.50 μm [32], and the transmittance is higher than 60%. The transition temperature (Tg) was measured using DSC (TA Q2000) at a heating rate of 10 °C/min under the protection of a flowing N2 atmosphere. As is shown in Fig. 8(b), the Tg of As2S3 is 188 ℃, which is a slightly lower than that of Ge10As22Se68 glass (173 ℃). Their thermal performance is compatible, so they can be drawn into fibers at the same temperature.
Fig. 8. (a) Transmission spectra of As2S3 and Ge10As22Se68 glasses; (b) DSC of Ge10As22Se68 and As2S3 glasses in 25–300 °C range.
The fiber preform was prepared by the drilling and the two-stage rod-in-tube techniques [33,34]. The all-solid microstructured fiber was a six-hole structure with core material of As2S3, and air holes are replaced by Ge10As22Se68-As2S3 glass rods. First, the Ge10As22Se68 glass (an outer diameter of 20 mm) was drilled by a computerized numerical control (CNC) precision machine to create a ∼10.6 mm diameter hole among its axes. The precision of the equipment is up to 10 μm, so we can precisely locate the position of the holes. Then as shown in Fig. 9(a), it was polished to an outer diameter of 13 mm and a thickness of 1.2 mm in a self-made mold. After this, the As2S3 glass (a diameter of 10.5 mm) was insert into the polished Ge10As22Se68 cladding tube, and drawn into six elonged thin-rods with a diameter of ∼1.7 mm. The six-hole As2S3 microstructure preform was drilled with a hole diameter of 1.7 mm and a hole pitch of 2.1 mm, as shown in Fig. 9(b). Finally, the six elongated Ge10As22Se68-As2S3 rods were inserted into the six-hole As2S3 preform to obtain an AS-ARF preform, as shown in Fig. 9(c).
Fig. 9. (a) the rod preform for the primary casing (the thickness and outer diameter of Ge10As22Se68 are 1.2 mm and 13 mm, respectively). (b) Cross section of the preform (the hole diameter is 1.7 mm; the hole pitch is 2.1 mm). (c) As2S3-Ge10As22Se68 AS-ARF preform.
4.2 Drawing and testing of the ARF
Then, the six-hole preform with six rods was drawn into ARFs with a fiber-drawing tower (SGC, customized, UK), a negative pressure of vacuum pump was used to extract the air between the holes and the rods. At the same time, the feed speed, drawing speed, pumping air pressure and other drawing parameters are precisely controlled, and the appropriate pumping pressure is the key parameter to make the structure fit closely. In addition, the preform was wrapped with two-layer PES (polyethersulfone) polymer films before drawing to increase the mechanical robustness of the fibers. During the pulling process of AS-ARF, high-purity argon gas (99.999%) is used to prevent oxidation of the preform. The fiber cross-section was observed by an optical microscope (Keyence, VHX-1000). The Fourier spectrometers were used to test the loss of fibers.
Figure 10(a) shows the cross-section of an AS-ARF prepared at a negative pressure of 40 mbar. Based on the negative pressure, the fiber structure is complete and there are no obvious defects. The fiber has an outer diameter of 304 μm, a core diameter of 60 μm, a tube diameter of 36 μm, and an average capillary thickness of ∼5 μm with a standard deviation of 0.3 μm. The attenuation of the fibers in the wavelength range of 2.5-8.0 μm evaluated by the cut-back method with the aid of FTIR is shown in Fig. 10(c). The results indicate that the AS-ARF exhibited a minimum loss of 7 dB/m at the wavelength of 4.8 μm. The absorption bands at 3.11, 4.01, 5.02, 6.31, and 7.8 μm were assigned to S-H, As-H, H2O and CS2 impurity bonds [35], respectively. After the 2.09 μm light source was coupled into the fiber, the near-field optical energy distribution image in the fiber was recorded via a near-IR optic fiber field analyzer (Xenics, XEN-000298) as shown in the insert of Fig. 10(c). It can be seen that the energy in the core is the strongest, while there is almost no energy in the six cladding tubes. This phenomenon proves the ability to light guiding for the fiber. In addition, the laser light coupled into the cladding is transmitted in a cored structure formed between the cladding glass and the air. Therefore, we can observe that there is energy in the outer layer.
Fig. 10. (a) Cross section of fabricated Ge10As22Se68-As2S3 AS-ARF; (b) The refractive index profile along the x-axis; (c) Transmission loss and near-field optical energy distribution image of the fabricated fibers.
According to the actually prepared AS-ARF cross-section, a numerical model was established, and the experimental data were compared with the simulation results. The theoretical loss calculated by the FEMs was shown in Fig. 11. According to the thickness of the actually prepared capillary, the calculated anti-resonant wavelengths are 6.08 μm and 3.65μm. In general, the calculated loss of the actual preparation of AS-ARF is very consistent with the design results. The difference in the loss spectrum comes from a slight structure distortion of the capillaries [36]. In the future, the loss can be reduced to a lower level by optimizing the capillary diameter and uniformity.
Fig. 11. The confinement loss changes with the wavelength. Orange line: the theoretical value of the optimized structure; blue line: the theoretical value modeled according to the actual fiber structure.
5. Conclusions
We proposed an all-solid chalcogenide-based ARF and investigated its optical characteristics, including mode area and HOMER. Through the optimized structure, the HOMER can reach more than 17000 with an ultra-large fundamental mode area of 5000 μm2 when Dcore = 100 μm. The AS-ARF shows the excellent bending resistance even with a small bending radius of tens of centimeters, and has a low normal dispersion of -3 ps/nm/km at 5 μm. Meanwhile, the chalcogenide-based AS-ARF was experimentally fabricated with a minimum loss of 7 dB/m based on the drilling and rod-in-tube methods. To our best knowledge, it is the first time to prepare the chalcogenide-based AS-ARF successfully. By further reducing background loss, the AS-ARF shows great potential for propagating high-power lasers in the mid-infrared region.
Funding
National Natural Science Foundation of China (61975086, U21A2056); Key Research and Development Program of Zhejiang Province (2021C01025); Fundamental Research Funds for the Provincial Universities of Zhejiang (SJLY2022004); Opening Project of Key Laboratory of Optoelectronic Detection Materials and Devices of Zhejiang Province (KLPMD2110); K. C. Wong Magna Fund at Ningbo University.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper may be available from the corresponding author upon reasonable request.
References
1. S. D. Jackson, A. Sabella, and D. G. Lancaster, “Application and Development of High-Power and Highly Efficient Silica-Based Fiber Lasers Operating at 2 μm,” IEEE J. Sel. Topics Quantum Electron. 13(3), 567–572 (2007). [CrossRef]
2. Y. Kawahito, T. Terajima, H. Kimura, T. Kuroda, K. Nakata, S. Katayama, and A. Inoue, “High-power fiber laser welding and its application to metallic glass Zr55Al10Ni5Cu30,” Materials Science and Engineering: B 148(1-3), 105–109 (2008). [CrossRef]
3. B. Azadgoli and R. Y. Baker, “Laser applications in surgery,” Ann Transl Med 4(23), 452 (2016). [CrossRef]
4. S. Sato, K. Igarashi, M. Taniwaki, K. Tanimoto, and Y. Kikuchi, “Multihundred-watt CO laser power delivery through chalcogenide glass fibers,” Appl. Phys. Lett. 62(7), 669–671 (1993). [CrossRef]
5. A. Sincore, J. Cook, F. Tan, A. El Halawany, A. Riggins, S. McDaniel, G. Cook, D. V. Martyshkin, V. V. Fedorov, S. B. Mirov, L. Shah, A. F. Abouraddy, M. C. Richardson, and K. L. Schepler, “High power single-mode delivery of mid-infrared sources through chalcogenide fiber,” Opt Express 26(6), 7313–7323 (2018). [CrossRef]
6. J. Ji, S. Raghuraman, X. Huang, J. Zang, D. Ho, Y. Zhou, Y. Benudiz, U. B. Ami, A. A. Ishaaya, and S. Yoo, “115 W fiber laser with an all solid-structure and a large-mode-area multicore fiber,” Opt Lett 43(14), 3369–3372 (2018). [CrossRef]
7. Y. Zhang, Y. Lian, Y. Wang, J. Wang, M. Yang, N. Luan, Y. Wang, and Z. Lu, “Study on dual-mode large-mode-area multi-core fiber with air-hole,” Opt. Fiber Technol 65, 102595 (2021). [CrossRef]
8. K. Saitoh, Y. Tsuchida, L. Rosa, M. Koshiba, F. Poli, A. Cucinotta, S. Selleri, M. Pal, M. Paul, and D. Ghosh, “Design of all-solid leakage channel fibers with large mode area and low bending loss,” Opt. Express 17(6), 4913–4919 (2009). [CrossRef]
9. M. Pal, K. Saitoh, M. C. Paul, D. Ghosh, and S. K. Bhadra, “Design and Fabrication of Large-Mode Area Air-Clad Leakage Channel Fiber With Superior Bending Characteristics,” IEEE Photonics Technol. Lett. 24(18), 1650–1652 (2012). [CrossRef]
10. J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Sci. Appl. 1(4), e8 (2012). [CrossRef]
11. L. Wang, D. He, C. Yu, S. Feng, L. Hu, and D. Chen, “Very Large-Mode-Area, Symmetry-Reduced, Neodymium-Doped Silicate Glass All-Solid Large-Pitch Fiber,” IEEE J. Sel. Topics Quantum Electron. 22(2), 108–112 (2016). [CrossRef]
12. A. Steinkopff, C. Jauregui-Misas, F. Stutzki, J. Nold, C. Hupel, N. Haarlammert, J. Bierlich, A. Tünnermann, J. Limpert, L. Dong, and A.L. Carter, “Single-mode propagation with 205 µm mode-field diameter in a passive large pitch fiber,” Proc. SPIE 10897, 108970W (2019). [CrossRef]
13. L. Dong, F. Kong, G. Gu, T. W. Hawkins, M. Jones, J. Parsons, M. T. Kalichevsky-Dong, K. Saitoh, B. Pulford, and I. Dajani, “Large-Mode-Area All-Solid Photonic Bandgap Fibers for the Mitigation of Optical Nonlinearities,” IEEE J. Sel. Topics Quantum Electron. 22(2), 316–322 (2016). [CrossRef]
14. O. Vanvincq, A. Cassez, R. Habert, H. El Hamzaoui, K. Baudelle, S. Plus, D. Labat, M. Bouazaoui, Y. Quiquempois, G. Bouwmans, F. Audo, T. Chartier, E. Lallier, and L. Bigot, “Large Mode Area Solid-Core Photonic Bandgap Yb-Doped Fiber With Hetero-Structured Cladding for Compact High-Power Laser Systems,” J. Lightw. Technol. 39(14), 4809–4813 (2021). [CrossRef]
15. X. Chen, L. Huang, X. Xi, H. Yang, Y. An, Z. Yan, Z. Pan, and P. Zhou, “Leakage channels enabled multi-resonant all-solid photonic bandgap fiber for effective single-mode propagation,” Opt. Express 29(14), 22455–22469 (2021). [CrossRef]
16. X. Ma, C. Zhu, I. N. Hu, A. Kaplan, and A. Galvanauskas, “Single-mode chirally-coupled-core fibers with larger than 50 microm diameter cores,” Opt. Express 22(8), 9206 (2014). [CrossRef]
17. H. Zhang, H. Hao, L. He, and M. Gong, “Single-mode annular chirally-coupled core fibers for fiber lasers,” Opt. Commun. 410, 297–304 (2018). [CrossRef]
18. C. Wei, R. Joseph Weiblen, C. R. Menyuk, and J. Hu, “Negative curvature fibers,” Adv.Opt.Photonics 9(3), 504–561 (2017). [CrossRef]
19. M. S. Habib, J. E. Antonio-Lopez, C. Markos, A. Schulzgen, and R. Amezcua-Correa, “Single-mode, low loss hollow-core anti-resonant fiber designs,” Opt. Express 27(4), 3824–3836 (2019). [CrossRef]
20. Z. Xing, X. Wang, S. Gu, and S. Lou, “Large mode area double-layer all-solid anti-resonant fiber for high-power fiber lasers,” Results Phys. 29, 104700 (2021). [CrossRef]
21. Z. Xing, X. Wang, S. Lou, Z. Tang, H. Jia, S. Gu, and J. Han, “Large-mode-area all-solid anti-resonant fiber with single-mode operation for high-power fiber lasers,” Opt. Lett. 46(8), 1908–1911 (2021). [CrossRef]
22. A. N. Kolyadin, A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. G. Plotnichenko, and E. M. Dianov, “Light transmission in negative curvature hollow core fiber in extremely high material loss region,” Opt. Express 21(8), 9514 (2013). [CrossRef]
23. J. Carcreff, F. Cheviré, E. Galdo, R. Lebullenger, A. Gautier, J. L. Adam, D. L. Coq, L. Brilland, R. Chahal, G. Renversez, and J. Troles, “Mid-infrared hollow core fiber drawn from a 3D printed chalcogenide glass preform,” Opt. Mater. Express 11(1), 198–209 (2020). [CrossRef]
24. A. Ventura, J. G. Hayashi, J. Cimek, G. Jasion, P. Janicek, F. B. Slimen, N. White, Q. Fu, L. Xu, H. Sakr, N. V. Wheeler, D. J. Richardson, and F. Poletti, “Extruded tellurite antiresonant hollow core fiber for Mid-IR operation,” Opt. Express 28(11), 16542–16553 (2020). [CrossRef]
25. G. Ghosh, M. Endo, and T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical fiber glasses,” J. Lightw. Technol. 12(8), 1338–1342 (1994). [CrossRef]
26. J. Xiao, J. Wang, T. Xu, M. Zhong, X. Liang, J. Shen, X. Wang, Z. Zhao, J. Wang, G. Wu, Z. Feng, X. Shen, Q. Nie, and R. Wang, “Large mode-area chalcogenide multicore fiber prepared by continuous two-stage extrusion,” Opt. Mater. Express 11(3), 104700 (2021). [CrossRef]
27. J. Tu, B. Zhang, Z. Liu, X. Zhou, K. Long, Z. Li, C. Lu, and C. Yu, “Chalcogenide-Glass Nested Anti-Resonant Nodeless Fibers in Mid-Infrared Region,” J. Lightw. Technol. 36(22), 5244–5253 (2018). [CrossRef]
28. F. Poletti, “Nested antiresonant nodeless hollow core fiber,” Opt. Express 22(20), 23807–28 (2014). [CrossRef]
29. J. Wang, “Numerical investigation of high birefringence and nonlinearity tellurite glass photonic crystal fiber with microstructured core,” Appl. Opt. 60(15), 4455–4461 (2021). [CrossRef]
30. L. Vincetti and V. Setti, “Extra loss due to Fano resonances in inhibited coupling fibers based on a lattice of tubes,” Opt. Express 20(13), 14350–14361 (2012). [CrossRef]
31. M. Meneghetti, C. Caillaud, R. Chahal, E. Galdo, L. Brilland, J.-L. Adam, and J. Troles, “Purification of Ge-As-Se ternary glasses for the development of high quality microstructured optical fibers,” J. Non-Cryst. Solids 503-504, 84–88 (2019). [CrossRef]
32. A. E. Kurganova, G. E. Snopatin, and M. F. Churbanov, “Purification of glass melts in the As-Se system with vacuum distillation,” Glass Phys. Chem. 38(3), 300–306 (2012). [CrossRef]
33. B. Zhang, W. Guo, Y. Yu, C. Zhai, S. Qi, A. Yang, L. Li, Z. Yang, R. Wang, D. Tang, G. Tao, B. Luther-Davies, and P. Lucas, “Low Loss, High NA Chalcogenide Glass Fibers for Broadband Mid-Infrared Supercontinuum Generation,” J. Am. Ceram. Soc. 98(5), 1389–1392 (2015). [CrossRef]
34. X. Zhang, Z. Liu, Y. Gui, H. Gan, Y. Guan, L. He, X. Wang, X. Shen, and S. Dai, “Characteristics and preparation of a polarization beam splitter based on a chalcogenide dual-core photonic crystal fiber,” Opt. Express 29(24), 39601–39610 (2021). [CrossRef]
35. M. F. Churbanov, A. P. Velmuzhov, M. V. Sukhanov, G. E. Snopatin, I. V. Skripachev, and V. G. Plotnichenko, “Arsenic-sulfide glasses with low content of hydrogen impurity for fiber optics,” Opt. Mater. 77, 87–92 (2018). [CrossRef]
36. W. Zheng, Y. Qin, O. Xu, M. Xiang, D. Peng, S. Fu, and J. Li, “Wideband low confinement loss anti-resonant hollow core fiber with nested U-shape tube,” Opt. Express 29(15), 24182–24192 (2021). [CrossRef]
