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Abstract
To go beyond the fundamental limits imposed by latency, nonlinearity, and laser damage threshold in silica glass fibers, the hollow-core fiber (HCF) technique has been intensively investigated for decades. Recent breakthroughs in ultralow-loss HCF clearly imply that long-haul applications of HCF in communications and lasers are going to appear. Nevertheless, up to now, the HCF technique as a whole is still hampered by the limited length of a single span and the lack of HCF-based functional devices. To resolve these two issues, it is of importance to develop ultralow-loss and plug-and-play HCF interconnections. In this work, we report on HCF interconnections with the lowest-ever insertion losses (0.10 dB for HCF to standard single-mode fiber (SMF) and 0.13 dB for HCF to itself in the 1.5 µm waveband) and in a pluggable means. Two fiber mode-field adapters, one based on a graded-index multi-mode fiber (GIF) and the other utilizing a thermally expanded core (TEC) SMF, have been tested and compared. An extra insertion loss arising from imperfect refractive index distribution in a commercial GIF is observed. Our HCF interconnections also realize a back-reflection of <-35 dB over a 100 nm bandwidth as well as other critical metrics in favor of practical applications. Our technique is viable for any type of HCF.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As the attenuation of state-of-the-art hollow-core fiber (HCF) steadily decreased from the level of tens of dB/km to the latest record of <0.174 dB/km [1–8] over the past decade, fiber optic technology is approaching a prime time to open a new era featured with ultimate low latency [9], negligible nonlinearity [10], and high laser power handling capability [11]. However, till now such a prospect is still hampered by some practical issues associated with short length of available HCF spans [12] and vulnerability to laser damage at HCF ends [13].
To fully exploit the merits of low-latency and low-nonlinearity in HCF for communications, assembling multiple HCF spans, whose typical lengths are less than 5 km, into a long link is a feasible solution [12]. To fully unleash the high-power delivery capability of HCF for lasers, decreasing the coupling loss to an ultimate low level in an all-fiber form is preferred. Moreover, the desire to integrate HCFs with the existing solid-core fiber (SCF) based networks with low costs and in a convenient manner also motivates the study of plug-and-play HCF interconnection techniques.
A standard single-mode silica fiber (e.g., SMF-28, Corning) can routinely realize an insertion loss (IL) of less than 0.05 dB by fusion splicing [14,15]. By contrast, the HCF fusion splicing is far less mature because of air-hole collapse and outer diameter mismatch [16]. Although these two issues can be mitigated to some extent by optimizing the arc discharge parameters of current, duration, and position [16,17] as well as by a reverse tapering approach [18], the quality of a fusion joint relies on case-by-case recipe optimization and expensive large-diameter fiber splicers, resulting in heavy time and cost consumption. Additionally, in a fused splice between HCF and SCF it is not allowed to eliminate the Fresnel back-reflection because anti-reflection (AR) or other functional coating layer will be destroyed under heating. So far, the lowest reported IL of an HCF/SMF-28 fusion splice is 0.44 dB [19]. In 2019, M. Komanec et. al. proposed a glue-based fiber-array (FA) assembly technique [20]. By utilizing a graded index fiber (GIF) mode-field adapter (MFA) and a 5-axis micro-positioning stage (x, y, z, pitch, and yaw), the FA method can diminish the mode-field mismatch and realizes a 0.15 dB IL for an HCF/SMF-28 joint with the help of AR coating [21]. However, from the viewpoint of practicality, manual adjustment across a five-dimension space strongly relies on the precision of the stages and skills of the operator. In many circumstances, where automatic adjustment is not viable, the FA assembly method will be extremely inefficient. Also, it does not provide the convenience of pluggability. The third technique of HCF interconnection is based on fiber connector [22]. Compared with the FA assembly, the drawbacks of the connector method are the lack of precision positioning and the bulky device size. Considering the non-ideal core-clad concentricity and the random offset of a HCF core relative to a ferrule axis, the lowest-ever reported IL of this method is 0.3 dB from a single-mode hollow-core photonic bandgap fiber (PBGF) to a custom-made large mode area SMF [22].
In this work, we develop a new approach for HCF connector and introduce an extra degree of freedom for offset alignment when interconnecting. As a result, 0.1 dB level of ILs and plug-and-play ability are realized for the first time to our knowledge. Such results are less than 1.5 times the theoretical limit calculated by mode-field mismatch.
2. Principle and method
The coupling loss of a fiber interconnection can be estimated by calculating the mode-field mismatch of two fibers [23]. Considering two single-mode optical fibers, one SMF-28 and the other conjoined-tube HCF (CTF in short), the fundamental mode field profiles are simulated by COMSOL Multiphysics. The structural parameters of the CTF are taken from Ref. [5] with the core diameter of 30.5 µm. As depicted in Fig. 1(a), the Gaussian fits yield the mode field diameters (MFDs, measured at the 1⁄e2 of the peak intensity) 2w and 2w’ of the two fibers to be 10.4 µm and 27.9 µm (at 1550 nm), respectively. In addition to the MFD mismatch (w against w’), the deviations in the three translational (x, y, z) and the two rotational (θ, ϕ) degrees of freedom need also to be minimized for a low-loss interconnection [Fig. 1(b)]. Assuming an ambient refractive index of namb = 1, the coupling losses at 1550 nm (in unit of dB) as a function of various parameters can be calculated using the formulae in Ref. [23], where a Gaussian-shaped mode field is assumed. Figures 1(c) and 1(e) show the coupling loss versus the three displacement mismatch parameters for SMF-28/SMF-28 and CTF/CTF interconnections, respectively. Figures 1(d) and 1(f) show the coupling loss versus the tilt and the MFD mismatch [10log10(w’/w)] of the two fibers. Equations (22), (24), (26), and (28) in Ref. [5] have been used. It is manifest that in order to keep the coupling loss in a low level (e.g., < 0.5 dB or < 0.25 dB), the allowed deviations in the three translational degrees of freedom for CTF is much larger than those for SMF-28, while the allowed deviations in the two rotational degrees of freedom for CTF is far smaller than for SMF-28. This can be attributed to the fact that the MFD of the CTF (for its fundamental mode) is much larger than SMF-28, therefore implying that the primary challenge for low-loss HCF interconnections is to reduce the angle deviations.
Fig. 1. (a) Scanning electron microscope images, simulated mode fields, and intensity profiles (along the marked axes) of a SMF-28 and a CTF; (b) Sketch of fiber alignment, involving of 3 translational and 2 rotational degrees of freedom; (c-f) Calculated coupling losses (in dB) at 1550 nm for SMF-28/SMF-28 and CTF/CTF interconnections as a function of various structural parameters. In (c,e), θ, ϕ = 0 and w' = w. In (d,f), x, y, z = 0. The white and the yellow contours refer to the losses of 0.5 and 0.25 dB, respectively. The green bands refer to |θ, ϕ| < 0.002 rad.
Connector-based optical fiber interconnections not only provide plug-and-play capability but also enable auto-collimation of two fiber ferrules. As depicted in Fig. 2(a-b), when a fiber is inserted into a 10.5 mm-long ceramic ferrule, the size discrepancy between the bore hole and the fiber outer diameter (of ∼20 µm) may result in a transverse offset (d) of ∼ 10 µm and an angular tilt (θ) of ∼ 0.002 radian for the fiber axis relative to the ferrule. According to Fig. 1(f), if the discrepancy of the mode fields of two optical fibers (in both diameter and shape) can be neglected, such level of angular tilt will not cause severe IL (<0.07 dB). Thus, if using fiber ferrules of such sizes, a connector-based interconnection can conveniently resolve the angle misalignment problem, which is usually regarded as the most difficult and time-consuming step in other HCF interconnection techniques.
Fig. 2. (a) Offset and (b) tilt of an optical fiber inside a ceramic ferrule; (c) Flow chart of the assembling procedure of a CTF connector.
To fabricate a good HCF connector, the HCF end must be stably fixed inside the ferrule with no contamination on the facet. Figure 2(c) shows the design and assembling flowchart of our HCF connectors. Firstly, a funnel structure is machined on the end of a ceramic ferrule for inhaling glue. After flat cleaving the protruding segment of the HCF, a UV-curable glue is adhered on the outer surface of the fiber (while taking care that it does not contact the end facet). Then, the HCF is pulled back into the flush position and the glue is cured by an UV lamp. By monitoring this operation under an optical microscope, we can prevent glue to ingress into the core of HCF. Comparing with the method in [22], we apply glues in the place closer to the ferrule end, which can diminish the movement of the HCF end relative to the ferrule end and favor the stabilization of device.
3. Results
3.1 CTF/CTF interconnection
After preparing two CTF connectors, we need to reduce the transverse offset between them, which is necessary for HCF interconnections considering the big core-clad non-concentricity (1∼2 µm for our CTF) and the random position offset of an HCF inside a ferrule (>5 µm in this study). To solve this problem, a metallic fiber-optic mating sleeve with 3 × 4 key slots [see Fig. 3(a)] is machined, which allows us to rotate the two connected fibers. The key slots are evenly arranged in the azimuthal angles, providing 12 optional transverse offsets (Δd) for the two fibers [Fig. 3(b)]. Ignoring the longitudinal separation and the angular tilt and using the equation of transmission coefficient, $T = (\frac{{2{w_1}{w_2}}}{{{w_1}^2 + {w_2}^2}})\exp [\frac{{ - 2{{(\Delta d)}^2}}}{{{w_1}^2 + {w_2}^2}}]$, in [23], the IL between two CTFs can be calculated by $\exp [\frac{{{d_1}^2 + {d_2}^2 - 2{d_1}{d_2}\cos (\varphi )}}{{{w^2}}}]$, with w1 = w2 ≈ 27.9/2 µm being the mode-field radii, d1 and d2 the transverse offsets of the mode-field centers of the two CTFs relative to the ferrule axis. Via this fiber rotating, Δd can be tremendously reduced, as shown in the inset of Fig. 3(b). A distributed feedback fiber laser and an optical power meter (PM, Thorlabs S122C) are then used to measure the power before/after the interconnection, and the power ratio refers to the IL of the interconnection. It is worthy to mention that the CTF before the interconnection is more than 100 m long for ensuring the single-mode operation and the length of the second piece of CTF is only ∼0.5 m (as such its propagation loss can be neglected). The experimental results of CTF/CTF interconnection are shown in Fig. 3(c), where the minimum IL at 1550 nm reaches 0.15 dB.
Fig. 3. (a) Schematics of a 3×4-slot mating sleeve and two CTF connectors; (b) principle of lateral offset reduction by using a multi-slot mating sleeve; (c) Measured ILs (at 1550 nm) of a CTF/CTF interconnection versus the relative rotation angle; (d) Minimum ILs of 10 plugging trials.
The same CTF/CTF interconnection has been unplug-and-plug several times. As shown in Fig. 3(d), the minimum IL at ∼1550 nm is measured to be 0.13 dB with the standard deviation of 0.03 dB. The blue dashed line in Fig. 3(d) refers to the record IL of 0.16 dB [17] for a PBGF-to-itself (PBGF: Photonic BandGap Fiber) fusion splicing.
3.2 CTF/SMF-28 interconnection
For a low-loss CTF/SMF-28 interconnection, mode-field adapting is pre-requisite. Two widely used methods of multimode interference in a graded-index fiber (GIF) [24] and mode-field expansion in a thermally expanded core (TEC) fiber [25] are compared. The principles of these two mode-field adapters (MFAs) are outlined in Figs. 4(a) and 4(c), respectively, where the periodic mode-field expansion and contraction along a GIF and the adiabatic mode-field evolution along a TEC fiber have been sketched. In experiment, we use commercial products of GIF (OM1, with the core diameter of 62.5 µm, YOFC) and TEC SMF (TECF-30 µm, GoFoton). After fusion splicing a SMF-28 pigtail with the GIF, we cleave the GIF segment to different lengths and take images of the mode field at the output ends using an infrared CCD camera. A small ellipticity of ∼9% is observed in these mode-field profiles [Fig. 4(a)]. We use a holographic analyzer to measure the refractive index (RI) distribution in the cross-sectional plane of the GIF at 632.8 nm. The high RI resolution (± 0.0001) and the high spatial resolution (0.175 µm) of the holographic analyzer enable us to identify the origin of the mode-field ellipticity. As shown in Fig. 4(b), an ellipticity of ∼11% is manifested in the RI map. By contrast, in both the mode-field image [Fig. 4(c)] and the RI map of the pigtail SMF of the TEC fiber [Fig. 4(d)], no ellipticity is discernible. Therefore, from the perspective of reducing mode-field mismatch in shape between a CTF and a SMF-28, the TEC fiber-based MFA method is adopted in this work.
Fig. 4. Mode-field evolutions from a SMF-28 to (a) a GIF or (c) a TEC fiber, respectively. Mode-field images at 1550 nm are taken at different places of the adapter fibers. Ellipticity is defined as (a - b)/a, with a and b being the long and the short radii of an ellipse, respectively. RI distributions of (b) the GIF and (d) a SMF-28 measured at 632.8 nm by a holographic analyzer, respectively. Scale bar, 20 µm.
Besides the MFD adaptation, TiO2/TaO2 8-layer AR coatings are deposited on both ends of our TEC fiber to mitigate the Fresnel reflection at the two glass-air interfaces, which sum up to an extra IL of ∼0.3 dB. After AR coating, the back-reflection is measured [Fig. 5(a)], showing a broadband (>100 nm) and low-back-reflection (<-35 dB) feature. We notice that even lower back reflection can be attained in an angled interconnection [26].
Fig. 5. (a) Measured return loss spectrum of a TEC fiber with (red line) and without (black line) AR coatings; (b) Schematic of a SMF-28/CTF/SMF-28 chain and the setup for loss measurement; (c) Measured insertion loss spectrum (black line) and the averaged loss spectrum (red line). The red dots refer to the half values of the ILs, corresponding to the estimated IL values of a single interconnection. The blue dot refers to the calculated minimum IL according to the mode-field mismatch in shape. Inset, calculated interference fringes of LP01 and LP11 modes.
Our CTF/SMF-28 interconnections are further downsized by removing the metallic shell [Fig. 3(a)] and using a C-shaped ceramic mating sleeve to hold two fiber optic cannulas. As sketched in Fig. 5(b), the new form of interconnection not only has a compact size of 46 mm × 4.6 mm × 4.5 mm and a light weight of 1.5 g, but also enables rotation with arbitrary angle, which further lifts the restriction upon the azimuthal degree of freedom for low IL. Using these compact-sized interconnections, a SMF-28/CTF/SMF-28 chain with AR coatings on the two TEC fiber ends and a ∼0.6 m CTF in the middle has been fabricated, see Fig. 5(b). Firstly, using a broadband source and an optical spectrum analyzer (OSA), a transmission spectrum through an SMF-28 was measured as a reference. Then, this SMF-28 was cut in the middle and the two fiber ends were spliced with the pigtails of the fiber chain. In this manner, two extra SMF-28 splices were added into the fiber chain with typical loss of <0.01 dB for each splice. In the end, Fig. 5(c) shows the measured IL of the whole fiber chain with 0.27 dB at 1550 nm and 0.19 dB at 1489 nm, respectively. Dividing these values by 2 yields the lowest-ever reported IL (<0.10 dB at 1489 nm) for a single HCF/SMF-28 interconnection. Additionally, the spectral ripples in Fig. 5(c) manifest an interference between the fundamental mode and the higher-order mode of LP11. The spacing of these fringes can be calculated by the effective indices of LP01 and LP11 modes, which yields a period of ∼3.1 nm at 1600 nm [the inset in Fig. 5(c)] and agrees very well with the measured one (∼3.2 nm). Further, the amplitude of the spectral fringes (∼0.08 dB) allows us to deduce that the LP11 mode component excited inside the middle CTF has a relative power weight of around -20.3 dB. This fiber chain measuring method has been used in Refs. [19–21].
In order to clarify the origin of the remaining IL, we calculate the mode field of the TEC SMF-28 based on a hypothetical RI profile from Ref. [27]. The mode-field mismatch between the TEC SMF-28 and our CTF comes from two folds: (1) different distributions along the radial direction, and (2) discrepancy between a circular mode and a hexagonally-shaped mode. Our calculation with fitted parameters yields a minimum IL of ∼0.112 dB at 1550 nm. Another calculation for the CTF-to-itself case also gives an IL ranging from 0 to 0.074 dB with variation of the relative azimuthal angle. The details of these calculations will be reported elsewhere. Altogether, it seems that our connector-based HCF interconnection has reached closely to the IL limit set by different mode shapes of fibers.
Regarding other metrics of a fiber joint for realistic applications, our CTF connectors can withstand a tension of 4∼5 N before breaking [Fig. 6(b)]. We also test water-proofing capability after glue sealing. An IL degradation of ∼0.05 dB over one night is measured [Fig. 6(c)]. A recent experiment also reported that a glue-sealed HCF joint can maintain high performance over 100 days in air [28].
Fig. 6. (a) Photos of a fabricated CTF patch cord. (b) Measured breaking tensions of CTF cannulas. (c) Measured IL variation. Inset: Photos of a glue-sealed CTF/SMF-28 interconnection immersed in water.
4. Conclusion
In summary, an HCF interconnection technique featured with ultralow loss and plug-and-play capability has been reported. Mitigating the issues associated with transverse offset, angular tilt, mode field diameter mismatch, and Fresnel reflection, we manage to decrease the IL to a record low 0.1 dB level (0.13 dB at 1550 nm for the HCF-to-itself case and 0.10 dB at 1489 nm for the HCF/SMF-28 case, respectively), which is only 0.03 dB higher than the theoretically predicted loss limit due to the mode field mismatch in shape. Our HCF interconnection technique can be extended to other types of HCF. Our results make it possible to connect short spans of HCF into a long link, to mitigate high-power laser damage at HCF ends, and to incorporate HCFs into standard SMF-based optical networks.
Funding
National Natural Science Foundation of China (61827820, 62075083, 62105122, U21A20506); National Key Research and Development Program of China (2017YFA0303800); China Postdoctoral Science Foundation (2020M683184); Basic and Applied Basic Research Foundation of Guangdong Province (2021A1515011646, 2021B1515020030, 32221295); Fundamental Research Funds for the Central Universities (21620316).
Disclosures
The authors declare no conflicts of interest.
Data availability
The datasets are available from the corresponding author on reasonable request.
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