Open Access
Add to BibSonomy
Abstract
As the Bragg fiber can guide light by tuning the structure parameters of claddings, it is possible to improve the ability of laser-power transmission in the mid-infrared with effective omnidirectional reflection, but it usually suffers from the disturbance of the air core and functional bandgap. Here, the structural parameters of three pairs of periodic cladding layers were optimized by the plane wave expansion method, and the thickness of each layer is 3.36 µm, consisting of Ge20As20Se15Te45 and As2S3 glasses with a refractive index contrast of Δn = 0.8. The simulation results showed that a wide bandgap of 1.2 µm can be realized in the fiber after structural optimization. Then, a fiber preform was prepared via an improved stacked extrusion based on seven thickness-compensated glass plates. The experimental results show that the all-solid Bragg fiber has three pairs of uniform periodic cladding and an extra-large core. The superior optical fiber structure can also be well maintained in the whole fiber length, and the average ratio of each cladding thickness to the fiber diameter is kept nearly at 3:100. Finally, the fiber loss at 1.55 µm and 2.94 µm is 12 dB/m and 18 dB/m, respectively. In all, such a well-structured all-solid chalcogenide Bragg fiber would pave a new way to develop high-quality laser transmission or optical sensors in mid-infrared.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The mid-infrared (MIR) wavelength region [1,2] is attractive for photonics, for example, a MIR sensor can detect many vital chemicals with their characteristic spectral absorption lines in this region due to molecular vibrations [3,4]. Traditional silica fiber cannot be used for MIR light transportation because of its strong intrinsic material absorption above 3 µm. On the contrary, the chalcogenide fiber possesses a broad infrared transmission range and thus is widely used in the MIR region. Especially chalcogenide Bragg fiber has shown its great potentials in the manufacture of high-quality fiber lasers [5] and optical fiber sensors [6] in MIR due to its unique optical properties such as tunable photonic bandgap (PBG) [7,8], single-mode transmission over a wide wavelength range [9,10], dispersion management [11,12] and low transmission loss [13,14].
Bragg fiber consists of a hollow core or low-index core surrounded by alternating concentric layers of high and low refractive index materials, it is first conceptualized by Yeh et al. [15]. The structure of the periodic layers can form a one-dimensional PBG that confines light in the core. Then, the optical characteristics of Bragg fiber, such as PBG, leakage loss, mode field distribution and effective mode field area, have been analyzed theoretically [16–18]. Hollow Bragg fiber has been used in CO2 laser transmission [19], spectral applications [20], and transverse resonant cavities [21]. But the structural instability of the hollow core greatly affects the fiber transmission properties. In principle, it has been reported that an all-solid structure could avoid the core collapse and cladding deformation [22–25]. Further development of all-solid Bragg fiber is limited by the lack of mature fabrication technology, thermal-matched materials with high contrast of refractive index, and a number of multi-layer. In 2004, Takashi et al. fabricated silica-core Bragg fiber with a wide bandgap of 1 µm by sputtering technique, and showed that the bandgap was easily tuned by thickness and index of the multilayer [26]. In 2005, Feng et al. reported a Bragg fiber based on glass stacking and extrusion, which had a circular glass core but varied cladding layers from 100 to 780 nm [25]. In 2007, Dupuis et al. reported a Bragg fiber with polymer core, in which the PBG position could be tuned by drawing fibers of different outside diameters [27]. Although all-solid Bragg fibers have shown great potentials in tuning bandgap, the experimental demonstrations have been limited to silica and polymer fibers, since it is challenging to choose thermal-matched materials and prepare accurate optical fiber structure based on other materials like chalcogenide glasses. So, it is urgent to develop novel fiber and effective fiber fabrication method based on other materials available.
In this work, an all-solid chalcogenide Bragg fiber with wide PBG was designed and fabricated via an improved stacked extrusion for the first time. The relationship between the PBG, confinement loss and fiber structural parameters were investigated in detail. The structural parameters of all-solid chalcogenide Bragg fiber with a wide bandgap of 1.2 µm were theoretically optimized. Two groups of fibers with uniform or non-uniform thickness glass were experimentally prepared. It is proved that the all-solid Bragg fiber with uniform cladding structure and negligible core deformation can be obtained based on thickness-compensated non-uniform glass plates. The fiber loss at 1.55 µm and 2.94 µm is 12 dB/m and 18 dB/m, respectively.
2. Fiber design
Figures 1(a) and (b) show the cross-sectional view and its refractive index profiles of the designed all-solid chalcogenide Bragg fiber, respectively. In Fig. 1 (a), the arrow shows radius direction from the center of the fiber. Along this direction, a low-index core is surrounded by the alternate layers with high and low refraction indices as shown in Fig. 1(b). The structure parameters include core radius R, radial multilayer period Λ, thicknesses of high index layer d1 and low index layer d2. The filling ratio is represented as F = d2/Λ. The refractive indices were alternately n1 and n2, where n1 > n2. Δn is the refractive index difference between high- and low-index layers. In Fig. 1(b), layer number M is 3 since there is 3 groups of the materials with periodic refractive index contrast. In this paper, the host material of low- and high-index layers is As2S3 and Ge20As20Se15Te45, respectively. Refractive indices of these glasses were measured by an IR ellipsometer (IR-VASE MARKII, J.A. WoollamCo.) as shown in Fig. 1(c), where the refractive index of Ge20As20Se15Te45 and As2S3 is 3.217 and 2.412 at 2 µm, respectively, and the refractive indices decrease with increasing wavelength. The large Δn of alternating layer materials can provide the possibility of forming the wide PBG. Furthermore, the glass transition temperature of As2S3 is very close to that of Ge20As20Se15Te45, which could be of great benefit to the preparation of the preforms and fibers.
Fig. 1. Cross section (a) and refractive index profile (b) of Bragg fiber; (c) Refractive index dispersion of Ge20As20Se15Te45 and As2S3 glasses.
To understand the characteristics of Bragg fiber, we first analyzed the PBG structure of the fiber by the plane wave expansion method (PWEM) [28]. The cladding had a periodic refractive index distribution, which can be regarded as one-dimensional PCF. The optical properties of the fiber were simulated using the full vector finite element method (FEM) [29,30], and a perfectly matched layer was added around the cladding to prevent energy leakage. Finally, the structural parameters of the Bragg fiber with a low leakage loss and a wide PBG were obtained.
3. Simulation and analysis
3.1 Fiber photonic bandgap
In the Bragg fiber, light is confined directly by the Bragg reflection of the multilayered claddings. Since the PBG properties of the fiber depend on Δn and F, the PBG can be tuned by designing the fiber cladding parameters. First, F was fixed at 0.5, and Δn was varied from 0.3 to 0.9. Figures 2(a)-(d) are the fundamental PBG with Δn of 0.3, 0.4, 0.6, and 0.8, respectively. Here, $\mathrm{Betap\;\ =\ \;\ \beta \Lambda }$ is the propagation constant and kΛ is the normalized frequency, the blue, red, and shaded regions correspond to the PBGs of the TE, TM, and hybrid modes, respectively. The variation trend of the PBG width and the normalized frequency are shown in Fig. 2(e). Blue and orange line represent the PBG width and the normalized frequency, respectively. The width of PBG gradually broadens, while the minimum normalized frequency of PBG decreases with increasing Δn. For each bandgap, the width of TE bandgap is close to that of TM bandgap near the vertical axis. But the TE bandgap is gradually wider than the TM bandgap with the increase of the wave vector. This is because of that, in the band structure of TM mode, the bandgap is reduced to zero when $\mathrm{\beta =\ (w/c)}{\textrm{n}_\textrm{2}}\textrm{sin}{\mathrm{\theta }_\textrm{B}}$, where ${\mathrm{\theta }_\textrm{B}}$ is the Brewster angle, and thus the incident wave at this angle cannot be coupled with the reflected wave. However, this angle does not exist in the TE mode.
Fig. 2. Fundamental PBG of the fiber at Δn of 0.3 (a), 0.4 (b), 0.6 (c) and 0.8 (d); (e) Variation of the PBG width (blue line, left axis) and the normalized frequency (orange line, right axis) with different Δn.
Then, with a fixing value of Δn = 0.8, F is changed from 0.1 to 0.9. Figures 3(a)-(d) are the fundamental PBG with F of 0.3, 0.5, 0.7, and 0.9, respectively. The width and normalized frequency of the fundamental PBG at different F are shown in Fig. 3(e). With the increase of F, the frequency of the PBG decreases monotonically, and the PBG width becomes broad firstly before F ≤ 0.5 and then narrow. From the results, the widest fundamental PBG can be obtained at a F value around 0.5 or 0.6.
Fig. 3. Fundamental PBG of fiber at F of 0.3(a), 0.5(b), 0.7 (c), and 0.9(d); (e) PBG width (blue, left axis) and normalized frequency (orange, right axis) of the fundamental PBG at different F.
We further compare the difference in high-order PBG in Fig.(s) 4(a) and (b) corresponding to F = 0.5 and 0.6, respectively. At F = 0.5, there are three wide high-order PBGs, and the widths of third and fourth PBGs are 0.18 and 0.16, respectively. But there are only one high-order PBG with a width of 0.18 at F = 0.6. The number of the high-order PBG with F = 0.5 is more than that with F = 0.6, and wider PBG enables multi-band light to be transmitted in the fiber. In all, the widest PBG can be obtained at F = 0.5.
Fig. 4. Comparison of high-order PBG when (a) F = 0.5, (b) F = 0.6; (blue area: TE mode; red area: TM mode; shaded area: Hybrid mode).
3.2 Fiber loss
With the fixed parameters of F = 0.5 and Δn = 0.8, we explore the influence of fiber structure parameters such as lattice period (Λ), core radius (R), layer number (M) on the fiber confinement loss (CL). The CL of the fiber is obtained from the imaginary part of the effective indices as shown in Eq. (1) [31], and the contribution from the scattering and absorption losses are not considered here.
In Fig. 4(a), the widest third bandgap was chosen to obtain a wider transmission range. The normalized frequency kΛ was defined at a value between 3.55-3.76. After mathematical transformation, the Λ was designed at a value between 6.56-6.88 µm. The CL curve as a function of Λ was presented in Fig. 5(a), where the other parameters are ncore = 2.367, n1 = 3.115, n2 = 2.367, R = 100 µm and M = 8, respectively. The loss initially decreases and then increases with increasing Λ, and the minimum loss of 6.79 × 10−4 dB/m for the fundamental mode (FM) appears at 6.72 µm. Furthermore, the inset of Fig. 5(a) shows the mode field distribution of FM in the proposed Bragg fiber with an optimized Λ=6.72 µm, where the light is well confined in the core.
Fig. 5. (a) CL curves as a function of Λ with R = 100 µm, F = 0.5 and M = 8 (inset: mode field distribution and intensity of FM at Λ=6.72 µm); (b) Variation of CL at different R with F = 0.5, M = 8 and Λ=6.72 µm (inset: mode field distribution of FM at R of 50 and 100 µm, respectively); (c) Variation of CL at different M with R = 100 µm, F = 0.5 and Λ=6.72 µm (inset: mode field distribution of FM at M of 2 and 6,respectively); (d) Reflectance for the Bragg fiber with Λ=6.72 µm, R = 100 µm, F = 0.5 and M = 6 (pale blue area: PBG windows).
We further optimized the structural parameters R and M. Figure 5(b) depicted the calculated CL as a function of R with Λ=6.76 µm, F = 0.5 and M = 8. The results show that the CL decreases with the increase of R. The insets in Fig. 5(b) are the mode field distribution of FM at R of 50 and 100 µm, respectively. It can be seen that, the mode field is more concentrated in the fiber with the increase of R from 50 to 100 µm. The loss curve as a function of M is illustrated in Fig. 5(c). When the layer number M changes from 2 to 6, the CL rapidly decreases from 0.11 dB/m to 0.005 dB/m. With further increase of M, the loss tends to keep nearly constant. It implies that further increase of the number of fiber cladding layers has no effect on the fiber loss. The insets of Fig. 5(c) are the mode field distribution of FM at M of 2 and 6. It can be seen that, increasing the number of cladding layers can effectively reduce the leakage of the mode field energy. Therefore, the layer number is optimized at 6 in the experiments of fiber drawing.
In all, the whole optimized fiber structure parameters are as follows: F = 0.5, Λ=6.72 µm, R = 100 µm and M = 6. The reflectance simulated from the optimized fiber structure is shown in Fig. 5(d), where the pale blue areas and non-pale blue areas indicates PBGs and photonic conduction band, respectively. The fiber has four PBG windows from 5.11 to 5.39 µm, 6.1 to 6.47 µm, 7.5 to 8.22 µm, 9.9 to 11.1 µm, respectively. The higher-order PBG at long wavelength is wider than the PBG at short wavelength, and the widest PBG appears in a range of 9.9 to 11.1 µm with a center wavelength of 10.5 µm.
4. Experiments
4.1 Glass synthesis
High purity Ge20As20Se15Te45 and As2S3 glasses were prepared by the conventional melt-quenching method. The pretreated high-purity raw materials of 5N were put into a quartz tube and melted in an evacuated ampoule that were subsequently melted in a swing furnace for 12 hours. After air quenching, Ge20As20Se15Te45 and As2S3 glasses were annealed at near transition temperature for 12 hours and then slowly cooled to room temperature. Finally, the core glass with a diameter of 9 mm and cladding glass with a diameter of 46 mm were obtained successfully. The prepared glasses were cut into glass slices with a thickness of ∼2 mm for preform fabrication, and their optical properties were characterized after optical polishing.
The transmission spectra of Ge20As20Se15Te45 and As2S3 glasses were measured by Fourier transform infrared spectrometer (Nicolet 380), as shown in Fig. 6(a). Although there are still a few impurity peaks such as O-H peak at 2.92 µm, S-H peak at 4.01 µm, Se-H peak at 4.12 µm and H2O peak at 6.31 µm. the glass transmittance is above 50% at a range from 2 to 12 µm. The glass transition temperature (Tg) was measured by differential scanning calorimetry (DSC) at a heating rate of 10 K/min. As shown in Fig. 6(b), the Tg of these glasses differ by only 11°C, and such a negligible difference of Tg can effectively avoid the deformation and eccentricity of the preform caused by the extrusion process [32,33].
Fig. 6. (a) Transmission spectra of the glasses (2 mm); (b) Differential scanning calorimetry curves of the glasses.
4.2 Fiber fabrication and propagation loss
Six pieces of Ge20As20Se15Te45 and As2S3 glasses with a thickness of 2 mm and a diameter of 46 mm were prepared as the periodic cladding materials, and a piece of As2S3 glass with a thickness of 15 mm and a diameter of 9 mm was used as the core. The Bragg fiber preform was prepared by an improved stacked extrusion process as shown in Fig. 7.
The As2S3 glass with a diameter of 9 mm was loaded into isolated inner barrel and six pieces of Ge20As20Se15Te45 and As2S3 glass with a diameter of 46 mm were alternately stacked in the outer barrel as shown in Fig. 7(a). Then, the core glass with the isolated barrel was extruded into the cladding under the pressure of vertical force in Fig. 7(b), until the core glass of As2S3 reaches the same horizontal position as the six pieces of Ge20As20Se15Te45 and As2S3 glass. Then, the cladding glass and the core glass were co-extruded at the same time in Fig. 7(c), forming an all-solid Bragg fiber preform with three pairs of periodic cladding layers. The fiber preform was shown in Fig. 7(d) with a typical length of 10-20 cm. Finally, the fiber preforms coated with PES polymer film were heated to 280°C and drawn into Bragg fiber under the protection of the inert argon gas to prevent fiber from oxidation.
Figure 8(a) is the cross-section image of the fiber. Because of the large index difference between the low-index and the high-index layers, the multilayer structure can be clearly observed. A 30-meter-long fiber with a diameter between 200 to 450 µm was drawn from the same preform in order to observe any possible structural deformation of the fibers with different diameter of D. The claddings were numbered from inside to outside, each cladding thickness was labelled as Ti (i = 1, 2, 3…). The change of the cladding thickness and the ratio of each layer thickness to the fiber diameter in long optical fiber is shown in Fig. 8(b), we can see that the thickness of each layer is extremely uneven, especially for the layers close to the fiber core. The thickness of the layers ranges from 1 to 100 µm. Such a variable thickness of each layer is far from the simulation results, in which each layer is fixed at 3.36 µm. Then such a 1m-long fiber was employed to evaluate the attenuation via the 1.55 µm laser using the cut-back method [4]. The fiber loss is 10 dB/m.
Fig. 8. (a)Cross-section image of the fiber; (b) Each layer thickness (all solid lines, left axis) and the ratio of each layer thickness to the fiber diameter (red dotted line, right axis); (c) Output spot diagram of the Bragg fiber.
Figure 8(c) is the output spot measured by a near-IR optic fiber field analyzer (Xenics, XEN000298) when a beam of 1.55 µm laser is coupled into the fiber. It can be seen that most of the light propagate in the cladding layers, since the inhomogeneity of Bragg fiber structure does not form PBG, making it impossible to completely confine light within the fiber core. Next, we try to improve the uniformity and optical properties of the overall structure of the fiber by optimizing glass thickness.
The material near the center of the extrusion die flows faster than that near the wall of the die during the extrusion, so that the thickness of each cladding ring decreases with increasing distance from the center [23,34]. Therefore, it should be possible to compensate for this non-uniformity via adjusting the thickness of the glass slices, in order to achieve preforms and fibers with controllable thickness of each ring [25]. We took the 2 mm glass plates corresponding to 6 µm cladding thickness of the fiber as the fixed proportion for the top layer in the six pieces of the glass plates as shown in Fig. 7(a), and compensated the size of the glass plates required for other layers according to this proportion. Finally, we obtained the glass plates with successively increasing thickness. The preparation process of the preform and fiber is consistent with the previous experiments. We again drawn a 30-meter-long fiber with the diameters between 200 to 400 µm. Cross-sectional photographs of the fiber with different lengths are shown in Fig. 9(a), where the fiber structure is highly circular and concentric and three pairs of periodic cladding are completely uniform in all cases. Compared four images in Fig. 9(a) for the fibers with different diameters, it also can be found that, the cladding layer becomes thinner with decreasing fiber diameter. This means that, the thickness of the cladding layer in the fiber with smaller diameter can satisfy optimized structural design with 3.36 µm thickness for each layer in Fig. 5(a).
Fig. 9. (a) The cross-section images of the Fibers with different diameters; (b) Each layer thickness (all solid lines, left axis) and the ratio of each layer thickness to the fiber diameter (red dotted line, right axis).
The thickness change of each layer in the long optical fiber and the ratio of each layer thickness to the fiber diameter is shown in Fig. 9(b), where the optical fibers with different diameters have similar cladding thickness with an error is less than 0.5 µm and almost constant of Ti/D. The maximum change of three pairs of the periodic cladding layers thickness is 2.3%, and the maximum change of each layer thickness is 6.3%. The average ratio of each layer thickness to the fiber diameter is about 3:100 in the whole fiber length of 30 m, and the minimum cladding thickness is about 6.14 ± 0.39 µm when the fiber diameter is 215 µm in a fiber length of 2 m. This demonstrates the feasibility of the use of thickness-compensated non-uniform glass plates to solve the problem of uneven cladding thickness in the fiber produced from uniform glass plates.
Since the minimum cladding thickness is about 6.14 ± 0.39 µm for the fiber we produced experimentally, we further simulated optical loss in the actual Bragg fiber from 1 to 7 µm, and the result is shown in Fig. 10(a), where many obvious low loss transmission windows in principle meets the requirements of PBG light guide. Then, unclad fiber was prepared using the core material and its loss was measured as shown in Fig. 10(b), where the fiber has some impurity absorption peaks such as O-H peak at 2.92 µm, S-H peak at 3.11 and 4.01 µm, and H2O peak at 6.31 µm. The minimum loss at a wavelength range of 1 to 7 µm is 4-5 dB/m. The theoretical total loss of the Bragg fiber as shown in Fig. 10(c) is approximately the sum of Fig.(s) 10(a) and (b), if the contribution of other factors to the total loss is ignored. Compared the value of the loss in Fig. 10(a) with that in Fig. 10(b), typical minimum loss in Fig. 10(a) is 0.5-3 dB/m, corresponding to the transmission windows for the Bragg fiber, while that in Fig. 10(b) is 4-5 dB/m, therefore, the matrix material has more significant impact on the overall loss level of the Bragg fiber. The loss of actual Bragg fiber was measured by 1.55 µm laser and 2.94 µm laser to be 12 dB/m and 18 dB/m, respectively, which are marked by red round and blue triangle in Fig. 10(c). The losses obtained from the lasers are basically consistent with the simulated total loss. The inset in Fig. 10(c) shows the output spot diagram when 1.55 µm light is coupled into 1 m Bragg fiber, most of the output energy is confined in the fiber core, and almost no energy is leaked into the cladding.
Fig. 10. (a) Calculated loss of the fiber with the cladding thickness of 6.14 µm; (b) The loss measured in the unclad fiber based on the core material; (c) Theoretical total loss; red round: loss at 1.55 µm; blue triangle: loss at 2.94 µm (inset shows output spot diagram from 1.55 µm laser).
5. Conclusion
In summary, we proposed an all-solid chalcogenide Bragg optical fiber consisting of periodic alternating layers of Ge20As20Se15Te45 and As2S3 glasses. The influences of filling ratio, periodic structure, and core size on photonic bandgap and confinement loss were investigated and the structure parameters of the fiber with a wide photonic bandgap of 1.2 µm were optimized. Then, we prepared two kinds of optical fibers based on uniform glass plates and thickness-compensated non-uniform glass plates, respectively. Further structural characterization showed that the use of thickness compensation glass plates can successfully fabricate an all-solid Bragg fiber with uniform layer thickness. The maximum change of three pairs of periodic cladding layers thickness is 2%, and the average ratio of the cladding thickness to fiber diameter is remained at 3:100 in a 30 m long fiber. The fiber has a minimum cladding thickness of about 6.14 ± 0.39 µm when the fiber outer diameter is 215 µm. The fiber loss at 1.55 µm and 2.94 µm is 12 dB/m and 18 dB/m, respectively, which are consistent with the simulated total loss of actual fiber structure. In all, we have developed a thickness-compensated method to control the thickness of the cladding layers, and realized all-solid chalcogenide Bragg fiber with wide PBG via the extrusion, and solve the hollow core depression and cladding deformation in the traditional Bragg optical fiber. The strategy we develop in the paper can be potentially used in the future to optimize the fiber structure and extrusion process to reduce the optical loss of the Bragg fiber.
Funding
National Natural Science Foundation of China (61875097, 61935006, 62205163, U22A2085); Zhejiang Provincial Natural Science Foundation of China (LQ21F050005, LY20F050010); Natural Science Foundation of Ningbo (2021J076); the Analysis and Measurement Foundation of Zhejiang Province (LGC19F050002); Ten-Thousands Talents Program of Zhejiang Province; Leading and top-notch personnel training project of Ningbo; Outstanding talent training program of Jiaxing; the K. C. Wong Magna Fund in Ningbo University.
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.
References
1. M. H. Zhong, X. L. Liang, J. Xiao, G. L. Wu, K. Jiao, X. G. Wang, T. S. Xu, J. Liu, Z. M. Zhao, X. S. Wang, R. P. Wang, Y. X. Zhou, P. Q. Zhang, Y. X. Liu, and Q. H. Nie, “Ultra-large mode area mid-infrared fiber based on chalcogenide glasses extrusion,” J. Am. Ceram. Soc. 104(1), 343–349 (2021). [CrossRef]
2. X. Feng, H. Ren, F. Xu, J. Shi, S. Qi, Y. Hu, J. Tang, F. Han, D. Shen, and Z. Yang, “Few-moded ultralarge mode area chalcogenide photonic crystal fiber for mid-infrared high power applications,” Opt. Express 28(11), 16658–16672 (2020). [CrossRef]
3. L. Wang, W. Ma, P. Zhang, L. Zhu, D. Yang, X. Wang, and S. Dai, “Mid-Infrared Gas Detection Using a Chalcogenide Suspended-Core Fiber,” J. Lightwave Technol. 37(20), 5193–5198 (2019). [CrossRef]
4. K. Jiao, J. Yao, X. G. Wang, X. Wang, Z. Zhao, B. Zhang, N. Si, J. Liu, X. Shen, P. Zhang, S. Dai, Q. Nie, and R. Wang, “1.2-15.2 µm supercontinuum generation in a low-loss chalcohalide fiber pumped at a deep anomalous-dispersion region,” Opt Lett 44(22), 5545–5548 (2019). [CrossRef]
5. S. Saitoh, K. Saitoh, M. Kashiwagi, S. Matsuo, and L. Dong, “Design Optimization of Large-Mode-Area All-Solid Photonic Bandgap Fibers for High-Power Laser Applications,” J. Lightwave Technol. 32(3), 440–449 (2014). [CrossRef]
6. O. Frazao, L. M. N. Amaral, J. M. Baptista, P. Roy, R. Jamier, and S. Fevrier, “Strain and Temperature Discrimination Using Modal Interferometry in Bragg Fibers,” IEEE Photonics Technol. Lett. 22(21), 1616–1618 (2010). [CrossRef]
7. J. Broeng, S. E. Barkou, T. Sondergaard, and A. Bjarklev, “Analysis of air-guiding photonic bandgap fibers,” Opt Lett 25(2), 96–98 (2000). [CrossRef]
8. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998). [CrossRef]
9. D. Mao, Z. Ouyang, J. C. Wang, and C. P. Liu, “Single-TM-mode Bragg fibers made of magnetic materials,” Opt. Express 16(2), 628–635 (2008). [CrossRef]
10. J. P. Yehouessi, O. Vanvincq, A. Cassez, M. Douay, Y. Quiquempois, G. Bouwmans, and L. Bigot, “Extreme large mode area in single-mode pixelated Bragg fiber,” Opt. Express 24(5), 4761–4770 (2016). [CrossRef]
11. P. Viale, S. Fevrier, P. Leproux, Y. Jaouen, and A. F. Obaton, “Modal properties of solid-core photonic bandgap, fibers,” Photonic Nanostruct 4(2), 116–122 (2006). [CrossRef]
12. W. Chen, S. Li, and P. Lu, “Dispersion-flattened Bragg photonic crystal fiber for large capacity optical communication system,” Frontiers of Optoelectronics in China 2(3), 289–292 (2009). [CrossRef]
13. K. J. Rowland, V. S. Afshar, and T. A. Monro, “Novel low-loss bandgaps in all-silica Bragg fibers,” J. Lightwave Technol. 26(1), 43–51 (2008). [CrossRef]
14. B. Hong, M. Swithenbank, N. Somjit, J. Cunningham, and I. Robertson, “Asymptotically single-mode small-core terahertz Bragg fibre with low loss and low dispersion,” J. Phys. D 50(4), 045104 (2017). [CrossRef]
15. P. Yeh, A. Yariv, and E. Marom, “Theory of Bragg fiber*,” J. Am. Ceram. Soc. 68(9), 1196–1201 (1978). [CrossRef]
16. C. Baskiotis, Y. Quiquempois, M. Douay, and P. Sillard, “Leakage loss analytical formulas for large-core low-refractive-index-contrast Bragg fibers,” J. Am. Ceram. Soc.B 30(7), 1945–1953 (2013). [CrossRef]
17. X. Ao, T. H. Her, and L. W. Casperson, “Gain guiding in large-core Bragg fibers,” Opt Express 17(25), 22666–22672 (2009). [CrossRef]
18. L. Shang, S. Feng, and G. Liu, “Hole-Assisted Solid Core Bragg Fibers With a High-Index-Contrast Cladding for Broadband Single-Polarization Operation,” J. Lightwave Technol. 38(21), 6104–6113 (2020). [CrossRef]
19. B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002). [CrossRef]
20. K. Kuriki, O. Shapira, S. Hart, G. Benoit, Y. Kuriki, J. Viens, M. Bayindir, J. Joannopoulos, and Y. Fink, “Hollow multilayer photonic bandgap fibers for NIR applications,” Opt. Express 12(8), 1510–1517 (2004). [CrossRef]
21. G. Benoit, K. Kuriki, J. F. Viens, J. D. Joannopoulos, and Y. Fink, “Dynamic all-optical tuning of transverse resonant cavity modes in photonic bandgap fibers,” Opt Lett 30(13), 1620–1622 (2005). [CrossRef]
22. E. Pone, C. Dubois, N. Gu, Y. Gao, A. Dupuis, F. Boismenu, S. Lacroix, and M. Skorobogatiy, “Drawing of the hollow all-polymer Bragg fibers,” Opt. Express 14(13), 5838–5852 (2006). [CrossRef]
23. D. J. Gibson and J. A. Harrington, “Extrusion of hollow waveguide preforms with a one-dimensional photonic bandgap structure,” J Appl Phys 95(8), 3895–3900 (2004). [CrossRef]
24. M. M. Zhu, X. S. Wang, Z. H. Pan, C. Cheng, Q. D. Zhu, C. Jiang, Q. H. Nie, P. Q. Zhang, Y. H. Wu, S. X. Dai, T. F. Xu, G. M. Tao, and X. H. Zhang, “Fabrication of an IR hollow-core Bragg fiber based on chalcogenide glass extrusion,” Appl Phys a-Mater 119(2), 455–460 (2015). [CrossRef]
25. X. A. Feng, T. M. Monro, P. Petropoulos, V. Finazzi, and D. J. Richardson, “Extruded single-mode high-index-core one-dimensional microstructured optical fiber with high index-contrast for highly nonlinear optical devices,” Appl Phys Lett 87(8), 081110 (2005). [CrossRef]
26. T. Katagiri, Y. Matsuura, and M. Miyagi, “Photonic bandgap fiber with a silica core and multilayer dielectric cladding,” Opt Lett 29(6), 557–559 (2004). [CrossRef]
27. A. Dupuis, N. Guo, B. Gauvreau, A. Hassani, E. Pone, F. Boismenu, and M. Skorobogatiy, “Guiding in the visible with “colorful” solid-core Bragg fibers,” Opt Lett 32(19), 2882–2884 (2007). [CrossRef]
28. C. Z. Li, W. Zhang, Y. D. Huang, and J. D. Peng, “Numerical study on Bragg fibers for infrared applications,” Int J Infrared Milli 26(6), 893–904 (2005). [CrossRef]
29. A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite-element method,” IEEE Photonics Technol. Lett. 14(11), 1530–1532 (2002). [CrossRef]
30. T. Fujisawa and M. Koshiba, “Finite element characterization of chromatic dispersion in nonlinear holey fibers,” Opt. Express 11(13), 1481–1489 (2003). [CrossRef]
31. K. Saitoh and M. Koshiba, “Leakage loss and group velocity dispersion in air-core photonic bandgap fibers,” Opt. Express 11(23), 3100–3109 (2003). [CrossRef]
32. K. Bhowmick, H. P. Morvan, D. Furniss, A. B. Seddon, and T. M. Benson, “Co-extrusion of multilayer glass fiber-optic preforms: prediction of layer dimensions in the extrudate,” J. Am. Ceram. Soc. 96(1), 118–124 (2013). [CrossRef]
33. D. Furniss and A. B. Seddon, “Thermal analysis of inorganic compound glasses and glass-ceramics,” Principles applications of thermal analysis 96, 410–449 (2008). [CrossRef]
34. E. Roeder, “Flow behaviour of glass during extrusion,” J. Non-cryst. Solids 7(2), 203–220 (1972). [CrossRef]
