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Abstract
A novel technique referred to as optical side leakage radiometry is proposed and experimentally demonstrated for non-destructive and distributed characterization of anti-resonant hollow-core optical fibers with high spatial resolution. Through in-depth analysis of the leakage light collection, we discover a unique polarization dependence, which is validated by our experiment. By leveraging this effect and employing Fourier filtering, this method enables accurate quantification of propagation attenuations for fundamental and higher order modes (with the uncertainty of <1 dB/km), identification of localized defects (with the resolution of ∼5 cm), and measurement of ultra-low spectral phase birefringence (at the level of 10−7) in two in-house-fabricated nested antiresonant nodeless hollow-core fibers. Such a fiber characterization approach, boasting unprecedently high accuracy and a potentially wide dynamic range, holds the potential to become an indispensable diagnosis tool for monitoring and assisting the manufacture of high-quality anti-resonant hollow-core fiber.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Over the past three decades, the hollow-core optical fiber (HCF) technology [1–5] has made remarkable progress, rivaling or even surpassing standard silica-core single-mode fiber (SCF) in numerous conventional optical metrics, such as attenuation [6], bandwidth [7], interconnection loss [8] and more. The inherent gas nature of HCF provides capabilities beyond the reach of SCF, including near-vacuum latency [9], ultralow nonlinearity [10,11], exceptionally high laser damage threshold [12], minimal inter-polarization crosstalk [13,14], ultralow Rayleigh/Brillouin backscatting [15,16], and low thermal sensitivity [17,18]. These significant advances owe much to the new design and fabrication of anti-resonant version of HCFs (referred to as ARF hereafter, distinct from earlier version of photonics bandgap HCFs or PBGF) with multi-layered tubular cladding structures [19–22]. The breakthrough in achieving low-loss property has positioned ARF favorably for various long-haul application scenarios, especially in data transmission [23,24]. Accordingly, evaluating a fiber in terms of attenuation, localized defects and discontinuities, and sometimes birefringence has become crucial in improving the quality of fabrication.
The widely adopted distributed measurement approaches for SCFs or PBGFs usually rely on detection of Rayleigh backscattering, employing methods like optical time domain reflectometry (OTDR) [25] and optical frequency domain reflectometry (OFDR) [26]. However, in contrast to the light guidance by evanescent fields in a SCF or PBGF, ARF predominantly exhibits a leaky mode nature with an outgoing boundary [27] (Fig. 1). The Rayleigh scattering induced backscattering from gas and gas-silica interfaces in ARF are nearly 30 dB and 40 dB lower in magnitude compared to silica fiber (∼ −72 dB/m) at telecom wavelength [15,28], respectively. Although OTDR and OFDR methods have successfully detected such level of Rayleigh backscattering in ARF [29–31] using setups with enhanced detection sensitivity, the sacrifice of spatial resolution to meter-scale seems inevitable and may greatly blur the measured traces. Moreover, the strong back-reflections at all SCF-HCF interconnections could substantially reduce measurement sensitivity and dynamic range. Effectively suppressing these back-reflections in a convenient way remains a considerable challenge for all the reflectometric methods [29].
Fig. 1. Illustration of (a) volumetric scattering, (b) surface scattering, and (c) leakage in a SCF, a PBGF, and an ARF, respectively. The different magnitudes of backscattering and the refractive index (RI) profile characteristics of these three types of fibers are denoted. Inset in (c): schematic view of multiple refraction when the leaked light passes through the silica jacket and the polymer coating layers. The beam directions inside different media can be determined by the Snell’s law.
An alternative solution involves probing side light along the length of a fiber [32]. Such methods inherently offer high spatial resolution (at the scale of centimeters) and a large dynamic range (without roundtrip fiber attenuation), and have been demonstrated in distributed characterization of PBGFs by employing an integrating sphere [33]. However, the distinct feature of directional radiation at a specific angle [34] and varying radiation patterns due to polarization changes [27] in the leakage light from ARFs add complexity to the light collection process. So far, to the best of our knowledge, a comprehensive study detailing the radiation angle and polarization relevance in side light measurement of ARFs has not been reported.
In this work, we propose an optical side leakage radiometry (OSLR) method for characterizing ARFs. We theoretically and experimentally verify the polarization-sensitive nature of leakage light collection, which is a unique characteristic specific to ARFs. The implementation of OSLR measurement on two in-house-fabricated nested antiresonant nodeless fibers (NANFs [20]) provides intricate details on propagation loss, localized defects, and phase birefringence with exceptional accuracy.
2. Theoretical analysis
Figure 2(a) illustrates the fundamental principle behind OSLR, where light radiated from a fiber is collected by an integrating sphere (IS). Within the IS, the light undergoes multiple reflections before being squeezed out of side ports and coupled to photodetectors (PD). The measured intensity of light (IPD) can be expressed as
where Ifiber is the intensity of the guided light within the fiber segment, αloss is the combined coefficients of leakage and scattering losses in the fiber, and ηIS stands for the light collection efficiency of the IS. β stands for the transmission coefficient across the silica jacket and the polymer (acrylate) coating layers, which can be safely treated as a constant in our measurement, and thus will not affect the subsequent analysis. Notably, due to the cylindrical symmetry of both the jacket and the coating layers, β remains constant for all azimuthal angles ($\phi $’s), considering a spherical coordinate system ($r,\;\theta,\;\phi $).Fig. 2. (a) The principle of leakage light collection by an IS. IS: integrating sphere; PD: photodetector. Schematics of (b) light leakage out of an ARF and (c) varied radial Poyting fluxes with different SOPs.
In case of SCFs or PBGFs, light escaping the fiber predominantly results from volumetric or surface Rayleigh scattering, leading to a wide spread in the polar angle ($\theta $) of light propagation [34]. As a result, most radiated light can be effectively captured by the IS, resulting in a near-unity ηIS.
On the contrary, in the context of ARFs, ηIS exhibits notable variation. First and foremost, the out-escaping light is primarily results from leakage [4,5], which differs in nature from the stochastic scattering process. Therefore, the radiation angle adheres to the propagation constant matching condition [34] [Fig. 2(b)]. The effective modal indices of an ARF can be approximately expressed by Marcatili and Schmeltzer’s formula [35], wherein the propagation constant matching condition governs the outward leakage angle to be
where λ is the wavelength, a is the core radius of the ARF, and unm is the mth zero of the Bessel function of the first kind Jn−1(x). Note that the presence of the jacket and the coating layers does not alter Eq. (2), because the leakage light will finally propagate in the air after multi refraction [see the inset of Fig. 1(c)]. As an instance, we take λ = 1550 nm, a = 15 µm, and u01 ≈ 2.405 for the fundamental (LP01) mode, the result of θ ≈ 2.3° hints that most leakage light from an ARF remains near the fiber for a long distance and may significantly escape through the output port of the IS. Considering the dimensions of a typical IS (e.g., the side length of 50 mm, and the input/output port diameter of 2 mm) and the diameter of a polymer-coated fiber under test (FUT) of 0.5 mm, the effective collection angle of the IS should be greater than arctan[(2-0.5)/50] ≈ 1.7°, as illustrated by Fig. 2(a). However, a small and directional leakage angle featured by an ARF may lead to notable and variable light escape out of the IS [see Fig. 2(a)].The second complexity arises in practical measurements where an ARF usually tilts at an angle within an IS, rendering ηIS sensitive to polarization. As illustrated in Fig. 2(c), variations in the state of polarization (SOP) of the guided mode result in changes in azimuthally-resolved radial Poynting flux [27]. In the case of a NANF, light primarily leaks out of the core through inter-tube gaps or in the directions of inner tubes [as shown by the lobes in Fig. 2(c)] [5], and the SOP of the core mode can influence the proportion of component leakage lobes. It is worth noting that this polarization sensitivity can be enhanced as the leakage angle decreases, e.g., at a short wavelength or with a large core size according to Eq. (2).
3. Validation of polarization relevance of light leakage
3.1 ARFs under test
To validate the polarization relevance of leakage light collection, we investigated two in-house-fabricated ARFs (NANF#1 and NANF#2). The lengths, core diameters, average glass wall thicknesses, gap spacings, average outer tube diameters, and average inner tube diameters of these two fibers are measured to be 140 m/450 m, 28 µm/27 µm, ∼455 nm/∼460 nm, 3.3-9.9 µm/4.8-7.3 µm, 22.9 µm/24.9 µm, and 11.8 µm/12.1 µm, respectively. The cut-back measured loss spectra of NANF#1 and NANF#2 are depicted in Fig. 3(a). Additionally, scanning electron microscope (SEM) images of the cross-sections are shown in the inset of Fig. 3(a).
Fig. 3. (a) The cut-back measured loss spectra of the two NANFs. Inset: SEM cross-sectional images. (b) FEM simulated longitudinal (in log scale) and radial (in linear scale) Poynting fluxes of the fundamental modes for both polarizations.
Utilizing finite element method (FEM) simulations based on SEM measured cross-sections of the two NANFs, Fig. 3(b) displays the radial Poynting fluxes of the fundamental modes at 1550 nm and of the two polarizations. Analysis of the radial leakage distributions plotted against azimuthal angle coordinate indicates clear polarization relevance in both NANF#1 and NANF#2, in accordance with Fig. 2(c). Notably, the polarization relevance is more pronounced in NANF#1 compared to NANF#2, probably due to the presence of two prominent inter-tube gaps in NANF#1 [highlighted by the yellow arrows in Fig. 3(a)].
3.2 Polarization induced variation of ηIS
The setup for polarization relevance measurement is illustrated in Fig. 4(a). Light from a laser source at 1550 nm (ID Photonics, CBDX1, with the line-width of <100 kHz) is free-space coupled into the FUT. The SOP of launched light is controlled by a polarizer and a half-wave plate (HWP). Two identical ISs (IS#1 and IS#2, Thorlabs, 2P4/M), providing spatial resolution of ∼5 cm, are placed near the two ends of the fiber with spacings of L1 and L2, respectively. The collected lights (IPD’s) are detected by three identical PDs (Thorlabs, PDF10C/M, with the specified dynamic range of ∼34 dB). Note that in IS#2, two PDs (PD2 and PD3) are mounted at the top port and the side port, respectively. In addition, an optical power meter (PM, Thorlabs, PM100D) is employed to simultaneously monitor the output power of the fiber (IPM).
Fig. 4. (a) The setup of leakage light collection measurement composed of two ISs. Pol.: polarizer; HWP: half-wave plate; FUT: fiber under test; PM: optical power meter. (b) Normalized values of IPD/IPM measured by IS#1 (blue line) and IS#2 (black/red lines) for NANF#1 with L1 = 5 m and L2 = 0.3 m. The dashed lines represent another measurement after carefully repositioning the fiber. (c) The same as (b) for NANF#2 and with L1 = 0.5 m. (d) The same as (b) for a single mode fiber (SMF).
The first measurement is implemented on the high-loss NANF#1. As the linear polarization angle of input light rotates, the collected leakage light power by the three PDs and the output light power by the PM yield normalized ratios of IPD and IPM, detailed in Fig. 4(b). Notably, IS#2 is placed very close to the output end of the fiber (L2 ≈ 0.3 m) to ensure a negligible loss due to guided light propagation from IS#2 to the output end. Conversely, IS#1 is situated far away from the input end of the fiber (L1 ≈ 5 m) to eliminate spurious high order modes (HOMs). Referring back to Eq. (1) and assuming IPM = Ifiber and unchanged coefficients of αloss and β, the measured IPD/IPM reflects the variation of ηIS.
In this manner, the black and the red curves in Fig. 4(b) unequivocally demonstrate the polarization relevance of leakage light collection in IS#2, displaying two cycles with the rotation of the input polarization angle. The ηIS’s measured by PD2 and PD3 are nearly the same, confirming an identical collection efficiency of the IS. Adjustments in the position and angle of NANF#1 inside the IS can significantly reduce the polarization sensitivity of IPD/IPM (so that ηIS), as shown by the dash lines in Fig. 4(b), however retaining the two-cycles-per-rotation feature. Measurements are also carried out in IS#1, revealing a same two-cycles-per-rotation feature, depicted by the blue line in Fig. 4(b). The offset of the blue curve relative to the black/red curves may be attributed to the birefringent nature of the fiber. Leveraging this polarization relevance, our measurement can probably provide information of extremely weak phase birefringence, as discussed further below.
Similar polarization relevance of leakage light collection is observed in NANF#2, where the polarization dependent attenuation of the entire fiber has no longer been measured by the output PM. Figure 4(c) shows the same two-cycles-per-rotation feature in NANF#2 when the two ISs are placed near the input (L1 ≈ 0.5 m) and the output (L2 ≈ 0.3 m) ends. The greater undulation of the blue curve compared to the black/red curves in Fig. 4(c) compared to Fig. 4(b) suggests that residual HOM components might not have been completely eliminated as IS#1 is very close to the input end of fiber.
To further justify our understanding to the leakage light collection process, we examine a standard single mode fiber (SMF). As shown in Fig. 4(d), the acquired IPD/IPM at PD2 and PD3 in IS#2 (the black and the red dash lines) vary in opposite trends with the rotation of the polarization angle, and the sum of these two curves seldom exhibits polarization relevance. These distinct features imply a different collection process between light scattering and light leakage.
4. Results of OSLR characterization
4.1 Experimental setup
As a fiber passes through an IS, distributed characterization of its optical properties can be implemented by the OSLR method. In our setup, as shown in Fig. 5, we utilize a fiber rewinder where the FUT coiled from one bobbin to another with the circumference of 1 m. In this work, the rewinding speed is kept to be less than 10 m/min, to minimize fiber vibration and then the fluctuation of ηIS. This speed limit could be raised in the future when the stability of rewinding setup is improved. Additionally, a fiber rotary joint (Chihong Tech., G007) is employed to launch continuous-wave laser light into the SMF pigtail of the FUT with a consistent efficiency. The photocurrent detected by a PD is recorded by a data acquisition card in real time, together with the fiber distance.
4.2 OSLR measurement of NANF#1: phase birefringence and attenuation
The OSLR measurement of NANF#1 is conducted with the laser power of ∼2 mW at 1550 nm. Figure 6(a) shows the original data. The leakage light trace exhibits a logarithmic decay from the very onset, indicating rapid removal of HOMs within NANF#1. FEM simulated losses of the LP11 mode group at 1550 nm range between 3000-5000 dB/km. The second notable feature of the OSLR trace is its periodic fluctuation, which may be attributed to the polarization relevance of leakage light collection discussed in section III along with a possible polarization dependent loss (PDL) at the SMF-ARF splicing point (see the inset of Fig. 5). It is worth to note that we have tested and ruled out the fluctuation of insertion loss originating from the fiber rotary joint when it rotates.
Fig. 6. (a) The OSLR trace of NANF#1 at 1550 nm. The inset shows a magnified view of the trace. (b) The amplitude of FT of the trace in (a). (c) The OSLR trace after low-pass filtering and inverse FT.
To decompose the fluctuation function, the OSLR trace is Fourier transformed (FT) after compensating for its mean decay. As shown in Fig. 6(b), the FT curve exhibits several peaks. Firstly, the peak at the spatial frequency of 1 m−1 is linked to the 1 m circumference of the bobbins. Because of the irregularity of the bobbin shape (slightly different from an ideal cylinder), the fiber inside the IS wobbles periodically during measurement, thus resulting in this 1 m−1 peak. Secondly, the spatial frequency peak of 2 m−1 represents the periodicity of two cycles per rotation in our OSLR configuration. As the SOP of the input light rotates (see the inset in Fig. 5), the insertion loss of the SMF-ARF splice and the leakage light collection efficiency of the IS (ηIS) vary periodically, contributing ∼70% and ∼30% to the 2 m−1 peak in Fig. 6(b), respectively. Thirdly and very interestingly, an explicit peak at ∼0.38 m−1 is observed in Fig. 6(b), originating from additional polarization relevance in our configuration, i.e., the fiber birefringence induced periodic SOP evolution. From the position of this peak, we derive the phase birefringence of NANF#1 at 1550 nm to be ∼5.9 × 10−7. In literatures, such a low phase birefringence (with a beating length of ∼2.6 m) can only be discerned by some sophisticated distributed measurement on the basis of polarization correlation [36]. Additionally, the gray arrows in Fig. 6(b) also label the peaks produced by the combination (sum or difference) of the above three spatial frequencies.
After filtering out all the peaks in the FT spectrum and applying inverse FT, Fig. 6(c) presents a smoothed OSLR trace. Its slope of ∼44.9 dB/km corresponds to the propagation loss of the fundamental mode of NANF#1, agreeing well with the cut-back measured result of ∼45.2 dB/km at 1550 nm.
Furthermore, by using two tunable lasers (Santec, TSL-550A, 1260 nm-1480 nm, and ID Photonics, CBDX1, 1530 nm-1565 nm), our OSLR measurement of the loss and phase birefringence also extends to a wide wavelength range. As shown in Figs. 7(a) and 7(b), the OSLR measured results (red points) coincide well with the cut-back measured loss spectrum (with the maximum difference of 1 dB/km) and the simulated spectral phase birefringence (with the maximum difference of 0.8 × 10−7), respectively. In our simulation, the cross section of NANF#1 is captured from SEM images, and a FEM solver with proper mesh and perfectly matched layer setting is implemented. The FEM simulation accounts for two contributions of birefringence in NANF#1, i.e., the form birefringence induced by the irregular pentagon core shape and the resonance birefringence caused by the non-uniform glass wall thicknesses [37] (see the inset of Fig. 7). It is worth to note that fiber bending will incur an additional birefringence of ±0.4 × 10−7 according to our simulations.
Fig. 7. (a) The spectral losses of NANF#1 measured by cut back method (black line) and OSLR method (red points), respectively. (b) The spectral phase birefringence’s of NANF#1 by simulation (black line) and OSLR measurement (red points), respectively. Inset: SEM image and the measured glass wall thicknesses of the five outer tubes. Note that t2 < t3 ≈ t4 < t1 < t5 and Δt ≈ 40 nm (∼9%).
4.3 OSLR measurement of NANF#2: localized defects
Figure. 8(a) shows three OLSR traces of NANF#2 after FT (inverse FT) and low-pass filtering treatment. Three different laser powers (16 dBm, 12 dBm, 8.8 dBm, respectively) at 1550 nm have been employed but the results remain nearly identical. These OSLR traces exhibit three discernible sections: the HOM dominant section in the initial part, the fundamental mode dominant section in the latter part, and the other segments relevant to local defects. In the initial ∼30 m section, the leakage light from HOMs (e.g., the LP11 mode) overwhelms because a HOM inherently has the greater leakage light collection than the fundamental mode owing to its larger attenuation of αloss and bigger leakage angle of $\theta$ (hence larger ηIS) [see Eqs. (1) and (2)]. In this segment, a mean loss of ∼300 dB/km is measured, roughly agreeing with the simulated losses of the LP11 mode group in NANF#2, ranging from 100-220 dB/km. In contrast, after the fiber length of 80 m, the light leakage mainly embodies the contribution of fundamental mode. The average loss of the fundamental mode is linearly fitted to be ∼7 dB/km, lower than the cut-back measured result of 8 dB/km at 1550 nm. This discrepancy can be partly ascribed to the fact that the cut-back measurement has accounted for some HOMs contributions, while the distributed characterization of OSLR provides finer details along the fiber.
Fig. 8. (a) Three OSLR traces of NANF#2 after FT and low-pass filtering. Three different input powers have been employed at 1550 nm. The inset shows a magnified view of two defect peaks at ∼360 m. (b) The amplitudes of FT of 80-450 m part of the OSLR trace in (a), respectively.
During the measurement of NANF#2, similar polarization relevance of leakage light collection is encountered. After doing FT to the 80-450 m segment of the original OSLR trace, the spatial frequency spectra of the fundamental mode are manifest in Fig. 8(b). The relatively lower 2 m−1 peak in Fig. 8(b) compared to that in Fig. 6(b) could probably be explained by the weaker polarization relevance of the radiation pattern of NANF#2 [see Fig. 3(b)]. Additionally, in Fig. 8(b), the fiber birefringence induced spatial frequency peak is also noticeable. The derived phase birefringence of the fundamental mode is ∼1.9 × 10−7 (with the beating length of 8.2 m), closely aligning with the simulated results of (2.1 ± 0.4) × 10−7 for NANF#2. This result reaffirms the unique capacity of the OSLR approach to measure phase birefringence of an ARF in a low level of 10−7.
5. Conclusion
In summary, non-destructive and distributed characterization of ARF is realized by using OSLR method. A comprehensive examination of the light collection within an IS, combined with the distinctive nature of leakage light guidance in ARFs, reveals a unique polarization relevance in side leakage measurement. Based on two in-house-fabricated NANF samples, we not only validate this polarization effect but also achieve phase birefringence measurement at an exceptionally low level of 10−7 (corresponding to a beating length of several meters).
Moreover, such measurements can offer longitudinal insights into an ARF, encompassing the HOM pervasive regions, propagation losses of both fundamental and HOM modes, and the precise identification of defect locations with a high spatial resolution (of ∼cm level) and a high dynamic range (up to 60 dB, limited by the used PD or PD set [33]). These attributes suggest that the OSLR technique has the potential to evolve into a critical tool for the quality inspection of ARFs.
Funding
National Natural Science Foundation of China (62075083, 62105122, 62222506, U21A20506); Basic and Applied Basic Research Foundation of Guangdong Province (2021A1515011646, 2021B1515020030, 2022A1515110218); Guangzhou Science and Technology Program (202201010460).
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.
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