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Hollow-core fibers (HCFs) are a revolution in light guidance with enormous potential. They promise lower loss than any other waveguide, but have not yet achieved this potential because of a tradeoff between loss and single-moded operation. This paper demonstrates progress on a strategy to beat this tradeoff: we measure the first hollow-core fiber employing Perturbed Resonance for Improved Single Modedness (PRISM), where unwanted modes are robustly stripped away. The fiber has fundamental-mode loss of 7.5 dB/km, while other modes of the 19-lattice-cell core see loss >3000dB/km. This level of single-modedness is far better than previous 19-cell or 7-cell HCFs, and even comparable to some commercial solid-core fibers. Modeling indicates this measured loss can be improved. By breaking the connection between core size and single-modedness, this first PRISM demonstration opens a new path towards achieving the low-loss potential of HCFs.
©2013 Optical Society of America
1. Introduction
Hollow-core fibers (HCFs) guide light with ultra-low nonlinearity, opening regimes of dramatically improved performance in telecommunication, sensing, power delivery, and other applications [1–7]. For several decades, commercial development of optical fibers has focused on silica, the second-best medium for guiding light. The breakthrough of using bandgap-guidance to trap light in a low-index core makes possible use of the only better medium: nothing. Light in a hollow core is effectively free from the bulk scattering, nonlinearity and other interactions it would have in any solid material. For telecommunications and sensing applications [7], this suggests an ideal waveguide, free of the interactions that create noise and dissipate signals, if only interactions at the air-glass interface at the core surface can be made negligible. Hollow core guidance offers additional game-changing benefits in specific applications: hollow-core fibers can operate beyond damage limits in high-peak-power applications [8], can guarantee the shortest possible delay in low-latency communication applications [9], etc. The impact of HCFs has been severely limited by the related problems of complex fabrication, sensitivity to structural imperfections, high loss, and unwanted modes. Since the initial hollow-core bandgap fiber work [1], loss has been reduced many orders of magnitude to reach the current record level of 1.2dB/km [5]. This dramatic improvement has stalled, however, because of unavoidable roughness thermodynamically locked into the core surface during draw. Scattering losses from this surface cannot be eliminated by further straightforward improvements in fabrication leaving us with a difficult tradeoff: a fiber can be low-loss or single-moded, but not both. A large core reduces surface scattering, but also guides multiple modes. Perfectly single-moded HCFs may not be necessary, but mode content measurements [10] show that typical 19-cell fibers (needed for losses <~10dB/km) have problematic mode content, and the number of low-loss modes grows quickly with further core size scaling [6]. At the same time, HCFs are intrinsically sensitive to structural irregularity due to their many high-contrast interfaces. This makes it difficult to repeatably achieve low loss and broad bandwidth, even for simple designs. Because of this sensitivity and the difficulties of fabrication, design freedom has been quite limited for HCFs that can be realistically made. Almost all published results on fabricated HCFs are essentially “step-index” designs. That is, they consist of a core in a uniform cladding, with slight adjustments made to the core-web thickness to mitigate surface modes. The standard tools used to control dispersion, mode content, etc., in traditional fiber design, have been avoided.
Here, we report that improvements in fabrication have allowed us to demonstrate a complex HCF design and achieve qualitatively improved optical properties. The fiber measured is intentionally multimoded to provide low attenuation, but unwanted modes are stripped from the core by resonant cladding features. The design concept for controlling mode content is robust to the significant irregularities and surface modes present in a real fiber. In addition to removing a key obstacle in HCF development—the tradeoff between loss and single-modedness—we thus demonstrate that design complexity and functionality beyond “step-index” is realistic if we combine state-of-the-art fabrication with robust design principles.
2. PRISM designs for suppression of unwanted modes
To be single-moded, a fiber must have orders of magnitude higher losses in any unwanted modes than in the fundamental. The key to achieving this selectivity is phase matching. As proposed in [11], shunt cores can be added to the cladding of a HCF that are phase-matched with the unwanted modes of the center core, providing a path for light to resonantly leak through the lattice and escape. Figure 1 illustrates this effect for a 19-cell center core with two 7-cell shunts. The unwanted LP11-like modes of the center core (red) have essentially the same effective index [in Fig. 1(b)] as the fundamental modes of the shunts (green)—precisely the condition for resonant (phase-matched) coupling. At the same time, since the shunts are smaller than the core, they have no modes that match the effective index of the fundamental core mode (blue) and so the fundamental remains low loss. Calculated losses for the phase-matched structure [Fig. 1(d)] are shown alongside those of the same design with no shunts [Fig. 1(c)] to illustrate the impact of the shunt: Selectivity is high enough to provide effectively single-moded operation with negligible excess fundamental-mode loss.
Fig. 1 Hollow fiber with resonant suppression of unwanted modes. a) Idealized geometry with 5 μm hole spacing, a 19-cell core and two 7-cell shunts. b) Effective index of modes vs normalized optical frequency, showing that shunt modes (green) are nearly index-matched to unwanted LP11-like modes (red), but not with the fundamental (blue). For the specific geometry calculated some surface modes are present in the bandgap (dots indicate surface modes crossing steeply through core modes, as well as LP21-like core modes), but a broad surface-mode-free region is present from normalized frequency Λ/λ = 3.1 to 3.5 (~180nm). c) Loss for the modes of a fiber without shunts compared to d) the same design with shunts, showing shunts provide highly selective suppression of unwanted modes.
There have been no previously reported attempts to fabricate fibers with improved single modedness according to this strategy, despite encouraging numerical results [12,13]. This is largely because the strategy is sensitive to fabrication irregularities and adds significant complexity to fabrication that is already state-of-the-art. Small imperfections, exacerbated by the fabrication complexity, can ruin the mode-suppression in addition to causing the usual high-loss wavelength regions associated with surface-mode crossings. This intrinsic design sensitivity means that small fabrication errors can completely destroy single-modedness. This is illustrated in Fig. 2 , showing a geometry identical to Fig. 1(a), but with slightly oversized core. Specifically, the geometry is dilated radially, applying a 5% increase in core size along with a semi-localized dilation of the cladding that diminishes as exp(-r/4.5μm) and preserves glass area. This small distortion leads to only a small shift in the effective index of core modes, and thus a small index-mismatch [Fig. 2(b)] between core LP11 and shunt modes, but causes an almost complete degradation of the calculated coupling: Losses [Fig. 2(c)] for the unwanted LP11-like modes are now only a few times larger than the fundamental mode loss, an indication of persistent and problematic modes. This example illustrates that unless fabrication of a design is nearly perfect, single-moded operation may be very difficult to achieve.
Fig. 2 a) Fiber geometry (solid) with a slightly enlarged center core, compared with the idealized geometry of Fig. 1(a) shown dashed. b) Effective index, now showing a small index mismatch between shunt (green) and LP11-like (red) modes. c) Loss shows that suppression of unwanted modes has been ruined by the core-size mismatch.
The design concept proposed in Fig. 1 can be made robust if we recognize that phase matching does not need to occur equally everywhere along the fiber in order to produce coupling. In fact, if the nominal fiber geometry has modes that are moderately close in effective index, then variations along the fiber length will shift the effective index of each mode enough to provide sufficient index matching along a useful fiber length. That is, perturbations along the fiber can cancel the index mismatch between modes caused by deviations from the intended fiber design.
This principle was recently demonstrated in a simple dual-hollow-core coupler [14] using bends, which are a simple and well-understood example of such a variation. For cores with separation a and orientation θ with respect to a bend of radius Rbend, the standard bend model of a tilted refractive index [15] implies that effective index difference is perturbed by acos(θ)ncore/Rbend. The core index ncore equals 1. If the orientation of the fiber cores relative to the bend drifts (intentionally or randomly), as in Fig. 3 , then the index mismatch sees a length-varying bend perturbation taking all values from - a/Rbend to a/Rbend. By introducing a bend and allowing orientation drift, we can achieve intermittent resonant coupling of all modes whose index mismatch falls within a range controlled through the bend radius [16]. If orientation drifts on something like a meter length scale, then for fiber lengths much longer than that, the effective loss of a mode may be estimated as a simple average over random orientations.
Fig. 3 Perturbed resonance for robust suppression of unwanted modes. (a) Schematic of a bend-perturbed fiber with drifting orientation, where a small index mismatch between modes can be cancelled intermittently. b) Effective index shows unwanted LP11-like modes (red) falling within the perturbed resonant region (light green) of the shunt modes (dark green) with a 10cm bend perturbation. c) Orientation-averaged loss (solid) shows LP11-mode suppression restored by perturbation, despite the core-size mismatch. The straight fiber losses for the fundamental and lowest-loss HOM are repeated for comparison (light blue dashed for the fundamental, pink for the LP11).
The robustness of this approach is illustrated in Fig. 3(c), where we repeat the loss calculation of Fig. 2(c) for the two LP01-like and four LP11-like modes (in a selected wavelength range), but this time including a simple perturbation: a 10cm diameter bend. When the shunt modes are perturbed by randomly-oriented bend perturbations, their effective index spans the green shaded region of Fig. 3(b). Since the red LP11 mode curves fall in this region, phase-matched coupling is achieved for some orientations of the bend. The average of mode losses calculated for a uniform sampling of bend orientations is plotted in Fig. 3(c). They show that although the unbent fiber has LP11-like modes that are off-resonance and low loss [Fig. 2], coiling creates a robust perturbed resonance condition that suppresses these unwanted modes, while producing negligible excess loss in the fundamental mode. Interestingly, the orientation-averaged losses are of comparable magnitude to some of the LP11-like modes of the nearly ideal geometry in Fig. 1(d). This highlights the fact that splitting between the different LP11-like modes prevents perfect phase matching even for perfect fabrication. In contrast, the perturbed fiber experiences perfect phase-matching at some positions, with the corresponding local losses >>100dB/km.
This fiber uses Perturbed Resonance for Improved Single Modedness (PRISM) to separate undesirable light components with high selectivity. For this approach to work, we need not have perfect fabrication or achieve perfect suppression of surface modes. The fabricated geometry does not need to be perfectly characterized and simulated in detail, since the bend radius can be adjusted empirically. This approach is thus suited to the reality of HCF design, where quantitative modeling is generally not possible [17], fiber geometry cannot be adequately characterized [18], and even major spectral features are more often empirically tweaked than systematically controlled [9]. The strategy works as long as the mismatch from resonance is small enough that it can be cancelled with a reasonable bend (e.g., without introducing significant bend loss of the fundamental). Using post-fabrication bend optimization, the PRISM effect has been achieved in a practical hollow-core fiber, as discussed below.
Calculations used a finite difference vector mode solver similar to [19]. The geometries calculated use lattice hole spacing Λ = 5 μm, 95% air-fill fraction, and an idealized fiber geometry: for Fig. 1 the core’s horizontal width is 5 lattice periods and core-web thickness is half the thickness of a lattice web. Calculated losses combine the tunneling loss with an estimate of surface scattering loss: Loss = Losstunneling + C × F, where F is the standard surface overlap integral [5]. The constant C is not precisely known, but is taken to be 81 here, based on previous measured losses. The loss in Fig. 3 averaged 18 mode calculations sampling 5 degree increments in orientation.
3. Effectively single mode hollow core bandgap fiber with 7.5 dB/km loss
We designed and fabricated a fiber according to the PRISM strategy. The fiber had a 19-cell center-core and two 7-cell shunt cores. The center-core diameter was 23.0 μm, the shunt hole size was 13.6 μm, hole spacing 4.5 μm, and air fraction around 95%. An SEM image of the fabricated fiber is shown in Fig. 4 , along with the loss of a 200 m length of fiber, measured by the cutback technique. The minimum measured loss was 7.5 ± 0.5 dB/km at 1590 nm. The fiber shows visible geometric distortions compared to the ideal structure of Fig. 1, (particularly in between the cores) and high-loss wavelength regions in the bandgap attributable to surface mode crossings. These deficiencies can be corrected with improved fabrication methods and slight design modifications.
Fig. 4 SEM image of the fabricated fiber and measured loss spectrum. Minimum loss was 7.5 ± 0.5 dB/km.
To assess the mode properties of the hollow core fibers and their susceptibility to bending, we used a new technique based on a sliding window Fourier transform of high-resolution transmission spectra [10,20]. This measurement is presented as a two dimensional plot, known as a spectrogram, representing the mode content as a function of both wavelength and differential group delay.
The sliding Fourier window calculation of spectrograms is based on measuring interference between coherent modes that propagate with different group delays in the fiber under test [10]. The input and output of 3m lengths of hollow-core fibers were fusion spliced to standard single-mode fiber. Note that because there are two SMF-HCF splices in the experiment, with each splice acting as a mode transformer, the mode content transmitted through the system is approximately half the mode content propagating in the HCF. A narrow linewidth (400 kHz FWHM) tunable laser was launched into the fiber under test, and the transmission was measured with a power meter. The frequency of the laser was tuned through the wavelength range of interest. The maximum tuning range of the laser was 1500 nm to 1610 nm, and the step size was 0.003 nm. A small subset of the transmission data with a width of approximately 3 nm was selected with a narrow window and Fourier-transformed. The window is then slid through the entire transmission spectrum. The data analysis of Ref [21] relating Fourier transform amplitude to mode amplitude was then applied, to produce a plot of mode content vs. wavelength and group delay. Because the modes are co-propagating, the modes are measured as a function of differential group delay, or difference in group delay between the fundamental mode and the higher order modes.
A low-loss, 19-cell HCF of a more conventional design (without shunts) was fabricated and its mode properties measured as a baseline for comparison. This fiber had a loss of 5.2 dB/km at 1520 nm, with the loss increasing to around 60 dB/km above 1530 nm. Spectrograms for this fiber are shown in Fig. 5 . The color scale shows higher-order mode content, relative to the fundamental mode, on a dB scale. Also shown in Fig. 5 are several higher-order mode images at different DGDs, obtained from a separate S2 imaging measurement.
Fig. 5 Persistent unwanted modes of a non-PRISM fiber. Spectrograms for a conventional 19-cell hollow core fiber with a low loss region from 1500 to 1530 nm. Mode images were obtained from a separate S2 imaging measurement. Two different coil diameters, 15 cm and 5 cm, are shown. No change in the higher-order mode content with coiling was observed.
The spectrograms show that at low loss wavelengths below 1535 nm, discrete scattering to core-guided modes is observed, but at high loss wavelengths above 1535 nm the discrete modes disappear into a continuum of HOMs over a broad range of group-delays. Mode imaging measurements have shown that the continuum of modes at high losses contain a strong surface mode component [10]. The mode content showed no observable change in the mode content when the coiling diameter was reduced from 15 cm to 5 cm. This is expected: it is known that higher-order modes of a 19-cell core are well-confined modes with calculated losses only a few times that of the fundamental.
Next, spectrograms for a 3 m length of the PRISM fiber were obtained as a function of coiling diameter (see Fig. 6 ). As with the conventional HCF, in the region of high loss (wavelength shorter than 1560 nm) a continuum of higher-order modes over a broad range of group delays was observed. In the region of low loss wavelengths, however, there were significant differences between the conventional 19-cell fiber and the PRISM fiber. First the number of higher-order modes guided in the low-loss region, as evidenced by the number of narrow lines, was substantially smaller in the PRISM fiber. Second, as the coil diameter of the PRISM fiber was reduced, the higher-order mode content in the low loss region gradually decreased, as expected from the theory discussed in the previous section, with HOM-free wavelengths obtained for coil diameters smaller than 8.9 cm. Mode images for the straight fiber were also obtained from an S2 measurement and are shown in Fig. 6(a). The two strongest remaining modes are two, similarly shaped, LP02-like modes, along with a weak, LP11 mode.
Fig. 6 (a), (b) Spectrograms show the wavelength-dependent mode-content of the PRISM fiber as a function of coil diameter. The color scale shows the mode strength in dB, relative to the fundamental mode. Mode images were obtained from an S2 imaging measurement (c) Integrating the spectrum along the DGD axis provides total HOM content vs. wavelength, and (d) subtracting coiled content from straight content yields bend-induced HOM suppression vs. coil diameter.
To better compare the HOM content between coil diameters in the PRISM fiber, the spectrograms were integrated along the group delay axis to provide a rough estimate of the total HOM content as a function of wavelength; see Fig. 6(c). By subtracting the HOM content for the straight fiber from the coiled fiber and normalizing to the fiber length, a measure of the bend-induced HOM suppression was obtained; see Fig. 6(d). As much as 5000 dB/km of total bend-induced HOM suppression was obtained.
In addition to measuring the spectrograms of the PRISM fiber, an S2 imaging measurement of the modal content was also performed. S2 (or Spatially and Spectrally resolved) imaging [10,21] spatially resolves the spectral interference that occurs between coherent modes propagating with different group delays in the fiber under test. The measurement can quantify the power level and relative group delays of higher order modes with respect to the fundamental mode as well as provide images of the higher order modes. The measurement was performed using a narrow linewidth tunable laser together with an InGaAs camera to obtain the wavelength dependence of the output beam profile from the hollow-core fiber.
The results comparing S2 imaging in a 10 m length of conventional 19-cell hollow core fiber (loss 5.6 dB/km), a commercially available 7-cell hollow core fiber (NKT HC-1550-02, loss = 16 dB/km) and the PRISM fiber (loss = 7.5 dB/km) are shown in Fig. 7(b) . In this measurement the PRISM fiber coil diameter was 8.9 cm. Analysis of the S2 data provides a plot of the mode beats vs. group delay. By performing the data analysis of the mode content over the entire range of group delays [22] the total HOM content and an image of the sum of HOMs is obtained. The total mode content in the 19 cell fiber was −7.6 dB (relative to the fundamental mode), −22 dB in the 7 cell fiber, and −27 dB in the PRISM fiber, with the PRISM fiber essentially free of the discrete scattering peaks evident in the 7-cell and 19-cell fiber. Furthermore the mode images shown in Fig. 7(b) reveal that higher-order modes in the 19-cell and 7-cell fibers primarily consist of core-guided modes (the LP02 and LP11 respectively), but in contrast core modes have been completely removed from the PRISM fiber, leaving only residual surface modes.
Fig. 7 HOM suppression in a PRISM. (a) S2 imaging results showing mode beats as a function of differential group delay of a 19 cell fiber, a commercial 7-cell fiber and the PRISM fiber. Also shown are the integrated higher order mode images for the different fibers, showing that the 19 cell and 7-cell fibers support strong core-guided HOMs, while the core-guided HOMs are stripped from the PRISM fiber, leaving only surface modes. (b) Measured HOM content as a function of length for a fiber coil diameter of 8.9 cm.
This is significant in that it shows PRISM fibers have moved beyond the tradeoff of loss and single-modedness which limits ordinary HCFs. Assuming the 7-cell fiber measured is a representative sample, the fabricated PRISM fiber surpasses both the single-modedness and record loss of 7-cell fibers. This is in spite of clear geometrical imperfections and surface modes. The calculations of Fig. 3 suggest that future PRISM fibers should be able to achieve losses similar to ordinary HCFs (without shunts) of similar core size, but with greatly improved single-modedness.
An S2 imaging cutback measurement was also performed on the PRISM fiber. A 20 m length of fiber was measured with the S2 setup, and the fiber length progressively cut back and characterized, to obtain change in mode content vs. length. The results of this measurement are shown in Fig. 7(c). In very short lengths of fiber (0.4 m) it can be seen that substantial higher-order mode content in the form of core-guided (LP11) modes is launched. However, these modes rapidly decay, such that within 5m of fiber length, the only modes left are small amounts of surface modes, suggesting that in 4.6 m length, the core-guided higher-order modes experience an attenuation of more than 13 dB, or approximately 3 dB/m loss relative to the fundamental mode.
Finally, Fig. 8 shows movies of the beam profile vs. wavelength for the conventional 19 cell fiber compared to the PRISM fiber, measured with the S2 setup. The fiber length in these measurements was 20 m. The presence of coherent higher order modes causes distortions to the beam profile that vary with wavelength. The higher order mode content present in the 19 cell fiber strongly distorts the beam profile and causes large changes with wavelength; see Fig. 8(a) (Media 1). In contrast, the stability of the beam profile of the PRISM fiber is greatly enhanced, with the beam profile showing little change with wavelength; see Fig. 8(b) (Media 2).
Fig. 8 Single frame excerpts from movies of beam profile vs. wavelength (a) conventional 19 cell fiber (Media 1). (b) the PRISM fiber. (Media 2)
It is worth noting that the measured HOM suppression for the fabricated fiber is greater than that of the calculated examples. Only qualitative agreement can be expected in HCF modeling, and so discrepancies are not surprising. More specifically, we use the standard model of loss including tunneling and surface-scattering, but neglecting mode-coupling. Mode coupling is thought to significantly increase analogous losses near a surface-mode-crossing resonance [23], and so it would not be surprising if the standard loss model greatly underestimated the degree of HOM suppression achieved in practice.
4. Discussion and Conclusions
In conclusion, we have demonstrated a robust new class of single-moded hollow-core fibers. The measured loss (7.5dB/km) and single-modedness of a fabricated fiber are simultaneously better than conventional 7-cell fibers, proving that the novel design strategy allows us to move beyond the usual loss tradeoff for hollow-core fibers.
The bend sensitivity of the modal content might initially suggest that since the PRISM fiber requires bending, it cannot be effectively utilized in straight-line applications such as long-haul transmission. In fact this is not a limitation. First, it is important to point out that the modal content of the PRISM fiber at large bend radius is far superior to a conventional 19-cell fiber without shunt cores. Compare, for example, Fig. 5(a) to Fig. 6(a). Furthermore, by appropriate cable design, it is possible to achieve the needed fiber curvature for enhanced modal suppression while deploying the cable in a typical “straight” arrangement.
Also, many applications of the PRISM fiber, such as transmission or ultra-short pulse propagation, will require wide bandwidth, low-loss regions. While the operational bandwidth of the current PRISM fiber is relatively narrow compared to what can be achieved with, for example, 7-cell fibers [24], we expect that by adding state of the art fabrication techniques to control surface modes, the operating bandwidth of PRISM fibers can also be extended.
Finally, removing the tradeoff between loss and single-modedness points the way to further reduction of loss by using larger core sizes, while maintaining single-modedness essential to most relevant applications. The success of the PRISM strategy also gives proof-of-principle that robust design principles combined with recent improvements in fabrication now allow us to move beyond “step index” hollow core fibers, towards increased functionality and greater design freedom.
Acknowledgments
Distribution Statement “A” (Approved for Public Release, Distribution Unlimited). The views expressed are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government.
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