1. Introduction

Hollow-core photonic crystal fiber (HC-PCF) has now been recognized as a versatile tool in the field of optics and beyond. To enhance their capability of handling real-world applications, one key pursuit of HC-PCF development is to combine broad spectral bandwidth, low transmission loss, and low bending sensitivity into a single fiber. So far, there are two types of fibers available, namely hollow-core photonic bandgap fiber (HC-PBGF) [1] and hollow-core anti-resonant fiber (HC- ARF) (or inhibited-coupling fiber) [2]. HC-ARF is a good candidate for broadband operation because glass webs in the cladding area, which can be approximately regarded as one dimensional optical structures [3], have much sparser (deleterious) resonances distributed in frequency domain compared to its HC-PBGF counterpart, whose cladding consists of an array of identical two-dimensional optical structures (i.e. silica rods) [4]. Recently demonstrated method of increasing the number of cladding layer [5,6] has proven to be an effective way to achieve ultralow loss HC-ARF. However, with respect to the third requirement, HC-ARFs are still very susceptible to bending [5,7] because of its leaky mode nature and small numerical aperture of the core mode, impeding many important applications in gyroscopes [8], optical communication networks [9,10], endoscopes [11] and nonlinear optics [12,13], where the fiber must be coined tightly, implemented around a sharp corner or in a compact form.

In HC-PBGF, the photonic bandgap (PBG) mechanism and the bound mode nature provide opportunities to simultaneously obtain ultralow transmission loss, ultralow bending sensitivity and sufficient bandgap width. However, while ultralow loss and ultralow bending sensitivity have been experimentally realized, the spectral bandwidth of fabricated HC-PBGF was usually narrow. For example, in [14], ultralow loss of 1.7 dB/km at 1565 nm and ultralow bending sensitivity have been achieved, but the 3 dB bandwidth (the wavelength range where the fiber loss is less than two times of its minimum value. Henceforth referred to as BW for short) was less than 40 nm. In [9], the fiber has a transmission loss of 3.5 dB/km at 1500 nm, but the BW was only 160 nm. In HC-PBGF, the bandgap width is largely determined by the air-filling fraction (AFF) of the cladding lattice [15], while the surface modes (SMs) localized near the core surround can penetrate into the bandgap thus makes the transmission window narrow. According to theoretical prediction, a triangular lattice PBGF with a high AFF (e.g. >0.95) [15] and a uniform core-surround thickness 50-60% that of the cladding struts [16] could guarantee a BW 0.3 times the central wavelength (Δλ/λ_c > 0.3) [15]. In realistic fabrication, however, a high AFF needs high inflation in the fiber drawing process, whose downside is a non-uniform glass wall thickness in the core-surround layer. Empirically, the distortion is exacerbated in large core HC-PBGFs whose core-surround contour is composed of multifold segments. For example, the 19- and 37-cell HC-PBGFs contain 18 and 24 segments in the core-surround contour respectively and it is difficult to completely control the thicknesses of all the glass segments during fiber drawing. As a result, the BW of 19-cell HC-PBGF so far is limited by 235 nm (Δλ/λ_c < 0.156, see Table 1) [17].

Table 1. Optical performance comparison of reported PBGFs*

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Eliminating SMs proves to be easier in 7-cell PBGF than in large core PBGFs. The BWs of 7-cell HC-PBGFs are 253 nm with the loss of 15 dB/km at 1550 nm, and >150 nm (limited by the measurement technique) with the loss of 9.5 dB/km at 1650 nm in [18]. In [19], ~230 nm bandwidth was obtained with the loss of 80 dB/km at 1440 nm. The relatively higher losses can be attributed to the small core size with higher spatial overlaps of the core mode and the glass (1% in 7-cell HC-PBGF vs 0.2-0.4% in 19-cell HC-PBGF [20]), resulting in higher surface roughness scattering loss (SSL). How to simultaneously achieve SM-free broad BW (Δλ/λ_c towards 0.3) and low transmission loss in HC-PBGF is still an open question.

In this work, we demonstrate that simultaneously achieving low loss and broad bandwidth is feasible in 7-cell HC-PBGF. By optimizing the fiber fabrication parameters, we managed to enlarge the core size of 7-cell HC-PBGF to 23 µm and achieved a loss value of 6.5 dB/km at 1633 nm as well as a BW of 458 nm. This represents an unprecedented performance in terms of BW and loss in triangular lattice 7-cell HC-PBGF. If counting for the loss below 25 dB/km, the transmission window extends from 1493 nm to 2003 nm, covering both the traditional telecom band (compatible for erbium-doped fiber amplifier) and the potentially new telecom band at 2 µm (adapted for thulium-doped fiber amplifier) [21]. By structural downscaling, we also demonstrate HC-PBGFs operating at 1440 nm and 1080 nm respectively.

2. Fiber fabrication and characterization

7-cell HC-PBGF was drawn using the modified stack-and-draw technique with no solid rods inserted in the interstitial places [18]. In order to maximize transmission BW, all the structural parameters have been optimized in the stacking stage. A very thin glass tube with the thickness ~20% that of the cladding tubes was added as the core tube, resulting in a cane with the core wall thickness ~60% of the cladding strut thickness [Fig. 1(a)]. This essential step helps to assure a SM-free transmission band and to minimize distortion of core-surrounding [16]. During the fiber draw, systematic studies were performed to find out the optimum pressurization condition. Firstly, a high pressure in the cladding ensures a big expansion ratio (a big AFF) and therefore a broad PBG. The lack of interstitial rods also entails a relatively bigger expansion ratio, enabling the glass nodes in the cladding area to distribute more separately. Here, we achieved an AFF of 0.956. Secondly, the pressure control inside the core region is crucial for maximum optical performance. On one hand, an over-expanded core may entail a lower surface scattering loss. On the other, distortion in the core-surround may give rise to strut SMs in the blue side of the PBG [22]. In previous work, 19-cell PBGF usually adopt an over-expanded core defect to achieve lower loss in sacrifice of the bandwidth [9,17], while 7-cell PBGFs usually possess a regular core size, i.e. 3 times the pitch [18,19] for a relatively broad bandwidth. This actually limits the loss achieved in 7-cell PBGF. Here, we intentionally over-expand the core defect to a diameter of 23 µm (in comparison to the 10-19 µm core diameter in typical 7-cell PBGFs [18–20,23]). Surprisingly, unlike the 19-cell PBGF where an enlarged core tends to distort the core-surround structure and introduced several SMs inside the PBG [9,17,24], here no SMs was observed inside the > 400 nm bandgap. This indicates that 7-cell PBGF is more robust to structural expansion than the 19-cell PBGF since its core surround contour only consists of 12 segments. Simultaneously attaining the two goals of low loss and broad bandwidth is probably easier in 7-cell HC-PBGF.

 

Fig. 1 (a) Optical microscopy image of a cane prior to fiber drawing. (b) SEM image of the 7-cell HC-PBGF. (c) Measured transmission spectra of 300 m (gray) and 3 m (black) long HC-PBGF under the same launching condition. (d) Cutback measured (black solid) and simulated (red dotted) loss spectra.

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Figure 1(b) shows a scanning electronic microscopy (SEM) image of a 7-cell HC-PBGF with the outer diameter of 175 μm, the core diameter of 23.5 μm, the pitch (Λ, hole-to-hole distance) of 6.1 μm and the hole diameter to pitch ratio (d/Λ) of 0.99. The strut thickness is estimated to be ~65 nm, and the average core wall thickness is ~40 nm. To measure the transmission loss, a standard cutback measurement was performed where a supercontinuum source is butt-coupled to a 300 m long fiber and then its 3 m cut-back section, with the output end connected to an optical spectral analyzer (OSA). The accuracy of the measurement was guaranteed by multiple cleaving the output end for both the full fiber length and the cut-back section, showing ignorable variation. Figure 1(c) and (d) plots the transmission and loss spectra. No SMs has been observed. The BW, denoted by loss < 13 dB/km, extends from 1530 nm to 1988 nm (except the OH peak at 1894 nm). This 458 nm wide BW is much broader than previously reported results [9,14,17–19,23]. Here, HCl gas absorption is observed at 1750 nm - 1850 nm region [25] and the disturbance around 1894 nm is caused by OH absorption [26], not SMs. By properly gas purging, it is believed that those OH induced loss peaks can be greatly suppressed [27]. If counting for the sub-25 dB/km bandwidth, it extends from 1493 nm to 2003 nm (or 51.15 THz) with the minimum loss of 6.5 dB/km at 1633 nm and 10 dB/km at 1550 nm. Simulations have also been performed using a finite-element mode solver (COMSOL Multiphysics) [28] with optimized mesh size and perfectly matched layer. All the structural parameters are extracted from the SEM image of the fiber with small adjustment within the range of uncertainties. In Fig. 1(d), the red curve shows the simulated loss including both the confinement loss and surface scattering loss. A reasonable agreement is shown between experiment and simulation.

To quantify the fiber’s performance under bending, the HC-PBGF sample is manually bent in radius R of 25 mm, 12.5 mm and 6.5 mm respectively. Their transmission spectra are compared with that of the quasi-straight fiber (R >10 cm) to deduce the bending loss (BL). We surprisingly find, under R = 25 mm for over 200 turns, the transmission spectra overlaps well with that of the quasi-straight fiber over the whole transmission band from 1493 nm to 2003 nm, indicating a negligible BL (<2 dB/km). Under R = 12.5 mm for 200 turns, the BL is still indistinguishable in the central part of the transmission band from 1600 nm to 1930 nm (< 10 dB/km) Fig. 2. Only at the short wavelength edge from 1470 nm to 1560 nm, the BL rises to 10-50 dB/km. For R = 6.5 mm with 200 turns, the high BL at the short wavelength edge causes a red-shift of the bandgap (1600 - 2040 nm with the BL less than 40 dB/km). This red shift of the bandgap edge can be ascribed to the increased coupling from the fundamental core mode to cladding modes under tight bending as observed and studied previously [29,30]. This remarkably low BL, compared to the single mode fiber with BL in the level of 5-15 dB/m at R = 10 mm [31] and the HC-ARF with BL in the level of 0.7-10 dB/km at R = 100 mm [5] make the 7-cell HC-PBGF the exclusive choice for many bending-insensitive applications.

 

Fig. 2 Bending loss spectra of the 7-cell HC-PBGF under R = 12.5 mm (black curve) and 6.5 mm (blue curve).Due to the short fiber length (15.7 m for 200 turns at R = 12.5 mm), measured loss under 10 dB/km is indistinguishable and could be regarded as noise. The insert shows the photos of the bent fiber under test with 200 turns each.

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Using a Mach-Zehnder interferometer with two delay stages, we measure the group index and dispersion of the fiber. We firstly adjust two arms to have the same length; then, the test fiber is placed straightly in one arm, and the delay stage in the other arm is adjusted to compensate for time delay [10]. From spectral interferogram acquired from an OSA, the phase difference is extracted, and the dispersion can be derived by applying polynomial fit. With the knowledge of the fiber length and the relative position of two delay stages, the group index can be inferred. At 1550 nm, we measure the group index (n_g) to be 1.00346 ± 0.00010 and the group velocity dispersion (GVD) to be 1.65 ps/nm/km (Fig. 3). The n_g curve shows a “U” shape, and the GVD curve shows an “S” shape with the zero-dispersion wavelength at 1540 nm.

 

Fig. 3 n_g (black curve) and GVD (blue curve) spectra of the 7-cell HC-PBGF measured from a 20 cm long HC-PBGF.

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HC-PBGF is generally multimode fiber. Using a spectral and spatial (S²) imaging technique [32], we characterize the modal contents after a fiber length of 5 m within the wavelength range from 1548 nm to 1552 nm. The two peaks at the group delays of 10.41 and 12.81 ps/m can be identified as LP_11a and LP_11b modes with the multipath interference (MPI) values to be −18.6 and −19.4 dB, respectively [Fig. 4]. The two peaks at the group delays of 22.02 and 23.22 ps/m can be attributed to the LP₂₁ and LP₀₂ modes, respectively. According to [33], adding shunt cores could further improve the singe modality with minor effect to transmission loss.

 

Fig. 4 S² analysis of the 7-cell HC-PBGF. A typical MPI curve as a function of the differential group delay for 5 m fiber.

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3. 7-cell HC-PBGF at other important wavelength

By structural downscaling, a series of fibers for transmission at shorter wavelengths were drawn from the same stack. Figure 5(a) shows a SEM image of a fiber operating at the traditional telecom band with the outer diameter of 145 μm, an average core diameter of 16.5 μm, an average hole-to-hole distance of 4.6 μm and an AFF of 95.6%. As shown in Fig. 5(c), this fiber has a flat transmission window from 1236 nm to 1656 nm with one OH absorption peak at 1364 nm, covering the full O, E, S, C, L telecom bands. The minimum attenuation is 14 dB/km at 1310 nm and the loss at 1550 nm is 17 dB/km. The second fiber operates at the Nd and Yb laser wavelength region. It has an outer diameter of 105 μm and a hollow-core diameter of 13.1 μm. The average pitch and AFF were 3.6 μm and 95.2% respectively [(Fig. 5(b)]. The minimum loss falls at 1070 nm with the value of 22.4 dB/km and the 3 dB BW of 258 nm [(Fig. 5(d)]. Such a broadband HC-PBGF at 1064 nm could be of particular interest for ultrashort laser pulse applications. No SM has been observed in any of these fibers, corroborating that low loss, broad BW could be combined in 7-cell HC-PBGF.

 

Fig. 5 (a&b) SEM images of the fabricated 7-cell HC-PBGFs centered at 1440 nm and 1080 nm. (c&d) Measured cut-back loss from 300 m to 5 m and from 100 m to 5 m respectively for the two fibers.

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4. Comparison with previous results

In Table 1, a comparison between our work and previously reported works is listed. Thanks to the ultrahigh AFF in our HC-PBGF as well as the complete exclusion of the SMs, we fully exploit the PBG resource and demonstrate a BW to central wavelength ratio (Δλ/λ_c) approaching 0.3. Meanwhile, the loss of 6.5 dB/km is also the lowest among the 7-cell HC-PBGFs. According to the prediction in [15], further improving Δλ/λ_c toward 0.4 requires an AFF to be nearly 0.97, namely strut glass thickness smaller than 40 nm. This will be very challenging for microstructured fiber if not impossible.

5. Conclusion

In conclusion, we have presented several low loss and broad BW 7-cell HC-PBGFs. The combination of low transmission loss (6.5 dB/km), low bending loss (<2 dB/km under the bending radius of 25 mm), broad BW (Δλ/λ_c approaching 0.3), and appropriate mode field diameter (around 18 μm) represents an attractive feature for compact all fiber systems for a wide range of applications in telecommunication, nonlinear optics, femtosecond pulse delivery, distributed gas sensing, spectroscopy, etc.