1. Introduction

Fused silica is the material of choice for optical fiber manufacture across a broad wavelength range ($\sim {350}\,\textrm{to}\,{2500}\,\textrm{nm}$) due to its technological maturity and optical properties [1,2]. Traditionally optical fibers have an all-glass construction with a solid higher refractive index core and a lower index cladding. To achieve single-mode operation, the size of the core is scaled with the wavelength, and thus UV and visible guiding solid-core fibers have relatively small cores ($\sim {2}\,\textrm{to}\,{5}\,\mathrm{\mu}\textrm{m}$), making coupling light into them more challenging. A small core also increasing the fiber’s non-linearity and reduces its power-handling capacity. Solid-core fibers also have limited single-mode bandwidth in the UV-visible (typically specified as ${100}\,\textrm{to}\,{300}\,\textrm{nm}$) meaning multiple fibers are needed to achieve guidance across the visible (${400}\,\textrm{to}\,{800}\,\textrm{nm}$) wavelength range. Moreover, the UV absorption edge of fused silica limits its use to ${>350}\,\textrm{nm}$, with exposure to UV (${<400}\,\textrm{nm}$) light also leading to solarization, where the UV light causes the formation of permanent defects in the glass that reduce its transparency [3].

Although these issues have not stopped solid-core fibers use in the UV-visible wavelength range, fibers with larger cores, lower non-linearity, flatter dispersion, better power handling, and greater bandwidth capable of single-mode UV-visible guidance would be ideal for a range of applications including quantum computing [4–7], ultra-fast pulse delivery [8–10], non-linear light generation [11], non-linear microscopy [12–14], gas sensing [15], and high value manufacturing [16,17]. This need is particularly acute when it comes to ${<300}\,\textrm{nm}$ single-mode guidance, as presently there are limited options available to flexibly deliver these wavelengths [18]. Continuous broadband guidance (and low dispersion) is also of particular importance when working with ultra-fast pulses, if their ultra-short duration is to be maintained.

Hollow core fibers (HCFs) guide light in a gas- or vacuum-filled hollow core and are hence an ideal solution as they offer all of the desired properties [19], and are nearly immune to solarization [3,20,21]. Although multiple methods can be used to confine light within a hollow-core [19,22] this work focuses on anti-resonant HCFs where a single-ring of non-contacting cladding capillaries are used to achieve this (fibers sometimes termed tubular, revolver, or negative-curvature). More advanced versions of this design are termed nested anti-resonant nodeless fibers (NANF), or conjoined fibers, where an extra membrane is added to reduce their optical loss [19,23]. The guidance mechanism in all these fibers results in minimal overlap between the guided light and the silica cladding material, hence the solarization immunity.

Anti-resonant, hollow-core fibers (AR-HCFs) offer multiple low-loss transmission windows bounded by high loss resonant regions, which can be calculated via the ARROW model [19,22]:

These transmission windows exhibit decreasing bandwidth with increasing resonance order, thus while fibers with thicker capillary membranes will guide UV-visible light in their higher order transmission windows, the presence of resonances between these windows reduces the potential bandwidth [24–27], and in turn, potentially limits their use. Thus, despite the thicker membranes making the structure more easily controlled during the fiber draw (as will be discussed later), and hence potentially improving the fibers optical performance, these higher order window UV-visible guiding fibers offer at most ${300}\,\textrm{to}\,{400}\,\textrm{nm}$ of continuous guidance, equivalent to $\sim$0.7-0.8 octaves [24,25].

In the case of the lowest order transmission window the lack of resonance on the long wavelength edge results in greater bandwidth, with 1.6 octaves demonstrated in the NIR [28] and $\sim$1.7 (through a short length) in the visible [29], offering the possibility of true broadband UV-visible (potentially from $\# {250}$ to beyond ${750}\,\textrm{nm}$) guidance. But to make this a reality requires the fabrication of fibers with thin (${<300}\,\textrm{nm}$) capillary membranes, which is technically challenging due to an increased likelihood of capillary contact during the fiber draw process, harming their optical performance. A number of post-processing fabrication techniques exist to reduce the membrane thickness of drawn fibers [30–32] but come with their own limitations, often in terms of fiber length.

In this work we present a new fabrication approach that allows the production of long lengths (${\sim 350}\,\textrm{m}$ thus far, potentially ${>2}\,\textrm{km}$ as described) of fiber with thin (${<300}\,\textrm{nm}$) capillary membranes. Further we use numerical modelling to explore the fluid dynamics of the draw process and limitations on the fabrication of AR- HCFs and explain the benefits of the proposed process. Finally, we demonstrate a series of example fibers with (${<300}\,\textrm{nm}$) membranes capable of broadband UV-visible guidance.

2. AR-HCF fiber drawing model and draw dynamics

Figure 1(A) shows a schematic of the geometry of a AR-HCF, where $g$ is the inter-capillary gap size, $D$ is the capillary outer radius, $\phi$ is the core diameter, $D_j$ is outer diameter, and $d_j$ is the inner diameter. AR-HCFs are commonly fabricated using a 2-stage stack and draw technique [33], where a macroscopic (few cm diameter) "stack" is constructed by stacking capillaries within an outer tube, which is then fused and drawn to millimeter sized canes. These canes are then inserted into a larger jacket tube and drawn to fiber. During the draw the core and capillaries are pressurised to achieve the desired structure, as will discussed in more detail later.

 

Fig. 1. A) Schematic of the geometry of a 7-capillary AR-HCF. B) Radial profile of the capillaries normalised to the mid-drawn contact (MDC) radius along $z$. The dashed red line is the radius at which MDC occurs. The inset shows an example microscope image of a fiber with MDC. C) Capillary outer diameter as a function of applied pressure. Target outer diameter indicated by the dotted green line.

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When drawing optical fibers using this approach, the reduction in diameter from preform to fiber leads to complex dynamics, and results in a structure termed a "neckdown". Fiber drawing models, based on the fluid dynamics of fused silica, provide a method to understand these dynamics and hence the draw process. We use an analytical steady-state model for basic capillaries derived from the Navier-Stokes equations [34], which provides a 1-dimensional solution for the longitudinal evolution of the outer and inner radius.

The neckdown profile is then found by:

Eqaution (2) and (4) form a coupled system of differential equations, with the preform geometry defining the boundary conditions at $z=0$. In our model the values of strain rate, pressure, and furnace temperature which result in the correct fiber geometry are found numerically via a goalseeking algorithm. The model is extended to AR-HCFs by first solving the jacket tube as described, then using its axial solution to solve the outer and inner radii of the internal capillaries [35]. The combined solutions provide the required fabrication parameters which satisfy the target geometry, such as furnace temperature, core pressure, and capillary pressure.

2.1 Mid-draw contact and pressure sensitivity

Surface tension exerts a contracting pressure inversely proportional to capillary radius during the fiber draw, as given by the Young-Laplace equation $p_\gamma = -\gamma /r$. The interplay of applied pressure and surface tension leads to the complex micro-structure dynamics encountered. At the start of the neckdown region the capillaries are large and gas pressure dominates. However, as the preform approaches fiber scale, a cross-over point is reached and surface tension starts to dominate and the capillaries contract. Therefore, if the target fiber geometry is to be reached, this unavoidable contraction phase must be compensated for by over expanding the capillaries during the pressure dominated phase. In the limiting case, the capillaries will need to be expanded such that contact occurs, an undesirable effect termed mid-draw contact (MDC), resulting in glass nodes which introduce additional high-loss regions to the fibers optical transmission, affecting its loss [22,35]. Figure 1(B) shows a microscope image of a fiber which has experienced MDC.

Due to the practicalities of the fiber drawing process (fabrication tolerances, pressure variation and drift, etc.), a buffer pressure to the predicted MDC point is required to ensure MDC does not occur, termed the MDC pressure buffer here and defined as $\Delta p_b = p_{mdc} - p_{to}$, where $p_{mdc}$ is the minimum pressure which results in MDC, and $p_{to}$ is the pressure required to reach the target geometry. A negative or zero value of $\Delta p_b$ indicates that the target structure cannot be reached without experiencing MDC. Using the draw model outlined in the previous section, it is possible to calculate the outer capillary radius throughout the neckdown. The capillary radius at which MDC occurs can be calculated from simple geometry. It is then a matter of stepping through the neckdown solution to see if the predicted capillary size is sufficient for MDC to have occurred. Figure 1(C) presents an example neckdown simulation demonstrating a fiber draw where MDC occurs. The pressure and surface tension dominated phases are also clearly visible.

When targeting thinner capillaries, the draw yield per meter of preform (hereafter termed draw yield) will increase. The resulting increase to the strain rate, $dv/dz$, must be balanced by increasing the furnace temperature if the target draw tension is to be maintained. Increasing the furnace temperature decreases the glass’ viscosity, making the capillaries more sensitive to the applied pressure at the start of the neckdown, increasing the likelihood of MDC. This rapidly becomes the primary limiting factor when targeting fibers with thin (${<300}\,\textrm{nm}$) membranes if draw tension is not increased above the original target; as will be discussed later.

Another dynamic to consider is the capillary’s sensitivity to applied pressure as its diameter is increased. This sensitivity will change as the capillary is expanded as its thickness will be reduced, and hence the relationship is non-linear. While this is not a limiting factor in itself, if the sensitivity becomes too high it can be problematic in terms of realising a specific capillary diameter or avoiding MDC due to practical issues, such as the pressure controller resolution. Pressure sensitivity can be determined by using the Fitt model to simulate capillary expansion with pressure and then calculating the slope at a desired outer diameter or pressure. An example is shown in Fig. 1(D). A lower sensitivity is also desirable from the perspective of producing uniform fiber.

3. Fabrication dynamics for thin-membraned fibers

There are principally two routes to avoiding MDC during a fiber draw - increasing the draw tension (making the glass stiffer and hence less sensitive to pressure) or reducing the size of the preform and hence the strain rate, $dv/dz$, as detailed above [36]. Both approaches potentially result in a reduction in the fiber yield, through a reduction in starting material in the case of a smaller preform, and fiber breakage in the case of increased tension, which is undesirable. However, as fiber breakage is stochastic in nature, has other downsides, and is easily understood, it will not be considered here.

The reduction in draw yield due to cane scaling can also be avoided by simply scaling its volume at the same rate as that of the desired fiber, and this is the approach that will be presented here. This has the additional benefits that the resultant strain rate will also remain constant meaning the glass viscosity does not need to be reduced to avoid MDC, and the capillary pressure sensitivity should be reduced, both of which are obviously desirable.

Using the fiber drawing model in 2, the relationship between draw yield and cane outer diameter to fiber capillary thickness at the limit of MDC for a 7-capillary AR-HCF can be explored. While there have been fibers with a range of different capillary numbers [3,19–21,23–32], a 7-capillary geometry was chosen for its good compromise between bend loss and high-order mode suppression [8]. However, the analysis report is fully general and could thus be scaled to other designs, including nested/conjoined tube fibers.

The fiber geometry used in the simulations shown in Fig. 2 were based on the fiber capillary thickness, $t$, with all parameters and corresponding formulae shown in Table 1, and varying the thickness over the range ${150}\,\textrm{to}\,{1000}\,\textrm{nm}$ in steps of ${50}\,\textrm{nm}$. The cane support tube and capillaries were set to a fixed ratio of inner to outer diameter of 0.86, and then for each target fiber scaled using mass conservation such that a chosen fiber draw yield is achieved. For practical reasons a small gap between the outside of the cane and inside of the jacket tube is necessary and for the simulations present here this is set to ${0.5}\,\textrm{mm}$. The jacket outer diameter is determined by goalseeking such that the target fiber outer diameter is met. This process was repeated for various draw yields. The simulations were set to a fixed draw stress of ${250}\,\textrm{MPa}$. While this is a high value for solid core fibers, this is inline with those typically used for HCFs [37]. It also offers a good compromise between the risk of fiber breaks during the draw and enables fair comparison.

 

Fig. 2. Simulations of fibers maintaining a specific draw yield, each line represents a draw yield. The shaded red regions represent $\Delta p_b \leqslant 0$, the MDC zone. A) Map of the target membrane thickness and cane outer diameter. Yellow dot indicates the cane-fiber combination displayed in Fig. 2(B) and (E). B) Example schematic of a cane. C) Effect of draw yield and cane outer diameter on MDC pressure buffer. D) Sensitivity of draw yield and cane outer diameter on applied pressure. E) Example schematic of a fiber.

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Table 1. Fiber geometrical parameters and their corresponding equations, used to build geometrically similar fibers scaled on the membrane thickness, $t$. Corresponding cane calculated using conservation of mass.

View Table

Each fiber and cane combination simulated is marked by a dot in Fig. 2(A), with each draw yield being represented by a different colour. In each subplot, the dotted red line and shaded region represent cane and fiber combinations with $\Delta p_b \leqslant 0$, the MDC zone. As expected, decreasing the draw yield (cane size) has the effect of reducing the minimum membrane thickness attainable without MDC, while also increasing the MDC pressure buffer and decreasing the pressure sensitivity. This is most clearly seen when comparing the intersection of the ${10}\,\textrm{km}$ and ${1}\,\textrm{km}$ yield lines with the MDC zone, with the ${10}\,\textrm{km}$ yield resulting in a minimum thickness of ${478}\,\textrm{nm}$ (and a pressure sensitivity of ${0.0047}{\,\mathrm{\mu}\textrm{m}/\textrm{Pa} }$), while the ${1}\,\textrm{km}$ draw has a minimum thickness of ${142}\,\textrm{nm}$ (and pressure sensitivity of ${0.00014}{\,\mathrm{\mu}\textrm{m}/\textrm{Pa} }$) for the chosen fiber geometry.

Another way to interpret the data presented is as follows: To achieve continuous guidance of the whole visible spectrum range (${400}\,\textrm{to}\,{800}\,\textrm{nm}$), a fiber with a capillary membrane thicknesses of less than $\sim {185}\,\textrm{nm}$ is needed, and hence a cane size of ${<2.04}\,\textrm{mm}$ would be required to avoid MDC. The exact cane size necessary to achieve differing fiber geometries will obviously be different but generally to produce a AR-HCF with thin membranes, and reasonable loss, a small diameter (${<2}\,\textrm{mm}$) cane is likely necessary, which may be problematic, as it will be both difficult to handle and may make pressurisation challenging.

Recently an alternative approach to HCF fabrication has been reported where self-pressurisation (induced by sealing of areas of the fiber preform) is used instead of active pressurisation [38]. Although practically this approach is different to the one outlined here, the underlying fluid-dynamics are the same, and hence it will suffer from the same limitations. However, the lack of active pressurisation may make the use of smaller canes more practical, even if these (and the resultant fiber preform) will still be difficult to handle. Further, self-pressurisation is inherently less controlled making the collection of long lengths of uniform fiber difficult.

4. Three stage HCF fabrication technique

A potential route to achieving all the benefits of a smaller diameter cane, whilst avoiding the associated problems, is to introduce an additional stage to the 2-stage stack and draw fabrication process described earlier. In this additional stage the jacketed fiber preform is drawn to an intermediate 2^nd cane stage, termed CS2 (with the first cane now being termed CS1), see Fig. 3 [39]. As such the fabrication process will then consists of: 1) build a stack and draw it to an initial CS1 cane, 2) jacket the cane and draw it to a 2^nd stage, CS2, cane, and 3) draw CS2 to fiber. This is accomplished by passing the preform through the fiber drawing tower furnace twice, but at different speeds, and has the major benefit of preserving the neckdown between the cane stages, allowing the smaller diameter cane to be pressurised through the larger one. A contour map of draw stress, CS2 outer diameter, and MDC pressure buffer for an example fiber is shown in Fig. 4, with a schematic of the target fiber inset. To ensure the fiber is achievable a minimum MDC pressure buffer of $\Delta p_{b} = {0.03}\,\textrm{kPa}$, as indicated by the dashed green line, was chosen. Based on the plot and pressure buffer requirement, a range of suitable CS2 diameters and draw stress values can be identified. In this process either draw stress or CS2 diameter (fiber yield) can be chosen as a free parameter, and used to tune the details of the fiber draw. Since draw stress also affects the total pressure requirement to achieve the desired structure, it was selected as the free-parameter in this case and used to tune the pressure; as shown by the overlaid dotted lines. Based on this contour map, a suitable fabrication window can be identified that will allow the desired fibre geometry to be fabricated given a specific total pressure or fibre yield (or potentially draw stress) requirement.

 

Fig. 3. Comparison of a conventional fibre draw of a 2-stage method with the proposed 3-stage technique. Left) The 2-stage technique with a single neckdown. Right) The 3-stage, with two neckdowns. Red cylinder represents the furnace. Note scale is exaggerated for clarity.

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Fig. 4. The effect of cane outer diameter and draw stress on both $\Delta p_{b}$ and pressure requirements when targeting a fixed fiber design. The shaded contours represent the MDC pressure buffer in steps of ${0.1}\,\textrm{kPa}$. Dotted lines show the required pressure (core + capillary). The solid black line represents $\Delta p_{b} = 0$ (fibers are not achievable to its right). The dashed green line shows $\Delta p_{b} = {0.03}\,\textrm{kPa}$.

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5. Experimental results

A series of 7-capillary fibers were drawn via the described 3-stage process. This fiber design was chosen as it has been shown to offer the best compromise between loss, bend-loss, and higher-order mode suppression for a single-cladding ring geometry [8,19]. Based on the targeted fiber geometries a series of contour plots, like those in Fig. 4, were generated to allow suitable draw conditions to be selected. These resulted in CS2 diameters of ${\sim 5.9}\,\textrm{to}\,{6.5}\,\textrm{mm}$ and draw stresses from ${\sim 110}{170}\,\textrm{MPa}$ being selected; resulting in theoretical maximum yields of ${\sim 1.5}\,\textrm{to}\,{3}\,\textrm{km}$ per meter of CS2.

In these draws several shorter bands were collected. The transmission of three representative bands is shown in Fig. 5. These measurements were made using a Energetiq EQ-99X laser-driven light source (likely absorption limited to ${\sim 280}\,\textrm{to}\,{2100}\,\textrm{nm}$), and a Teledyne-Princeton Instruments HRS-500 and PIXIS-256 spectrometer (capable of measuring ${200}\,\textrm{to}\,{\sim 1100}\,\textrm{nm}$).

 

Fig. 5. Left) Transmission profiles between 250 nm to 1100 nm for AR-HCFs A, B, and C fabricated with 3-stage fabrication technique. Transmission spectra measured at fibers lengths ${1.5}\,\textrm{m}$, ${5.2}\,\textrm{m}$, and ${6}\,\textrm{m}$ respectively. Right) A,B, and C Scanning electron microscope images.

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Based on the position of the short-wavelength edge of the transmission windows in these fibers, as indicated in the figure, and the ARROW model, Eq. (1) [22], their membrane thicknesses are estimated to be 254($\pm$8), 207, and ${167}\,\textrm{nm}$ for A to C respectively. These thickness estimates are in reasonable agreement with those obtained from the included SEMs for fibers A and B. However, the SEM of fiber C predicts a thickness of ${<130}\,\textrm{nm}$. We attribute this discrepancy to how the SEMs electron beam interacts with the thin membranes and believe the (thicker) figure obtained from the transmission is likely to be more accurate.

Fibers B and C guide from 444 and ${362}\,\textrm{nm}$ to beyond 1000 and 1100 nm respectively in their lowest order (1^st) anti-resonant (AR) window, and hence demonstrate continuous guide of the entire (or nearly entire) visible (${400}\,\textrm{to}\,{800}\,\textrm{nm}$) wavelength range, as well as part of the NIR. In the case of fiber C, this represents >1.6 octaves of bandwidth. Due to equipment limitations and strong atmospheric absorption below a wavelength of ${200}\,\textrm{nm}$ it was not possible to measure fiber C’s 2^nd AR transmission window or the short wavelength edge of fiber B’s 2^nd window, but based on the membrane thicknesses determined, these fibers are predicted to guide ${190}\,\textrm{to}\,{290}\,\textrm{nm}$ and ${231}\,\textrm{to}\,{365}\,\textrm{nm}$ respectively, also making them highly interesting for UV applications.

Figure 6 [A] and [C] show microscope images of the start and end of the ${346}\,\textrm{m}$ band associated with the fiber reported in Fig. 5 [C]. These images show some structural evolution along the band has occurred; primarily the core size has increased by ${\sim 0.7}{um}$ (3.5%) due to a mixture of the fiber inner diameter increasing (${40.2}\,\textrm{to}\,{40.5}\,\mathrm{\mu}\,\textrm{m}$) and the cladding capillary diameter reducing (by ${\sim 0.1}\,\mathrm{\mu}\textrm{m}$). This sort of evolution is sometimes seen during fiber fabrication, particularly towards the end of a fiber draw, as was the case with this band.

 

Fig. 6. [A] Microscope image of start of (${346}\,\textrm{m}$) band associated with the fiber reported in Fig. 5 [C]. [B] Transmission through full ${346}\,\textrm{m}$ band. [C] Microscope image of the end of band.

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Figure 6 [B] shows a transmission measurement of the full ${346}\,\textrm{m}$ band, measured using the same setup as the measurements in Fig. 5. This full band guides from ${\sim 600}\,\textrm{to}\,{800}\,\textrm{nm}$ which, while considerably narrower than Fig. 5 [C], represents ${\sim 0.4}{}$ octaves of bandwidth, similar to the specified single-mode bandwidth of commercial visible (solid-core) fibers. This bandwidth narrowing is likely due to a combination of the underlying loss profile of the fiber and the structural evolution seen along the fibers length. Both of these will be addressed in future draws as this process is further refined. As the measurements shown in Fig. 5 [C] and Fig. 6 [C] were made under different conditions they are unsuitable for loss determination, but a recent preliminary loss measurement suggests the loss of this fiber is ${<100}\,\textrm{dB/km }$ from ${\sim 500}\,\textrm{to}\,{800}\,\textrm{nm}$ [40]. Full characterisation of all the fibers shown in Fig. 5 is currently underway.

The fibers shown in Figs. 5 and 6 demonstrate the benefits of the 3-stage draw process as it would be extremely difficult to achieve the same geometries (using the same preform design) via the traditional 2-stage process as, for example, draw stress of 360, 511, and 753 MPa would be required (if a $\Delta p_b \geqslant {0.003}\,\textrm{kPa}$, sufficient to avoid MDC, is to be maintained) for fiber A to C respectively, making fiber breakage during drawing highly likely. The ${346}\,\textrm{m}$ length reported in Fig. 6 also represents a >3x improvement in fiber yield compared to the current state of the art for AR-HCFs with ${<200}\,\textrm{nm}$ membranes [3,29]. As the theoretical maximum yield of the preform design currently being used is ${>2}\,\textrm{km}$, it suggests this process may already be suitable for commercial fabrication.

6. Conclusion

In this paper we have explored the fluid dynamic limitations imposed upon hollow-core fiber design by the fabrication process. Based on this analysis a viable new route to the fabrication of anti-resonant hollow-core fibers with thin (${<300}\,\textrm{nm}$) membranes in lengths exceeding several hundred metres per draw has been demonstrated. Using this method, a series of UV-visible-NIR guiding fibers have been demonstrated including one, with ${\sim 167}\,\textrm{nm}$ membranes, capable of guiding light from ${\sim 360}{}$ to >1100 nm, >1.6 octaves of bandwidth. This work expands what is possible in terms of anti-resonant hollow-core fiber fabrication and offers a potential route to the commercial manufacture of hollow-core fibers suitable for broadband UV-visible guidance.