A large mode-area (LMA) chalcogenide multicore fiber (MCF) with 13 hexagonally arranged cores has been designed and fabricated for mid-infrared (MIR) high power laser delivery. The dependence of mode distributions, bending loss and dispersion characteristics on the fiber structure parameters has been investigated by the method of finite element analysis at a wavelength range from 3 to 5 μm. An ultra-large fundamental mode (FM) effective area of ∼8000 μm2 as well as a low normal dispersion down to -46 ps/nm/km at 3 μm are theoretically obtained, which is of great benefit to high power MIR laser delivery. The fiber possesses a calculated low bending loss less than 0.075 dB/m as the bending radius is larger than 0.4 m. Finally, a well-structured 13-core fiber consisting of Ge9As23Se68 and Ge10As22Se68 glasses is fabricated via the continuous two-stage extrusion method, and this fiber shows a low optical loss of 0.28 dB/m at 6.6 µm, which is the lowest fiber loss for a micro-structured chalcogenide fiber obtained via extrusion, to the best of our knowledge.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Fibers with a large-mode area (LMA) have attracted much attention, especially in the field of fiber amplifiers, fiber lasers and high-power laser delivery systems , because the decrease of the the nonlinear effects and transverse mode instability [2,3] in the LMA fibers can enhance the power threshold of the fibers. Generally, large effective mode-area (Aeff) of the fiber can be achieved by increasing the core size and thus decreasing nonlinear effects, or by reducing numerical aperture (NA) and thus decreasing amplified spontaneous emission (ASE) . However, the increase of the core diameter makes the fiber multi-moded. Furthermore, it is difficult to have conventional step-index fibers with very small NA values. Therefore, various kinds of LMA optical fibers have been studied, for example, chirally coupled core fibers , leaky channel fibers , large-pitch photonic-crystal fibers , multi-trench fibers , or asymmetric core fibers . All of them were investigated through selective doping  or mode-differentiated losses . Moreover, most of these LMA fibers were based on photonic crystal fibers (PCFs), which were relatively complex and expensive to be fabricated, and also difficult to be cleaved and spliced .
Recently, multicore fibers (MCFs) have been introduced as a candidate for the LMA fibers because of their flexible design in controlling the optical properties of the modes compared with the conventional optical fibers. The individual cores of the MCFs can be separated with enough space or placed closely, corresponding to the uncoupled and coupled MCFs, respectively. The coupled MCFs are expected to be used in phase locking and coherent beam combing (CBC) which has been investigated intensively during the past few years, because they are promising to achieve larger mode field area and output power . M. M. Vogel et al. reported a measured LMA of 465 μm2 at 1.05 μm from a evanescently coupled single-mode MCF with 19 hexagonally arranged cores . J. Ji et al. designed and fabricated an all-solid Yb-doped MCF with hexagonal ring structures, and calculated fundamental in-phase mode area which was up to 1571 μm2, corresponding to a conventional step-index fiber with a mode field diameter around 45 μm . S. Zheng et al. theoretically investigated a 19-core fiber with 4 air-hole cores symmetrically arranged on two sides of center core, and achieved a maximum LMA about 4025 μm2 at 1.55 μm and a low bending loss less than 1 dB/m when bending radius was larger than 0.34 m . Unfortunately, the use of the MCFs is mostly limited in the near-infrared (IR) region below 2 μm. Emerging applications in the fields like military, optical tomography, sensing  and so on, require further extension of the use of the optical fibers to MIR region (3-5μm). In terms of this, chalcogenide (ChG) glasses are excellent materials for MIR fibers because of their chemical stability, excellent transparency in MIR. However, due to their mechanical brittleness, it is challenging to prepare a ChG preform with uniform structure, and this leads to almost no reports on high quality LMA ChG MCF.
In this paper, a ChG MCF with 13 evanescent-field coupled cores embed in a cladding was proposed for achieving LMA in order to deliver high laser power in the MIR. The dependence of mode distributions, bending loss and dispersion characteristics on the fiber structure parameters was discussed at a wavelength range from 3 to 5 μm. An ultra-large FM area can be theoretically achieved up to ∼8000 μm2 at 3 μm with a single-mode operation. The MCF possesses a caculated low bending loss less than 0.075 dB/m when the bending radius is larger than 0.4 m, and it theoretically possesses low normal dispersion less than -18 ps/nm/km at 3–5μm wavelength. Finally, we fabricated the all-solid MCF by a unique isolated multicore extrusion based on the continuous two-stage method. The core sizes meet for single mode criterion and agree well with the designed sizes.
2. Design of fiber structure and numerical simulations
2.1. Fiber structure and analysis method
We designed an all-solid LMA ChG MCF with two rings of hexagonally arranged cores as presented in Fig. 1(a). The core consists of 13 circular Ge9As23Se68 rods with a high refractive index (RI) n1, and the cladding of the MCF is Ge10As22Se68 with a low RI material, n2. The proposed structure is different from the conventional 19-core MCF with equally single core size and core-pitch. In our case, the diameter of the high index rod in the first and second ring is defined as d1 and d2, respectively. And the diameter of the central rod is equal to that of any rod in the first ring. Λ1 is the center distance between one of the high RI rods in the first ring and the central rod, and Λ2 is the pitch between any two nearest rods in the first and second rings. Figure 1(b) shows the RI of core and cladding materials measured by an IR ellipsometer (IR-VASE MARKII, J. A. Woollam Co.) and the calculated NA in 2-12 μm wavelength range.
The numerical simulations were performed with the commercial software Comsol Multiphysics based on the fully vectorial finite element method (FEM). During the simulation, a user-defined, well-optimized circular perfectly matched layer (PML) and a perfect electric conductor were used together. The Sellmeier coefficient can be calculated by the Sellmeier equation  based on the measured refractive indices:
The effective mode area (Aeff) is given by the following Eq. (2):
2.2. Effect of structural parameters on the mode area
In our design, to achieve a very large effective FM area of the MCF in the MIR region, we chose two materials with small RI difference as shown in Fig. 1(b) to reduce the numerical aperture (NA) of the MCF. The supermodes field distribution of the coupled MCFs is formed through evanescent field coupling  between the adjacent and non-adjacent cores. It is well known that with a proper design of the core-pitch, the core size and the NA of the single core, evanescent field coupling of the multiple cores can form the FMs when these modes are phase-matched. The dependences of Aeff of the FM on the structure parameters d1, d2, Λ1 and Λ2 were thus studied at the 3–5 μm wavelength region and the results were presented in Fig.(s) 2(a)-(d). From these figures, we can see obviously that Aeff gradually increases as Λ1 increases in Fig. 2(a) and the increase becomes significantly with the increase of Λ2 in Fig. 2(b). However, Aeff decreases with the increase of d1 and d2 as shown in Fig.(s) 2(c) and (d). Here, increasing in Λ1 and Λ2 can result in a larger mode area, and the effect of Λ2 on Aeff is greater than that of Λ1. However, as d1 and d2 decreases, more individual mode field spreads out, leading to the increase of the overlap among these modes. That is to say, evanescent field increases in low index region and finally the overall size of the formed FM distribution becomes larger . Either increasing core-pitch or decreasing core diameter can lead to an effective increase in Aeff of the MCF. From Fig. 2(b), we can see that, when the core parameters are optimized properly, i.e., d1 = 2.2 μm, d2=5 μm, Λ1=5 μm and Λ2=40 μm, the FM Aeff is up to ∼8000 μm2 near 3 μm and as high as ∼19000 μm2 at 5 μm. Based on these results, we set d1, d2, Λ1 and Λ2 to 2.5 μm, 12 μm, 8 μm, and 60 μm respectly and caculated the Aeff whose value is 9378 μm2 at 3 μm. Regarding the influence on Aeff, the decreasing influence of larger d1 and d2 is smaller than the increasing influence of larger Λ1 and Λ2. Therefore, the Aeff still shows an increasing trend.
The modal field distributions at 4 μm corresponding to two different values of Λ1 (Λ1=5 μm and 6 μm), d1(d1=2.2 μm and 2.4 μm), d2 (d2=5 μm and 5.2 μm) and three different values of Λ2 (Λ2=20 μm, 25μm and 30 μm) are given in Fig.(s) 3(a)–(f). From Fig.(s) 3(a)–(c), d1, d2 and Λ1 are fixed and we can see that the overall field distributions are more discrete in nature with increasing in Λ2 from 20 μm to 25μm and 30 μm. In addition, from Fig. 3(c) and (d), d1, d2 and Λ2 are fixed and the same result can be observed as Λ1 increases from 5 μm to 6 μm though the change is not very obvious compared with that in Fig.(s) 3(a)–(c). That is to say, for larger values of Λ1 and Λ2, the propagation of light is governed by the discrete nature of the system. The reason is that overlap among these eigen modes decreases and large amount of fractional field power gets confined in the region of high index rod while Λ1 & Λ2 increases. However, when the values of d1 and d2 decreases, the overlap among these eigen modes increases, and hence the mode field area of FM gets larger, finally leading to more uniform FM field distribution. Compared with Fig. 3(d) d2=5 μm and (e) d2=5.2 μm, which has the same Λ1, Λ2 and d1, for the smaller former, overlap of among these modes increases and FM field distribution seems to be more uniform. This is the same as the more obvious result attained by comparing Fig. 3(d) d1=2.2 μm with (f) d1=2.4 μm, which has the same Λ1, Λ2 and d2.
2.3. Single mode operation of the designed MCF
For this multi-core fiber structure, its single mode operation can be numerically analyzed via relating the fiber to an equivalent step-index fiber (E-SIF). In this case, the single-mode criterion can be determined by calculating the normalized frequency V by approximating this MCF structure to an E-SIF structure. V is defined as :
Where λ is the operating wavelength, a is the effective core radius of the E-SIF, ncore is the effective core index and nclad is the cladding index of the multi-core fiber. Because there is no obvious core-and-cladding boundary, the core radius a is defined as the center-to-center distance between the center-rod and the most far rods from the center of the core region, in other words, a is approximated to be the radius of the mode field. The effective core index ncore has been calculated by averaging the square of the refractive index in the core region of the MCF as follows [20,21]:
We set Λ1=6 μm and Λ2=30 μm, and analyzed the relation between V parameter and wavelength λ under five different values of d1 and d2, as shown in Fig. 4(a) and (b). The V value increases with decreasing wavelength, and increasing d1 or d2 from 3 to 5 μm. Generally, single-mode operation can be obtained when the V value is smaller than 2.405. It can be observed that all the V values are kept at a value below 2.405 for the proposed structures in the wavelength range we investigated. From Fig. 2(c) and (d), we can see that the value of Aeff at 5 μm is up to 12273 μm2 and 13,349 μm2, corresponding to d1=2.5/d2=5/Λ1=6/Λ2=30 μm and d1=2.2/d2=5.1/Λ1=6/Λ2=30 μm, respectively. Therefore, with structure optimization, the proposed fiber has a theoretical ultra-large Aeff that can effectively operate as single-mode in the MIR regime.
2.4. Bend characteristics
The LMA fibers which are expected to be applied in high power fiber lasers or amplifiers with high beam quality, are often accompanied by a crucial bending loss, because the fiber RI and transmission characteristics change with the bending structure. In above section, we have optimized structural parameters and achieved large Aeff with theoretical single-mode operation. In this section, the structural parameters are fixed at d1 = 2.2 μm, d2=5μm, Λ1=6 μm and Λ2=30 μm, and then we calculate the bending loss of the LMA fiber at 4 μm. The bending loss α is related to the imaginary part of FM effective RI, which is calculated by the COMSOL Multiphysics, with the following formula :
We presumed the right in the horizontal direction to the x-axis positive direction, and the y-axis positive direction is upward in the vertical direction. When the fiber was bent in the x-axis positive direction, the equivalent cross-section RI distribution of the fiber was calculated as follows :22].
The relationship between bending loss α and bending radius R in the conditions of d1=2.2 μm, d2=5 μm, Λ1=6 μm and Λ2=30 μm at 4 μm is displayed in Fig. 5(a), and the relationship between Aeff and R is shown in Fig. 5(b). HEx and HEy are two kinds of polarization states of FM HE11. Obviously, the evolution of α and Aeff in two polarization states of FM is same when the value of R changes. From Fig. 5(a), we can see clearly that α decreases as R increases and finally tends to be flat, and α remains smaller than 0.075 dB/m while R is larger than 0.4 m. Meanwhile, α is greater in y direction than that in x direction. Figure 5(b) shows that Aeff increases slowly with the increment of R. When R=0.8 m, the Aeff values in both x and y direction are larger than 8300 μm2.
2.5. Dispersion characteristics
For conventional single mode fiber, the transmission performance would be affected by the various nonlinear distortions, which is similar to MCF. The dispersion characteristics of the designed LMA fiber has been investigated by the Eq. (3). Variation of the dispersion coefficient (D) with λ under five different values of d2 is shown in Fig. 6. From this figure, it is obvious that the fiber with this structure possesses normal dispersion in the 3-5 μm wavelength range. All of the dispersion values are less than -18 ps/nm/km and the minimum value is down to -46 ps/nm/km. With these low dispersion values, the designed fiber would be almost distortion-free in the form of FM for high power light propagation. In addition, from Fig. 6(b), we can see more clearly that the dispersion value decreases with the increase of d2.
3. Fiber fabrication and optical measurements
High purity glasses including core glass Ge9As23Se68 and cladding glass Ge10As22Se68 were prepared through the conventional melt-quenching method. The raw materials were purified by vacuum distillation, in which metal Mg was added to remove oxide impurities, and the details were described in Ref. [23,24]. The transmittance of Ge9As23Se68 and Ge10As22Se68 glasses with only slight CO2 peak at 4.26 μm and Se-H peak at 4.50 μm, which is higher than 65% is shown as Fig. 7. Finally, core glasses with a diameter of 9 mm and cladding glasses with a diameter of 46 mm were prepared, and then both of them were cut into 15 mm-long glass rods for preform fabrication.
We prepared the 13-core MCF preform with a continuous two-stage extrusion method , from 7-core in the intial stage to 13-core in the final stage. In the first stage, the glass rods including seven core glass rods and a cladding rod were extruded into a 9-mm diameter seven-core preform with a core-cladding diameter ratio of about 1: 5. In detail, the seven core glass rods with 9 mm diameter were pushed into the first 46-mm diameter cladding rod for the central core of the component . The second stage is 13-core preform fabrication. After annealing, a 15 mm length seven-core glass rod was cut out from such the prepared seven-core preform. And then, the seven-core glass rod together with other six core glass rods were extruded into the second 46-mm cladding rod to form the final 13-core preform. The diameter ratio of the inner seven cores, the outer six cores, and the cladding is 1:5:46. During the specific extrusion process, we used a unique isolated peel-off technique  based on the continuous two-stage extrusion. The 13-core fiber was drawn at in a home-made drawing tower equipped with high-purity Argon protection which can prevent the preform from oxidation during drawing process. And the drawing temperature was 240°C. Duo to fragile nature of chalcogenide fibers, PES (polyether sulfone) and PP (polypropylene) polymer films were coated around the preform to protect the fiber during the drawing . Eventually, the polymer wrapped ChG MCF with a diameter of about 500 µm were drawn successfully, whose parameters of d1, d2, Λ1, Λ2 were 2.5 µm, 12 µm, 8 µm, 60 µm,respectively. The core sizes of d2 and Λ2 were slightly bigger than d2 and Λ2 in the simulation due to continuous two-stage extrusion, while the diameters of d1 and Λ1were in agreement with the simulation parameters. The cross-section image of the MCF as shown in Fig. 8 was observed by an optical microscope (VHX-1000E, Keyence). It can be seen clearly that there were clear 13 cores (seven small cores in the central ring and six large cores in the outer ring) and no obvious bubbles, particles, or other defects, and a sight deformation of the six cores occurred in the outer ring during the second extrusion stage, which could be further improved with fine tuning of the extrusion parameters.
The fiber loss in a range of 2 - 12 µm was evaluated using a 2.0 m-long fiber based on the cut-back method with the help of a FTIR spectrometer (Nicolet 5700) and an external HgCdTe (MCT) detector cooled with liquid nitrogen . We cut back the fiber with five lengths of 30 cm by a precision fiber optic cleaver (FK11-LDF, Photon kinetics, Inc.) to make the core-cladding interface tidy and smooth. The attenuation was calculated by Loss=10×log(P1/P2)/L, where P1 is the input power, P2 is the output power, and L is the removed length of fiber, and the results were shown in Fig. 9(a). We can see that several absorption peaks appear at 2.9 μm/3.5μm and 4.25 μm /4.75 μm, corresponding to H-O and Se-H contaminants, respectively. The slight fluctuates of the curve at a range from 6.0–7.5 μm are caused by the light leakage in the protecting polymer layer around the fiber. In a word, the MCF fiber shows a low optical loss in MIR, which is less than 1.5 dB/m in the range of 5.2-8.5 µm, with a minimum value of 0.28 dB/m at 6.6 µm. After FTIR light source was coupled into the 13-core 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 Fig. 9(b).
We proposed an all-solid chalcogenide-based MCF and investigated its optical characteristics including mode area, bending loss and dispersion characteristics for MIR (3–5 μm) light delivery. With optimized structure, this MCF theoretically shows an ultra-large fundamental mode effective areas of ∼8000 μm2 at 3 μm wavelength in single mode operation. Meanwhile, a low normal dispersion down to -46 ps/nm/km at 3μm for almost distortion-free in high power laser propagation and a relatively low bend loss less than 0.075 dB/m when the bending radius is larger than 0.4 m can be achieved. We experimentally fabricated such a 13-core multicore fiber with a low loss of 0.28 dB/m at 6.6 µm in a single-mode operation based on a continuous two-stage extrusion. To our best knowledge, it’s the first time to prepare ChG MCF with two-ring structure based on extrusion. This ChG MCF shows great potential on high power laser propagation in 3-5 μm wavelength region.
National Natural Science Foundation of China (, 61705091, 61875097, 61627815, 61775109); Natural Science Foundation of Zhejiang Province (LR18F050002, LY20F050010); Natural Science Foundation of Ningbo (202003N4101); Ten-Thousands Talents Program of Zhejiang Province; Leading and top-notch personnel training project of Ningbo; K.C. Wong Magna Fund in Ningbo University, China.
The authors declare no conflicts of interest.
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