We demonstrate here for the first time, to the best of our knowledge, an effective method to achieve low-loss light coupling from solid-core fibers to anti-resonant hollow-core fibers (AR-HCFs) by fiber tapering technique. We establish the coupling models by beam propagation method (BPM), and the simulation results show that the coupling efficiency can be optimized by choosing a proper waist diameter of the tapered solid-core fiber. Two types of AR-HCFs have been tested experimentally, and the maximum light coupling efficiency is ∼91.4% at 1.06 µm and ∼90.2% at 1.57 µm for the ice-cream AR-HCF, and ∼83.7% at 1.57 µm for the node-less AR-HCF. This work provides a feasible low-loss light coupling scheme for AR-HCFs, which is very useful for implementing all fiber systems.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Since the photonic bandgap hollow-core fiber (HCF) was firstly reported in 1999, HCF has attracted intensive attention due to the potential practical advantages in reducing Fresnel reflections, inhibiting nonlinear effect, allowing broader transmission bands compared to solid-core fibers . Several kinds of HCFs have been fabricated in recent years [2–6] and one of them, the anti-resonant hollow-core fiber (AR-HCF) has developed rapidly in the past years because of its easily adjustable broad transmission bands and potential low attenuation, especially in the mid-infrared bands [4,5]. The development of AR-HCFs, which provides a perfect platform for the interaction of the gaseous medium with light, greatly promoted the investigations of fiber gas lasers (FGLs). Since the first experiment of gas stimulated Raman scattering (SRS) in AR-HCF was reported in 2012 , FGLs in gas-filled AR-HCFs based on SRS [8–14] and population inversion [15–19] have been intensively studied in the past several years. It has been demonstrated to be a new and effective scheme for laser emission in fibers, especially mid-infrared fiber lasers. However, up to now, all these FGLs are in the structure of free space light coupling, where the pump laser is launched into the HCF’s core through mirrors and lens. By this method, although very high coupling efficiency has been achieved [14–17], such systems are bulky and sensitive to environment, even tiny external perturbations will decrease the coupling efficiency, meanwhile increase the overlap of the pump light and the cladding microstructure, causing damage to HCFs. All these will limit the applications of FGLs based on AR-HCFs in the future. If we can make them with all-fiber structures, they will be much more stable and compact. Therefore, it is important to study low-loss coupling between AR-HCFs and solid-core fibers towards all-fiber structure.
In general, fiber splicing is the most common way to achieve all-fiber system, mainly include CO2 laser splicing [20,21], and electric-arc splicing done by commercial fusion splicer [22–24]. Due to the microstructure destruction of the HCFs, the splice loss is usually very high. All these methods are unsuitable for AR-HCFs, because the special microstructures in AR-HCFs are very easy to be damaged during the fusion splicing process, which may destroy the conditions of light transmission and cause catastrophic coupling loss. In 2016, to study the harnessing and enhancement of the optical tweezer forces for trapping small objects of different sizes and shapes at relatively small powers in HCFs, S. Xie et al. inserted a tapered single-mode fiber into a photonic bandgap HCF and got ∼87.8% coupling efficiency , which provides us a potential route for the light coupling from solid-core fibers to AR-HCFs. Because of the big differences in structure and light guiding principles between the photonic bandgap HCFs and AR-HCFs, it is necessary to investigate this coupling scheme for AR-HCFs.
Here, we firstly demonstrate an effective method to achieve low-loss light coupling from solid-core fibers to AR-HCFs by fiber tapering technique. In order to obtain an optimal coupling efficiency (defined as the power of all modes at the output of the HCF to the power at the output of the tapered fiber), we focus on the variation of the mode field diameters (MFDs) of the tapered fibers theoretically and experimentally. According to the simulation results by beam propagation method (BPM), for both ice-cream and node-less AR-HCFs with large MFDs, the coupling efficiency achieves the highest when the waist diameters are around 40 µm. The experimental results show that the maximum coupling efficiency is ∼91.4% at 1.06 µm and ∼90.2% at 1.57 µm for the ice-cream AR-HCF, and is ∼83.7% at 1.57 µm for the node-less AR-HCF. The differences from the simulation results are mainly due to the offset and bending of the tapered fibers, which should be avoided in the following study.
2. Principle and simulation
2.1 Mode field variation by tapering
As one of the most important post-processing techniques, fiber tapering can remarkably change the shape of the fiber and its optical properties and thus plays an important role in the fabrication of various optical devices. Fiber diameter can be decreased by pulling the fiber along its axis while softening the fiber with a small heat source . During the tapering process, the core and the cladding diameters of the original fiber change with the same ratio.
A schematic of a down-tapered fiber is shown in Fig. 1. It consists of a waist area, two taper areas and two original areas. Tapered fibers with different parameters, such as the shape of the taper area and the diameter of the waist area, can be fabricated by using different tapering parameters. After the tapering process, the fiber is cleaved at the waist area where the mode field is designed to match with the HCF.
In order to simulate the light propagation in the tapered fiber, we build a numerical model for the tapered fiber with BPM. Figure 2 shows the simulation results of the MFD evolution with waist diameters in different lengths of taper area and waist area. It can be seen that the MFD of the tapered fiber experiences two processes. Firstly, the MFD increases as the waist diameter decreases before reaching the maximum value. It is because during the down-tapering process, the fiber core is too small to hold the light which leaks into the cladding, resulting in the increment of the mode field. The largest MFD for both HI-1060 (at 1064nm) and SMF-28 (at 1550 nm) can be achieved when the waist diameter is down-tapered to about 40 µm. In the second process, when the waist diameter is down-tapered to be less than 40 µm, the MFD is mainly dependent on the cladding diameter. Thus the decrease of the waist diameter causes the decrease of MFD. We can also see that the length of the taper area will influence the MFD. As shown in the figures, when the length of the taper is shorter than 15 mm, the MFD becomes unstable. It is because short taper area means wide taper angle, which will increase the loss and affect the mode field transmission .
2.2 Simulation model
Figures 3(a) and 3(c) show the transmission bands of two kinds of AR-HCFs used in our experiments. The inset scanning electronic micrographs (SEMs) show that the ice-cream type AR-HCF has a closed core area formed by eight ice-cream shape capillaries while the node-less type AR-HCF has an open core area formed by ten circular shape capillaries. For these AR-HCFs, existing theoretical models are unable to give quantitative descriptions of their optical performance . The specific solution mainly depends on numerical simulation. In this paper, we use the BPM to simulate the light propagation in such AR-HCFs. The parameters of the AR-HCFs are measured through the SEMs and the results are shown in Table 1. With these parameters, the simulation models of AR-HCFs are established, as shown in Figs. 3(b) and 3(d).
For these AR-HCFs with large MFDs and untapered solid-core fibers, if we use electric-arc splicing, the most important factor to cause loss is mode field mismatch . For example, when the wavelength of the light source is 1064 nm, the coupling efficiency is only 12.5% for MFD of 34 µm (AR-HCFs) and 6.2 µm (HI-1060 solid-core fibers) . In addition, due to the destruction of the air hole structure, the actual coupling efficiency will be much lower than we expected. Therefore the electric-arc splicing is not suitable and it is necessary to decrease the mode field mismatch. The simulation results in section 2.1 show that the tapered fiber has a larger MFD than the untapered fiber, and thus by tapering the fiber and inserting it into the interior of AR-HCF, it is possible to increase the coupling efficiency in the connection of AR-HCF and normal fiber. We establish a coupling model for inserting a tapered fiber into an AR-HCF by BPM, as shown in Fig. 4. HI-1060 and SMF-28 are used as input tapered fibers in simulation. The length of original area, taper area and waist area is set to 20 mm, 21mm and 6mm. Both ice-cream type and node-less type AR-HCFs are simulated and the length of the AR-HCFs is set to 100 mm. The tapered diameter is varied between 10 µm and 100 µm.
2.3 Simulation results
2.3.1 Ice-cream type AR-HCFs
Figures 5 and 6 show the ice-cream AR-HCF coupling simulation results. When the waist diameter of the tapered fiber is 10 µm, 20 µm, 30 µm and 40 µm, the longitudinal transmission light fields are shown in Figs. 5(a) and 5(b). We can see that the laser energy confined in the hollow core increase with the increasing of the waist diameter. When the waist diameter is 40 µm, the energy within the hollow core is the highest, which is in good agreement with the theoretical and measured results of the coupling efficiency with the waist diameter, as shown in Figs. 6, 7, 9 and 10. Besides, when the output light of the tapered fiber enters the HCF, a periodic variation of light field occurs along the propagation direction, which may be due to the multimode interference in the HCFs. Figure 5(c) shows the variation of transverse light field along the HCF in an interference period at 1064 nm.
Here, we care more about the total power coupled into the HCF because the power of all modes will contribute to the power conversion to the wanted laser wavelength for fiber gas lasers [15–18]. From Fig. 6, we can see that the coupling efficiency is the highest when the waist diameter is around 40 µm. It is because in this case the MFD of the tapered fiber is the maximum (∼22 µm), as shown in Fig. 2, which is close to the equivalent MFD of the HCF (∼33.5 µm). While the waist diameter deviates from 40 µm, the coupling efficiency decreases due to the mode field mismatch. In addition, the highest coupling efficiency is 94.6% at waist diameter of 41 µm for HCF inserted by the HI-1060 tapered fiber at 1064 nm, and 97.2% at waist diameter of 39 µm for HCF inserted by the SMF-28 tapered fiber at 1568nm.
2.3.2 Node-less type AR-HCFs
Figure 7 shows the node-less AR-HCF coupling simulation results. Similar to the ice-cream AR-HCF coupling simulation results, the coupling efficiency achieves the highest when the waist diameter of the tapered fiber is around 40 µm. And in the coupling model of the HCF inserted by the HI-1060 tapered fiber at 1064 nm, the highest coupling efficiency of 88.1% is achieved at waist diameter of 41 µm. In the coupling model of the HCF inserted by the SMF-28 tapered fiber at 1568 nm, the highest coupling efficiency of 93.0% is achieved at waist diameter of 41 µm. The coupling efficiency is slightly lower than that of the ice-cream AR-HCF. Despite that the MFD of the tapered fiber (∼22 µm) is very different from the HCF (∼71 µm), the simulation results show that the coupling efficiency is still pretty high. The reason is that the calculated coupling efficiency in the simulation models takes all modes power into consideration. Therefore in this coupling model, the total coupling efficiency may be high but the fundamental mode power may only occupy a small part.
3. Experimental results and discussion
3.1 Experimental setup
The coupling system for AR-HCFs and tapered fibers is established with high precision stages, as shown in Fig. 8. In this system, an AR-HCF and a tapered fiber are placed on three-dimensional stages. In order to realize high precision adjustment and coupling, the coupling observation is carried out by well-designed two-dimensional microscopes. The simulation and experimental results both show that the insert length of the tapered fiber into the HCF almost have no influence in the coupling efficiency. In our experiments, the tapered fiber was inserted into the HCF by tens of micrometers, as shown in Fig. 8(b). Here, we use a single-mode fiber laser as light source and connected it to a single-mode bare fiber with a flange at one end. We use a photoelectric detector (THORLABS PM100D & S302C) to measure the output power from the tapered fiber. Then, the tapered fiber is inserted into the hollow core of the AR-HCF by three-dimensional stages and two-dimensional microscopes. The output power from the AR-HCF is measured by the same type photoelectric detector and the coupling efficiency can be calculated by the ratio of the two values.
To begin, tapered fibers with different waist diameters are fabricated by using HI-1060 and SMF-28 solid-core fibers. The length of taper area is 18∼22 mm. The length of waist area is 4∼6 mm. And the waist diameter of the HI-1060 tapered fiber is increased from 10 µm to 50 µm by 5 µm increments. The waist diameter of the SMF-28 tapered fiber is increased from 10 µm to 100 µm by 5 µm increments. The AR-HCFs used in the experiments are the ice-cream type AR-HCF and node-less type AR-HCF, as shown in Fig. 3.
3.2 Results and discussion
The experimental and simulated results of the ice-cream type AR-HCF are shown in Fig. 9. At first, we insert HI-1060 tapered fibers into a 10 cm ice-cream AR-HCF and measured the coupling efficiency of 1064 nm in such coupling system. The experimental results are shown in Fig. 9(a). It can be seen that for ice-cream type AR-HCF, when the waist diameter of the HI-1060 tapered fiber is about 40 µm, the maximum coupling efficiency is about 91.4%, which is a little lower than the simulated results of 94.5%. Besides, the change trend of the experimental results is in good agreement with the simulation results. These prove the feasibility of improving coupling efficiency from normal fibers to ice-cream AR-HCFs by fiber tapering technique. When the tapered diameter is 40 µm, the experimental transverse output field from the HCF can be seen in the inset of Fig. 9(a), which shows that the most of the energy is confined in the hollow core.
Then we insert SMF-28 tapered fibers into the same type ice-cream AR-HCF with 2 m length and measured the coupling efficiency of 1568 nm in such coupling system. The experimental results are shown in Fig. 9(b). Similar to Fig. 9(a), the experimental results are in good agreement with the simulated results, and when the waist diameter is about 40 µm, the maximum efficiency is about 90.2%. But the discrepancy between the simulated results and experimental results is larger than that in Fig. 9(a). It is because the ice-cream AR-HCF used in the condition of Fig. 9(b) is 2 m while the HCF in the simulation model is 10 cm, and thus the high order modes induced in the coupling process are in high loss, causing the energy measured at the output of the HCF lower than the simulated results. When the tapered diameter is 40 µm, the experimental transverse output field from the HCF can be seen in the inset of Fig. 9(b), measured by HgCdTe infrared camera (Xenics, MCT-2327). We can see that most of the laser energy is also confined in the hollow core.
When the HCF is replaced by a 10 cm node-less AR-HCF, the tapered fibers are SMF-28 and the injection light is 1568 nm, the experimental results are shown in Fig. 10. It can be seen that for node-less type AR-HCF, when the waist diameters of SMF-28 tapered fibers are about 40 µm, the maximum coupling efficiency is about 83.7%. Though it is lower than the simulated result of 93.0%, the measured value seems very high in the condition of mode field mismatch. We think it is because the HCF used in the experiments is only 10 cm long, and thus high order modes do not attenuate rapidly. So at the output of the HCF, the power meter can receive most of the light.
Though the change trends of the simulated results are in good agreement with the experimental results, as shown in Fig. 9 and Fig. 10, the experimental results are lower than the simulated results. The nonuniform taper in the taper process may deteriorate the transmitting mode field, which affects the coupling efficiency. The damage to the end face of tapered fiber in the insertion process, which may reduce the laser energy injected into the HCF. The offset of the tapered fiber in the HCF may results in more laser energy leaking out of the hollow core. Actually, we did find the damage of the waist areas of tapered fibers during the experiment, resulting in the degradation of the beam quality. In order to have a general understanding of the impact of the above factors on the coupling efficiency, we carried out a simulation study. Figure 11 shows the simulated results of the influence of the offset and bend of tapered fibers on the coupling efficiency. The inset in Fig. 11(b) is the schematic of the bending of the tapered fiber due to the gravity. As we insert the tapered fiber into the HCF by only tens of micrometers, so the end of the tapered waist can be approximately adjusted in the middle of the HCF. It can be seen that, the offset of tapered fibers is an important factor affecting the coupling between AR-HCFs and tapered fibers. When the offset is 6 µm, the coupling efficiency is only half of the original for SMF-28 tapered fibers and 63% of the original for HI-1060 tapered fibers. Therefore it is the key to keep the tapered fibers in the center of AR-HCFs without offset. From Fig. 11(b), we can see that the influence of the bend of tapered fibers is weaker than the offset. When the displacement of the waist caused by bending is 25 µm, the coupling efficiency drops to about 81% of the original for HI-1060 tapered fibers and 82% of the original for SMF-28 tapered fibers. If the bending is small, the coupling efficiency hardly changes. Thus the bending of the tapered fibers should be controlled within a certain range. These simulated results are obtained in the case of 10 cm AR-HCF, so the actual coupling efficiency will become lower when the AR-HCF is long.
In this paper, we have demonstrated an efficient method for light coupling from the solid-core fibers to AR-HCFs using fiber tapering technique for the first time. The variation of the waist diameters of the tapered fibers results in the change of MFDs, so choosing appropriate waist diameter can decrease the mode field mismatch between the single-mode solid-core fiber and AR-HCF. We established the simulation model by BPM and carried out the experiments. Both for the ice-cream type and node-less type AR-HCFs, the coupling efficiency achieves the highest when the waist diameters are around 40 µm. We experimentally obtain the coupling efficiency of ∼91.4% at 1064 nm and ∼90.2% at 1568 nm for the ice-cream AR-HCF, and of ∼83.7% at 1568 nm for the node-less AR-HCF. The offset, bending and damage of the tapered fibers will affect the coupling, and all these problems need to be avoided in the following experiments for a higher efficiency. Our work provides a feasible low-loss light coupling scheme for AR-HCFs, which is very useful for implementing all fiber systems, for example all fiber FGLs. However, for a practical system, stable sealing package is very important. We can design a special package structure to do this, for example using glass capillaries, which was firstly proposed by R. Pennetta, et al. 
Natural Science Foundation of Hunan Province (2019JJ20023); National Natural Science Foundation of China (61705266).
We thanks Professor Jonathan C. Knight from University of Bath in UK for providing the hollow-core fiber for our experiments.
The authors declare no conflicts of interest.
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