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Abstract
We report simultaneous low coupling loss (below 0.2 dB at 1550 nm) and low back-reflection (below −60 dB in the 1200-1600 nm range) between a hollow core fiber and standard single mode optical fiber obtained through the combination of an angled interface and an anti-reflective coating. We perform experimental optimization of the interface angle to achieve the best combination of performance in terms of the coupling loss and back-reflection suppression. Furthermore, we examine parasitic cross-coupling to the higher-order modes and show that it does not degrade compared to the case of a flat interface, keeping it below −30 dB and below −20 dB for LP11 and LP02 modes, respectively.
Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. Introduction
The attenuation of hollow-core fibers (HCFs) has steadily been decreasing over the past few years, with values as low as 0.174 dB/km at 1550 nm recently reported [1]. This level of attenuation is comparable with that of standard single-mode fiber (SSMF) and is rapidly approaching the lowest ever value reported for any fiber (0.142 dB/km for pure silica core fiber (PSCF) [2]). Moreover, substantially lower losses than those possible in SSMF/PSCF were already achieved at wavelengths both below 1300 nm (e.g., 0.30 dB/km at 1060 nm and 0.60 dB/km at 800 nm [3]) and above 1800 nm (e.g., 0.85 dB/km at 2000 nm [4]). Besides loss, HCF performance significantly surpasses that of SSMFs in many other important aspects, mostly thanks to the light propagation through an air-filled core as opposed to silica glass. For example, HCFs have several orders of magnitude lower nonlinearity than SSMFs [5] and light propagates at a speed close to that of light in vacuum [6], which reduces signal latency.
However, there are several challenges that need to be addressed to facilitate the use of HCFs across the fullest range of practical applications. For example, most existing optical systems are based on SSMFs, requiring efficient interconnection between SSMF and HCF when only some of the fibers, or fiber components, are to be replaced by HCF variants. Such an interconnection should ideally offer low insertion losses and low back-reflection (ideally below −60 dB, similarly to angle-polished connectors). In some instances, it is also important to minimize unwanted coupling into higher-order modes to achieve required levels of performance. The latest-generation of low-loss HCFs provides for very high attenuation of higher-order modes (e.g., above 2 dB/m [3]), making them effectively single-mode after light propagation over several 10s of meters. However, when shorter lengths are used (e.g. in Fabry-Perot gas sensors [7], CO$_{2}$ filled hollow-core fiber gas cells used as frequency references for laser stabilization [8], for high-power pulsed laser delivery [9]), it is important to minimize coupling into the higher-order modes in order to ensure they operate robustly in the single-mode regime.
To achieve a low-loss SSMF-HCF interconnection, several challenges must be addressed. Firstly, the large mode-field diameter mismatch between the fundamental mode of a low-loss HCF and the fundamental mode of SSMF (e.g. $\sim$24 µm for nested antiresonant nodeless fiber, NANF [10] as compared to $\sim$10.4 µm for SSMF at 1550 nm) needs to be accommodated. This is typically addressed by inserting a mode-field adapter (MFA) between the HCF and SSMF [10–12]. Although MFAs have been reported that can adapt the difference in mode field diameter (see Table 1 for an overview), they typically do not account for the slight difference in the mode-field shapes and this ultimately places a limit on the minimum levels of achievable interconnection loss and excitation of unwanted higher-order modes [10].
Table 1. Achieved coupling loss between the fundamental modes of an HCF and SSMF and back-reflection level. The best-achieved values are shown in bold.
Another challenge in SSMF-HCF interconnection is the $\sim$3.5% Fresnel back-reflection that typically occurs at the interface between SSMF and HCF. This back-reflection is also responsible for an additional interconnection loss of 0.16 dB (corresponding to 3.5%). Published results that discuss the reduction of this unwanted back-reflection are summarized in Table 1, including (i) angle-cleaving [13,18], (ii) use of a thin nanospike at the SSMF tip [17], and applying an anti-reflective (AR) coating [10,16]. Unfortunately, none of them has achieved simultaneous low insertion loss (e.g., below 0.2 dB) and low back-reflection (ideally below −60 dB).
This is achieved by depositing an AR coating on an angled MFA, which as we show in this work, reduces the interconnection loss via two effects. Firstly, the angle necessary to achieve back-reflection below −60 dB is reduced with the AR coating from 8$^{\circ }$ to 2$^{\circ }$. This reduces the loss of our interconnection from 0.43 to 0.33 dB. Further loss reduction is achieved by reducing the Fresnel reflection by depositing the AR coating on the interface. This allows us to further reduce the loss from 0.33 down to 0.17 dB. Finally, we show that the low back-reflection level is maintained over more than 400 nm bandwidth and that coupling into higher-order modes is kept low (e.g., below −30 dB for the LP$_{11}$ mode). The presented configuration can be made into a permanent interconnection by gluing, as previously demonstrated, e.g., in [10,19].
2. Interconnection design and component optimization
The components described in this section and their assembly are schematically shown in Fig. 1. We use fiber array technology that is well-established in telecom, e.g., for pigtailing of planar lightwave circuits, with some modification to accommodate for HCFs. For the mode field adaptation from SSMF to HCF, we used a short piece of a graded-index (GRIN) fiber [10,20]. We showed previously that a length of 300$\pm 50$ µm of standard OM2 multimode fiber (core diameter of 50 µm, numerical aperture of 0.20) spliced on the SSMF enlarges the SSMF mode field diameter to 23.2 µm, enabling an insertion loss as low as 0.15 dB for SSMF-MFA-HCF interconnection with flat, AR-coated interfaces [10].
In this work, the MFAs were made as described in [10], but with an angled end facet. Firstly, we prepared a "fiber array", which is essentially a small rectangular silica glass block (thickness of 2 mm; width of 3 mm, and a length of 17-19 mm) with a hole for the fiber [21]. Subsequently, we spliced a short piece (about 500 µm) of OM2 GRIN with SMF-28, inserted it through the hole in the fiber array, and glued it in place using a UV-curable glue. Finally, we polished it to the desired angle and length, thereby forming the MFA. The final length of the angle-polished GRIN segment is then given as an average length between the two edges of the GRIN fiber.
We prepared six pairs of angled MFAs with angles of 0, 2, 4, 6, 8, and $10^{\circ }$, all with a GRIN length of 265 µm. This length is close to the 1/4 pitch that adapts the mode field to 23.2 µm and thus should provide low-loss coupling with the fundamental mode of our HCF which has a mode-field diameter of 24 µm. Firstly, we characterized the back-reflection of the as-polished MFAs at 1550 nm. Subsequently, we deposited a 4-layer TiO$_2$/SiO$_2$ AR coating on them and re-measured the back-reflection at 1550 nm. Finally, we characterized the back-reflected signal over a broad spectral range (1200-1650 nm).
The back-reflected signal power at 1550 nm was measured using the setup shown in Fig. 2(a). The light source that we used for these experiments was based on amplified spontaneous emission from an erbium doped fiber amplifier (EDFA) filtered with a 10-nm (1550$\pm$5 nm) optical band-pass filter (OBPF). The signal was subsequently split using a 3 dB fiber splitter and the MFA under test was spliced to one of its outputs. The other coupler output was cleaved with a large angle to strongly suppress any back-reflection. The back-reflected signal from the MFA was then measured using a power meter (PM, Thorlabs S154C) placed at the reflective port of the 3 dB coupler. The setup was referenced using a flat-cleaved SSMF with a known back-reflection of 3.5%.
Fig. 2. Setup for back-reflection measurement of the prepared mode-field adapters, (a) used for measurement of back-reflected power averaged over the 1545-1555 nm wavelength range, and (b) for measurement of the back-reflection over a 450-nm (1200-1650 nm) spectral range.
For the broadband back-reflection measurements (Fig. 2(b)) we used a supercontinuum light source (SC source, NKT EXR-15) and an optical spectrum analyzer (OSA, Yokogawa AQ6370C).
The measured back-reflection values for all MFAs at 1555 nm, both with and without the AR coating, are shown in Fig. 3. For uncoated MFAs, we observed back-reflection level below our target of −60 dB with 8 and 10$^{\circ }$ angled MFAs. We found that the minimum measurable back-reflection in our setup was approximately −66 dB, likely limited by parasitic back-reflections from the 3 dB splitter or the angle-cleave of the unused 3 dB splitter fiber port. We reached this limit when measuring uncoated MFAs with angles of 8 and 10$^{\circ }$. For MFAs with the AR coating, back-reflections below −60 dB were already achieved with an angle of only 2$^{\circ }$. For larger angles of AR-coated MFAs the level of back-reflection approached our measurement limit of −66 dB.
Fig. 3. Average back-reflected signal power measured over 1550$\pm 5$ nm as a function of the angle of the mode-field adapters with (solid squares) and without (empty circles) the anti-reflective coating.
Back-reflection spectra over a 450 nm bandwidth measured with flat and 2$^{\circ }$ angled MFAs are shown in Fig. 4. For the flat AR-coated MFA, the back-reflection suppression is provided simply by the virtue of the AR coating, which shows a back-reflection of −50 dB over a 30 nm bandwidth at 1580$\pm$15 nm. For the angled uncoated MFA, the back-reflection suppression is broadband and below −40 dB, slightly improving at shorter wavelengths, achieving −50 dB at 1200 nm. Indeed, the combination of both methods provides the best performance. The AR-coated 2$^{\circ }$ angled MFA shows <−60 dB back-reflection over almost the entire measured spectral range. It is worth mentioning that the AR-coated MFAs with higher angles than 2$^{\circ }$ showed back-reflections below our measurement limit.
Fig. 4. Measured back-reflection spectra of flat and 2$^{\circ }$ mode-field adapters with and without AR coating.
The HCF we used is a NANF type that operates in the second antiresonant window [10,22]. The fiber structure consists of six non-touching glass-capillaries, each with a nested capillary, see inset in Fig. 1. The core diameter is 32.5 µm. We have measured the mode-field diameter as 24.1 µm at 1550 nm. The attenuation of the fundamental (LP$_{01}$), LP$_{11}$ and LP$_{02}$ modes calculated using the structure of the manufactured fiber (using the finite element method) are 0.6 dB/km, 35 dB/km and 2100 dB/km, respectively [10]. All modes of higher order suffer even higher attenuation and are therefore not considered.
The NANF was also fixed into a fiber array. However, the approach for fixing the NANF is slightly different to that of the SSMF-GRIN fiber array, as its end-face cannot be polished. Similar to the SSMF-GRIN case, we started with an empty fiber array. However, here we flat cleaved the NANF before insertion into the fiber array. We pushed the inserted NANF slightly out of the end of its fiber array (as shown in Fig. 1) and then glued it in place using a fast UV curable glue that was applied from the back.
As the MFA end-facet is angled and the HCF end-facet is flat cleave, optimum light coupling requires to be aligned with a relative angle, as shown in Fig. 1. Here we see that this angle creates a gap between the MFA and HCF, which is the main reason why the HCF is extended slightly from its fiber array, as shown in the photograph of the aligned interconnection, Fig. 1. Permanent interconnection using such angled connection can be achieved by gluing the two fiber arrays together [19].
3. Coupling analysis
The SSMF-HCF coupling loss was measured using the setup shown in Fig. 5. We began with the loss measurement at 1550 nm with the switch in Fig. 5 in the (a) position. We used two identical connections (at the HCF input and output) and provide the loss of a single connection as one half of the total insertion loss. This approach eliminates contributions from coupling into higher-order modes, which otherwise would lead to an underestimate of the loss between the fundamental modes of the HCF and SSMF [21].
Fig. 5. Setup used for measuring coupling loss and back-reflection. The switch in position (a) is used for interconnection loss measurement and the switch in position (b) is used for back-reflection measurement.
The two light sources used here are the same as those used for the MFA back-reflection characterization, shown in Fig. 2. At both NANF input and output, the fiber arrays were aligned using 5D stages (Thorlabs NanoMax MAX313D/M with pitch and yaw adjustment platform APY002/M). The input side was connected with a 3 dB splitter, where we connected the light source and either a PM or the OSA in the backward direction. The output side was then split with a 3 dB splitter and the signal was characterized with both a PM and an OSA.
To reference our measurement setup, we spliced together pigtailed ends of the input and output sides of the two 3 dB splitters. We then broke this splice and spliced in our aligned NANF with two GRIN MFAs. This results in our measured interconnection loss being slightly higher than the actual loss (since it contains one more splice than the reference measurement). As SSMF-SSMF splices typically have a loss below 0.01 dB, we neglect this, as this level is below our measurement resolution of 0.01 dB. We also neglect any contribution from the NANF loss, which in our experiment is about 0.006 dB (10 m long NANF with a loss of 0.6 dB/km). Since the measured component contains one more splice and also includes the attenuation of the NANF itself, as compared to the reference measurement, our measured overall component loss is overestimated. Subsequently, the actual coupling loss is slightly smaller than the values we give here.
The coupling losses measured prior to and after deposition of the AR coating are shown in Fig. 6. In both cases, the connection loss increases with an increase in the MFA angle. The flat MFA showed a similar performance as reported previously [10] with a minimum loss of 0.15 dB for AR-coated MFAs and 0.31 dB without the AR coating, showing the expected 0.16 dB (3.5%) difference. As the MFA angle is increased, the improvement thanks to the AR coating progressively reduces down to 0.12 dB for the 10$^{\circ }$ angle MFA. We believe this is due to the reduced effectiveness of the AR coating at higher angles, as it was optimized for zero incidence angle.
Fig. 6. Measured SSMF-NANF insertion loss for various mode-field adapter angles with and without the anti-reflective coating.
Additionally, in Fig. 7 we show broadband transmission measured using the setup shown in Fig. 5(b)) for mode-field adapters with 0, 2 and 8$^{\circ }$ angles. We see that transmission loss of all three samples varies by less than 0.2 dB over 1450-1650 nm spectral range. At wavelengths below 1450 nm, the NANF loss increases as we approach the edge of its transmission window.
Fig. 7. Broadband measurement SSMF-NANF-SSMF transmission using selected mode-field adapters with angles of 0 (flat), 2, and 8$^{\circ }$, all with deposited anti-reflective coating.
The back-reflected spectrum of the assembled SSMF-NANF-SSMF component measured with the broadband SC light source and OSA (Fig. 5 with the switch in the (b) position) is shown in Fig. 8. Back-reflection below −60 dB was already achieved over more than a 400 nm bandwidth with the 2$^{\circ }$ MFA with the AR coating.
Fig. 8. Measured back-reflection spectra of the SSMF-NANF-SSMF component for flat and 2$^{\circ }$ angled MFAs, both with the AR coating.
We have evaluated the cross-coupling into higher-order modes at the SSMF-NANF interface using the method described in Ref. [10]. This method uses a Fourier transform of the SMF-NANF-SMF transmission spectra (1545 - 1555 nm in our case), and further analysis that also takes into account the propagation loss of these higher-order modes (which is significant for the LP$_{02}$ mode in our NANF). Examples of the Fourier transformed spectra are shown in Fig. 9, showing data corresponding to the smallest (flat) and the largest (10$^{\circ }$) MFA angles. The highlighted peaks are associated with the LP$_{11}$ and LP$_{02}$ modes for which we obtained the differential group delays from simulations. We evaluated the cross-coupling [10] for all our interconnections and always observed values below −30 dB and −20 dB for the LP$_{11}$ and LP$_{02}$ modes, respectively. This characterization has demonstrated that higher-order mode coupling does not degrade significantly with an increase in the MFA angle.
Fig. 9. Fourier transform of the transmission spectra for (a) flat and (b) 10$^{\circ }$ MFAs showing the higher-order mode coupling.
To showcase the advantage of our low back-reflection interconnection, we reproduced experiments from [13,18], where a significantly larger angle (8$^{\circ }$) was used and associated with significantly higher loss. In our demonstration, an optical signal generated by a frequency-modulated laser (Cobrite DX4) was sent through our SSMF-NANF-SSMF interconnection (10 m NANF) with flat, uncoated MFAs (i.e., similar to a typical spliced connection) and also our 2$^{\circ }$ MFAs with AR coating. The output was then measured using a photodiode (Thorlabs PDA10CF) and captured with an oscilloscope (Keysight MSOS104A), Fig. 10. We see that the transmission through the sample with the flat, uncoated MFAs shows 7% power variations compared to the transmission through the sample with 2$^{\circ }$ MFAs with AR coating. This unwanted phenomenon is caused by the light reflecting off the two flat MFAs, which form a parasitic Fabry-Perot cavity. Using our 2$^{\circ }$ AR-coated MFAs, we completely eliminated this adverse effect.
Fig. 10. Comparison of transmitted laser signal power through the SSMF-NANF-SSMF sample when flat MFAs without AR coating and AR-coated 2$^{\circ }$ angled MFAs are used.
4. Conclusion
We have demonstrated low-loss (0.17 dB) SSMF-NANF interconnection with back-reflection below −60 dB over a bandwidth in excess of 400 nm. This is achieved by using an optimized mode-field adapter with an angle of 2$^{\circ }$ in combination with a deposited AR coating.
Even without depositing any AR coating, the back-reflection can be suppressed below −60 dB, albeit at the cost of slightly increased coupling loss of 0.43 dB. This level of back-reflection performance was also achieved with the uncoated mode field adapter with an angle of 8$^{\circ }$.
We have also characterized unwanted cross-coupling into the higher-order modes and found out that they are kept below −30 dB and −20 dB for the LP$_{11}$ and LP$02$ modes, respectively, even for the largest studied mode-field adapter angle of 10$^{\circ }$.
This work represents the first SSMF-NANF interconnection that has simultaneously ultra-low insertion loss and an excellent level of back-reflection suppression. Thus, this interconnection approach should enable the seamless integration of hollow-core fibers into systems based on standard single-mode fibers.
Funding
Grantová Agentura České Republiky (22-32180S); Ministerstvo Školství, Mládeže a Tělovýchovy (CZ.02.2.69/0.0/0.0/18_053/0016980); Engineering and Physical Sciences Research Council (EP/P030181/1); European Research Council (682724); Royal Academy of Engineering.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data in this paper is accessible through the University of Southampton research repository [23].
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