1. INTRODUCTION
Achieving ultralow loss has been a primary mission within the realm of fiber optics for decades. Over the past half-century, silica-based solid-core fibers have approached the intrinsic Rayleigh scattering loss (RSL) limit of silica glass of 0.14 dB/km [1], leaving little room for further optimization. To push the boundaries of low-loss transmission, researchers have turned their attention to antiresonant hollow-core fibers (AR-HCFs) [2–5]. These fibers can surpass the fundamental RSL limit associated with solid material [6,7], as ∼99.99% of light is confined within an air core, which has an RSL 4 to 5 orders of magnitude lower than that of solid glass [8]. Recent advancements in AR-HCF technology have led to significant reductions in attenuation, with losses dropping to a record-low 0.11 dB/km [9]. This progress holds the potential to revolutionize optical fiber-based applications, especially those requiring long fiber lengths and high performance.
With AR-HCF technology achieving this ultimate level of loss performance, researchers are now comparing its optical metrics with those of solid-core fibers across various parameters. In general, AR-HCF offers several advantages, including 31% lower latency, over 3 orders of magnitude lower nonlinearity, 70% lower chromatic dispersion (compared to standard single-mode fibers at 1550 nm), octave-spanning low-loss bandwidth, and significantly higher damage thresholds [2–5]. Despite these numerous advantages, one of the primary challenges that remains for AR-HCFs is achieving single-mode operation, which is difficult to resolve due to the inherently multimode nature of HCFs [2,5,10].
From an application standpoint, the key mission of optical fiber communications is to transmit large volumes of data over long distances with higher fidelity. Effectively confining light to a single spatial mode is the main strategy to avoid detrimental multipath interferences and ensure high-fidelity transmission [11]. In fiber optical gyroscopes (FOGs), rotational sensitivity improves with the length of the optical path, but nonlinearities and environmental sensitivities in the fiber glass introduce nonreciprocal errors, which fundamentally degrade measurement accuracy [12]. HCFs have the potential to mitigate these errors but face new challenges arising from their multimode nature [13]. As a strong contender for both applications, HCF must overcome the challenge of simultaneously achieving ultralow loss and ultrahigh mode purity.
From a physics perspective, HCFs are multimode by nature, whether based on photonic bandgap (PBG) or antiresonant reflection (AR) mechanisms. In PBG-HCFs, both the fundamental mode (FM) and higher-order modes (HOMs) are confined inside the core, as the PBG cladding prohibits light from propagating through it [10]. In AR-HCFs, light is guided via leaky waves [14,15], with both FM and HOMs satisfying AR conditions within the core, though HOMs experience greater leakage due to their larger glancing angles [14–17]. This is intrinsically different from solid-core fiber, where total internal reflection guidance mechanism governs light propagation. In this case single-mode operation is defined by the V-number of the fiber being less than 2.405 [18].
Several strategies have been proposed to suppress HOMs in AR-HCFs. One approach is to arrange the tubular elements in the cladding asymmetrically, introducing wider gaps that enhance leakage of both FM and HOMs, with HOMs experiencing higher loss [19]. This method is suitable for applications requiring short fiber length, where FM loss is not critical. A more widely adopted approach involves controlling the size of the cladding cavities to allow phase matching between cladding air modes and the core’s HOMs, selectively filtering the latter out [20]. In fivefold double-nested antiresonant nodeless fibers (5-DNANFs), the middle and small nested tubes are deliberately expanded and contracted, respectively, to create a sufficiently large air cavity between them for phase-matching HOMs [21]. However, this requires sacrificing the effectiveness of the air cavity as an AR element [15–17] in order to suppress HOM, creating a trade-off between achieving ultralow loss and maintaining robust single-mode operation.
Here, we introduce what we believe is a novel fourfold truncated DNANF (4T-DNANF) design. We demonstrate that 4T-DNANF can elegantly achieve both ultralow loss and robust single-mode operation, either focusing on one attribute or balancing both simultaneously. Experimentally, with different structural parameters, we demonstrate two combinations: one with an FM loss of 0.1 dB/km and HOM loss of 430 dB/km, and another with an FM loss of 0.13 dB/km and HOM loss of 6500 dB/km. This results in a record-high HOM extinction ratio (HOMER) of 5×104 for HCFs.
2. DESIGN PRINCIPLE
Figure 1(b) illustrates our novel 4T-DNANF design [22]. The purpose of truncating the four large tubes by a 120° segment is not only to reduce the microstructure diameter, as previously done with the fivefold version of the truncated NANF [23], but more importantly, to prevent the cladding air modes in the voids behind the intertube gaps from phase matching with the core FM, which occurs when they share a similar mode field area, leading to an increase in loss by more than 1 order of magnitude. To make a direct comparison, we optimized the structural parameters of both the 4T-DNANF and the fivefold untruncated DNANF [5-DNANF, Fig. 1(a)] to operate at the second-order anti-resonant band at 1550 nm. We simulated the confinement losses (CLs) of the LP01 and LP11 core modes at 1550 nm and calculated their loss ratio using the lowest loss value of LP11 mode, denoted as HOMER. These simulations were conducted using the finite-element method (FEM) with an optimized perfectly matched layer (PML).
Fig. 1. Fiber design and optical property simulations. Cross sections of (a) the 5-DNANF, (b) the 4T-DNANF, and (c) the 4T-DNANF with larger gap, with their structural parameters listed aside. (d), (e), (f) FEM-simulated CLs of the LP01 (black), LP11 (red) core modes, and HOMER (blue) as a function of ?1/?core and ?2/?core for (a), (b), and (c), respectively, where ?1 and ?2 are the thicknesses of the first and second air layer in the cladding and ?core is the core radius. (g) Minimum achievable CL for the structures in (a) and (b) as a function of gap size (black curve, with core radius and glass wall thickness fixed) and core radius (blue curve, with glass wall thickness fixed and gap size linearly scaled), respectively. (h) Effective indices of the core LP01/LP11 modes (black/red), the first cladding air crescent LP01 mode (blue), and the second cladding air crescent LP01 mode (green), along with their corresponding mode-intensity profiles (|?|) in linear scale. The plots inside the green and blue dashed squares show the intensity (|?|) of the core and cladding modes on a logarithmic scale, respectively. (i) Simulated CL and HOMER as a function of wavelength at two ?1/?core values of 0.65 and 0.88, using the structural parameters of (c).
The results in Figs. 1(d) and 1(e) indicate that both the CL and HOMER are strongly influenced by the thicknesses of the first and second cladding air crescents (labeled as ?1 and ?2, respectively) represented by the red and green shaded areas in Figs. 1(b) and 1(a). For the 5-DNANF structure, our simulation in Fig. 1(d) closely aligns with the findings reported in Ref. [21], confirming that utilizing the second cladding air crescent [green shaded area in Fig. 1(a)] is the most efficient approach in filtering out the LP11 core mode while keeping LP01 mode loss low. In this configuration, the maximum HOMER achieved is 4700, with the LP01 core mode’s CL of 0.11 dB/km at ?2/?core=1.1 (?1/?core=0.12).
In contrast, the 4T-DNANF structure outperforms the 5-DNANF in terms of both achievable HOMER and CL. Specifically, when ?1/?core=0.96, the HOMER in the 4T-DNANF reaches an impressive value of 3.2×105, with the CL of the LP01 core mode remaining below 0.01 dB/km. To investigate the cause of this drastic increase in HOMER, we plotted the effective indices (?eff) of relevant modes in Fig. 1(h). At ?1/?core=0.74 (?2/?core=1.05), phase matching occurs between the LP11 core mode and the second cladding air crescent mode, resulting in a HOMER level of 104. This is higher, but comparable to the level observed in the 5-DNANF case. However, when ?1/?core=0.96, the LP11 core mode phase matches with the first cladding air crescent mode, boosting the HOMER to 3.2×105. The proximity of the first cladding air crescent to the core makes it significantly more effective in filtering out HOMs than the second cladding air crescent. This stronger coupling is evident in the intensity distributions of the degenerate modes at the two anticrossing points, shown in the insets of Fig. 1(h) (log scale).
It is important to note that in the 5-DNANF structure [Fig. 1(d)], although phase -matching between the LP11 core mode and the first cladding air crescent mode can also occur at ?1/?core≈1.03, the LP01 core mode loss increases to an unacceptable 0.5 dB/km, with a HOMER of 4496 [black dashed circle in Fig. 1(d) and Ref. [20]]. This is because enlarging the first cladding air crescent for better HOM suppression requires dramatically reducing the size of the middle tube to obtain a ?2/?core ratio of 0.22 [schematically shown in the inset of Fig. 1(d)]. Under this circumstance, when light inside the core attempts to leak away along a certain radial direction [the yellow dashed arrow in Fig. 1(d)], it may not experience the obstruction of the middle tube, resulting in a much weaker light confinement. While this effect is also present in the 4T-DNANF, it is much less pronounced, as the middle tube remains sufficiently large relative to the core size [?2/?core=0.83, schematically shown in the inset of Fig. 1(e)] in the fourfold cladding arrangement. As a result, the CL of the LP01 core mode increases only slightly from its minimum value by 0.003 dB/km. The 4T-DNANF structure, therefore, allows for the simultaneous achievement of both high HOMER and low CL. Note here that FEM simulation indicates that the next lowest losses after LP11 are associated with the LP21 and LP02 modes, which exhibit significantly higher HOMER values of 1.2×106 and 1.9×106 at ?1/?core=0.96, respectively. As a result, their impact on single-mode performance is negligible.
Next, we examine the minimum achievable CL in both fiber structures, accepting some trade-off in HOMER. For the 5-DNANF, the CL reaches 0.009 dB/km at ?2/?core=0.8 (?1/?core=0.45), while the HOMER is only 25. In contrast, the 4T-DNANF achieves a CL of 0.002 dB/km at ?1/?core=0.8, while maintaining a HOMER of 4300—similar to the maximum achievable HOMER in the 5-DNANF. Although this level of loss is not yet achieved in experiments, as other loss contributions, including surface scattering loss (SSL), microbending loss (MIBL), and gas absorption loss, all exceed 0.01 dB/km, exploring the minimum CL remains valuable. Not only does it present the fundamental intrinsic loss mechanism, but more importantly, a lower CL provides greater flexibility in adjusting structural parameters for practical applications.
As illustrative examples, we consider two specific scenarios. The first involves reducing the core size to match that of a standard single-mode fiber (SSMF) for intradata center applications or to minimize the bending loss for gyroscope applications. A smaller core size leads to a larger glancing angle for FM, significantly increasing the leakage loss. It has been predicted that for a DNANF structure, the CL increases as ?core−10 [5]. To assess the impact of core radius variation on loss performance, we used the minimum loss points from Figs. 1(d) and 1(e) (highlighted by the gray solid circles) as a reference and scale down the structure (with the glass wall thickness fixed). The simulation results are shown in the blue curves in Fig. 1(g). For small core radii, the achievable CL of the LP01 core mode in 4T-DNANF is 1 to 2 orders of magnitude lower than that in 5-DNANF. At ?core around 8 µm, where the mode field diameter roughly matches that of SSMF, 4T-DNANF exhibits a CL of several dB/km [24], compared to the hundreds of dB/km CL of 5-DNANF [25], making the former far more suitable for small-core-radius applications.
The second case considers the intertube gap size, a critical parameter in fiber fabrication. The simulation results in Figs. 1(d) and 1(e) were based on an optimal intertube gap size of approximately 4 µm. However, in practical fiber fabrication, a small gap between adjacent tubes requires higher draw tension to prevent contact between them, which can increase the risk of fiber breakage. Relaxing the gap size requirement is likely one of the approaches to increasing the fiber yield. In Fig. 1(g), we fixed all key parameters, including the core radius and glass wall thickness, for the lowest CL in Figs. 1(d) and 1(e) and only varied the gap size (black curves). If we consider an acceptable CL level of 0.1 dB/km, the permissible gap sizes are 5.4 µm for the 5-DNANF and 7.6 µm for the 4T-DNANF. While 5.4 µm remains challenging, a gap size of 7.6 µm offers greater flexibility in fiber fabrication.
Fig. 2. AR-HCF fabrications and loss measurements. (a)–(e) SEM images of the five fabricated 4T-DNANFs with their structural parameters listed in (l). Scale bar, 50 µm. (f) Measured transmission (blue and red) and loss (black) spectra of Fiber #1. The measurement uncertainty is indicated by the grey shaded area. (g) Loss spectrum of Fiber #1 measured with a wavelength resolution of 0.05 nm, revealing the absorption lines from CO2 gas. (h) one-way OTDR traces of a 4T-DNANF (Fiber #1), a G.654E fiber, and a G.652D fiber in the left axis, and accumulated losses measured by two-way OTDR in the right axis. (i) Same as (f) for Fiber #5. (j) S2-imaging measurement of Fiber #5 with varying fiber lengths. The insets show the reconstructed mode-intensity profiles at two different differential group delays. (k) Fitted loss curve of the LP11 mode derived from (j) for Fiber #5. (l) Summaries of structural parameters, modal losses, and HOMER for the five AR-HCFs. The variations in structural parameters are obtained by measuring the cross-section at both ends of the several-km-long fiber. (m) Measured average losses of the LP01 and LP11 modes in the 1540–1560 nm range, along with the corresponding HOMER for Fibers #1 to #5.
Relaxing the gap size makes our fiber fabrication process, discussed in Section 3, more manageable. Accordingly, Fig. 1(f) presents simulation results based on the relaxed structural parameter of a 7 µm gap size, as depicted schematically in Fig. 1(c). In the region where ?1/?core ranges between 0.4 and 0.8, corresponding to unitizing the first cladding air crescent to filter out HOMs, a CL below 0.04 dB/km with a HOMER close to 104 is achievable. When ?1/?core is between 0.8 and 1, corresponding to unitizing the second cladding air crescent to filter out HOMs, a CL ranging from 0.04 to 0.15 dB/km with a HOMER above 104 is attainable. In Fig. 1(i), we scan the spectral range from 1300 to 1700 nm with two fixed ?1/?core values of 0.65 and 0.88, representing two strategies: achieving a loss below 0.1 dB/km with an acceptable HOMER under 104 or achieving a HOMER above 104 with a slightly higher total loss above 0.1 dB/km (allowing room for SSL and MIBL). These two strategies are employed in our fiber fabrication, as discussed in the next section.
3. FIBER FABRICATION AND CHARACTERIZATION
To implement this design strategy, a series of 4T-DNANFs with different ?1/?core values were fabricated, with their scanning electron microscopy (SEM) images shown in Figs. 2(a)–2(e). These fibers were produced using a modified two-step stack-and-draw method, where large tubes were precut at specific angles with high-power lasers before stacking. The key structural parameters are listed in Fig. 2(l). We focus on Fiber #1 and Fiber #5 for detailed analysis of their optical performance.
Fiber #1 has an average ?1/?core of 0.65, corresponding to the simulation results in Fig. 1(i, solid curves), designed for a total loss of less than 0.1 dB/km. A total fiber length of 4.2 km is fabricated. Given this relatively short fiber length at this ultralow loss level, the loss value must be determined with great care. Here, three independent loss measurements were conducted with the fiber wound on a standard drum with a diameter of 32 cm. The first measurement involved a cutback loss assessment from 4.2 km to 20 m using a supercontinuum source (YSL Photonics, SC-5) and an optical spectrum analyzer (OSA, Yokogawa, AQ6370D). The supercontinuum was butt-coupled to 4T-DNANF through a mode field adaptor to minimize the excitation of HOMs. For both long and short lengths, three traces with different output fiber cleaves were acquired to minimize cleaving and OSA coupling errors, with their averaged traces shown in the blue and red curves of Fig. 2(f). The measured loss spectrum, depicted in the black curve in Fig. 2(f), exhibits an attenuation baseline below 0.1 dB/km from 1514 to 1600 nm, covering most of the C+L band. The measurement uncertainty arising from variations in cleaves, coupling, and light source drift is labeled by the shaded area. At 1550 nm, the loss is 0.09±0.01dB/km. The spectral peaks from 1480 to 1510 nm are due to the atmospheric water absorption [26]. Another major absorption peaks in the C+L band originates from atmospheric gases, which can hardly be detected at 0.5 nm resolution on the OSA. However, by increasing the resolution to 0.05 nm and repeating the cutback measurement from 1560 to 1620 nm, we can clearly observe loss peaks with frequency spacing of several tens of gigahertz, resulting in an additional 0.1 dB/km loss at specific wavelengths. Database records indicate that these peaks strongly overlap with the vibrational and rotational absorption lines of CO2 molecules [27]. To eliminate all these peaks, careful purging of the fiber preforms to prevent air from entering the core is necessary, which will be the focus of our next phase of work. The second independent loss measurement was performed at a fixed wavelength of 1550 nm with a stable distributed feedback (DFB) laser and a power meter. Ten data points were recorded at 5-min intervals, each with a new cleave, before and after the cutback, to ensure minimal error. This resulted in a loss figure of 0.1±0.01dB/km [pink star point in Fig. 2(f)]. The third measurement was done using optical time domain reflectometry (OTDR) at 1550 nm. Here, both one-way and two-way OTDR [28] were carried out. Using one-way OTDR, a comparison with commercially available G.652D an G.654E fibers showed a trace with a lower backscattered intensity but a gentler slope, corresponding to a fitted loss of 0.11 dB/km [Fig. 2(h), left axis]. Note that the as-drawn fiber has a subatmosphere pressure [29], and since the fiber had been exposed to the atmosphere for some time, air enters the fiber from both ends. The stronger backscattering from the air compared to the glass surfaces means that the steep trace at the beginning and the end actually represents the distribution of gas rather than the fiber loss [30]. Therefore, only the middle section from 1 to 3.5 km is used to determine the slope. The two-way OTDR measurement, conducted in accordance with the methodology outlined in [28], provided a more accurate means of extracting the distributed loss, independent of the gas distribution. The fitted loss was 0.09 dB/km [Fig. 2(h), right axis]. Based on these three sets of measurements, we conclude that fiber #1 achieved a loss of 0.1±0.02dB/km in the C-band. It is possible that in certain wavelength regions, the loss has reached even lower level. However, accurately determining such a low loss level requires fiber lengths exceeding 10 km, which will be a focus of future work. Given that the simulated CL reached 0.02 dB/km in Fig. 1(i), we speculate that MIBL and SSL together contribute approximately 0.08 dB/km to the overall loss. Notably, several measures have already been implemented to mitigate microbending loss, such as applying a thicker silica jacket and a double acrylate coating with a soft primary layer and a hard secondary layer, leading to a bare fiber outer diameter of 240 µm and a coated diameter of 480 µm. However, microbending likely remains a significant contributor to the total loss. For SSL, while the approach suggested in [31] may offer a potential reduction, it has not been incorporated into our fiber fabrication process. Though accurately quantifying the individual contributions of MIBL and SSL experimentally remains challenging, we believe that these two loss components could be further reduced with technical advancements, a goal that will be the focus of future work.
For Fiber #5, the measured average ?1/?core is 0.88. This corresponds to the simulation results in Fig. 1(i) (dashed curves), which were designed to achieve very high HOMER. The loss of the FM was measured in the same way as Fiber #1 and shows a loss level of 0.13±0.01dB/km at 1550 nm, as shown in Fig. 2(i). To measure the loss of the HOMs, a combination of cutback and spatially and spectrally (S2) resolved imaging measurement was conducted with a scanning bandwidth of 20 nm from 1540 to 1560 nm and a resolution of 0.2 nm [32–34]. The output light spot from the fiber was magnified to µµ150µm×150µm by lens and imaged by a CCD (WiDy Sens 320, NIT) camera with 100pixels×100pixels. An offset coupling of approximately 2 µm was employed to maximize the intensity proportion of HOMs. Despite this, no HOMs were observed for fiber lengths longer than 7 m. The fiber was cut back incrementally to lengths of 6, 5, and 4 m, and at each length, multiple S2 measurements were performed with different cleaves. A linear fit was applied to determine the mode loss. The same measurements were also performed on multiple segments of the same fiber, and the measured loss of LP11 mode were found to be consistently similar. The results, shown in Figs. 2(j) and 2(k), reveal an LP11 mode loss of 6.5 dB/m, with no other mode content observed. The same method was applied to Fiber #1 with a 20 m long length, showing a LP11 mode loss of 0.43 dB/m. In telecommunication, it has been noted that fibers with an HOM loss of 1–2 dB/m is consistent with the standard “cable cutoff” definition [35]. While Fiber #1, which utilizes the second cladding air crescent to filter out HOMs, does not meet this HOM loss threshold, Fiber #5 exceeds this requirement by a significant margin. For applications demanding high mode purity, such as FOG, it is highly advantageous to increase the FM loss by just 0.03 dB/km (when comparing Fiber #5 to Fiber #1), yielding a more than tenfold improvement in the HOMER, from 4300 to 5×104.
The measured loss of LP01 and LP11 modes of Fibers #1 to #5 are listed in Fig. 2(l). All five fibers show FM losses under 0.2 dB/km. A clear trend of increasing LP11 mode loss with ?1/?core is observed, as shown in Fig. 2(m), confirming the importance of the first cladding air crescent in HOM filtering. These fibers demonstrate strategies for achieving ultralow FM loss with acceptable HOM loss or very high mode purity still with very low loss for various applications.
The fiber’s other optical properties, such as chromatic dispersion (CD) and bending loss, are comparable to those other AR-HCFs with the same core size. The CD value is measured to be 2–4 ps/nm/km in the C-band, and no distinguishable bending loss is observed for radii of 8 cm over 300 turns. These properties will not be elaborated upon here.
4. DISCUSSION AND CONCLUSIONS
Low loss AR-HCFs typically consist of multiple AR layers [17], including both silica membranes and air cavity. While the silica membranes are typically highlighted for their role in AR, the air layers are equally important. These air layers serve two critical functions: they not only contribute to the antiresonant guiding mechanism but also play a key role in stripping out HOMs. The choice of a 4T-DNANF design over 5-DNANF is directly related to the optimization of the air cavity. By fine-tuning its dimensions, the 4T-DNANF achieves a superior balance between low FM loss and high HOM extinction, overcoming the inherent multimode nature of HCFs. The flexibility in tuning the core and cladding parameters also opens up new possibilities for further reducing loss and enhancing performance in future fiber designs. These findings represent a significant contribution to the development of next-generation optical fibers for advanced communication and sensing technologies.
