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Various simple anti-resonant, single cladding layer, hollow core fiber structures are examined. We show that the spacing between core and jacket glass and the shape of the support struts can be used to optimize confinement loss. We demonstrate the detrimental effect on confinement loss of thick nodes at the strut intersections and present a fabricated hexagram fiber that mitigates this effect in both straight and bent condition by presenting thin and radially elongated nodes. This fiber has loss comparable to published results for a first generation, multi-cladding ring, Kagome fiber with negative core curvature and has tolerable bend loss for many practical applications.
© 2015 Optical Society of America
1. Introduction
Hollow core fibers have attracted strong interest in recent years for the transmission of pulsed beams whose peak power would exceed the damage threshold of a solid glass core and for gas/liquid filling applications where light benefits from a long interaction length with the medium that fills the core. In both situations a large core may be useful either to reduce peak intensity for power delivery, or to increase the in and out-filling speed. Even in a hollow core, air ionization can be a limiting factor in the transmission of high intensity pulses if the beam is confined to too small a mode area [1, 2].
Several types of hollow core fiber exist. Simple capillary [3], or tubular fibers [4,5], can provide a large core but bend losses limit their use in many practical situations. Hollow core photonic bandgap fibers (HC-PBGF) can have low confinement loss and have good bend loss [6–8], but their structure is complex and at shorter wavelengths (visible and near 1µm) it becomes more difficult to provide a large core because from electromagnetic scaling laws the lattice and hence the core must scale with wavelength. Kagome fibers can provide a hollow core of some tens of micrometers diameter with transmission windows much wider than HC-PBGFs [9]. Until the advent of Kagome fibers with a negative curvature core boundary [10], loss over a wide bandwidth was limited to ~0.5dB/m. With a negative curvature core boundary, loss in a multi-layer Kagome was reduced initially to 180dB/km and most recently (and remarkably) to 17dB/km at 1064nm [11]. However in these most recent results multiple cladding layers are required to provide good bend loss [12]. Simple (single cladding layer) structures have also attracted recent interest. Confinement is due to anti-resonance [13,14] of a thin glass layer defining a hollow core. Loss of ~200dB/km at yellow wavelengths was achieved in such a fiber however loss in the wide fundamental window was >1dB/m for wavelengths 900nm to 1700nm [15]. Negative core curvature has also provided guidance at long wavelengths where silica loses transparency [16,17], the latter reference demonstrating a loss of 34 dB/km at 3050 nm but with severe loss degradation under bending. Also, silica fibers with a single layer of non-contacting tubes were recently reported that produced low loss in 3 wavelength bands from 2.5 µm to 5 µm and guidance in bands located near 5.8 µm and 7.7 µm [18]. These results at wavelengths longer than 2.5 µm where silica becomes highly absorbing, demonstrate the small modal overlap with the glass layer in negative curvature fiber designs. In [18] the authors noted that non contacting capillaries aided preservation of negative curvature through fiber drawing. We expect that the fabrication of similar fibers for operation in the fundamental window at visible and near IR wavelengths to become much more challenging because the wall thickness of the capillaries must be reduced by a factor of ~20.
Our aim in this work was to develop a simple fiber that: had both tolerable loss and bend loss over a wide window that included common laser wavelengths, such as 1064nm; that permitted effectively single mode guidance in a large hollow core; and preferably did not require extreme fabrication conditions [9], which may be a barrier to future exploitation. Our target of much shorter wavelengths than the published results [16–18] implies that the required thickness of the glass web cannot be produced by a simple distortion-free down that scales the preform structure to the final fiber. To achieve the web thickness of interest, pressurization during fiber draw is required. This stretches the glass struts between the intersections of the structure tending to straighten them. Accordingly we look for a structure that, at least in part, provides a loss benefit comparable to negative curvature. In this paper we examine a number of simplified geometries and show that the hexagram structure can provide lower confinement loss than another simple structure studied and that the separation of the outer solid glass region also influences loss. We compare the loss of some fabricated hexagram fibers with numerical predictions and show that the difference may be explained by slight thickening at the intersections between glass struts, i.e. by the presence of nodes. We then demonstrate that the detrimental effect of nodes on loss may be mitigated by tilting the nodes whilst retaining the hexagram shape of the cladding struts. A fabricated hexagram fiber with a single layer of cladding holes, tilted nodes and a straight sided core boundary is shown to have a loss over a ~200nm window similar to the first generation of negative curvature multi-layer Kagome fiber and with bend loss characteristics that make it suitable for many applications.
2. Fiber design
2.1 Circularly symmetric fibers
We begin our investigation by comparing capillary fibers, i.e. a simple circular hole in a thick glass cladding, where the thickness t of the outer or jacket glass layer is much larger than the wavelength λ [3], and tubular fibers, where the requirement t>>λ is lifted [4, 5]. Throughout this work we consider fibers that have core radius r>>λ and are made of silica glass and air. The loss dependence on core radius r and bend radius R for a capillary fiber, α(r,R,λ), is given by [3],
The first term on the right hand side is the loss of the unbent fiber and the second introduces additional loss due to a bend (k1, k2 are constants). For a tubular fiber the local minimum loss between high loss peaks is given by (w1, w2 are constants that depend on mode number) [5],
In [4,5] the high loss peaks come directly from solutions for the various air guided modes of a hollow slab waveguide (and is a good approximation for a tubular fiber if the core diameter is large compared to the wavelength)but they may also be explained by resonance of the air guided core mode with modes of the glass tube [13, 19]. The wavelengths of these (high loss) resonances is given by,
where n is the refractive index of the glass and m = 1,2…… Both Eqs. (1) and (2) show that whilst loss in a straight fiber may be reduced by making the core radius arbitrarily large, this adversely affects bend loss. We now introduce an idealized jacketed tubular fiber where a glass tube is suspended coaxially without support in a hollow glass jacket. This is a purely theoretical construct used to gain insight. The confinement loss of a capillary, a tubular and a jacketed tubular fiber were numerically simulated both for fixed r,t over a range of wavelengths and at a wavelength anti-resonant with the thin tubular layer for a range of core radii. The results are shown in Figs. 1(a) and 1(b), respectively. Fits to the numerically obtained data points for the capillary and tubular fibers gave the r−3 and r−4 relationships expected from Eq. (1) and Eq. (2) respectively [Fig. 1(b)]. The jacketed fiber showed an r−5 dependence and lower confinement loss at all wavelengths. The radial gap between the glass tube and jacket may be optimized to decrease loss further. In Fig. 1 the calculated loss shows a difference for jacketed fibers with optimized and non-optimized jacket separation. Therefore confinement in this fiber is not only due to anti-resonance of the glass tube.
Fig. 1 (a) Calculated confinement loss of various circularly symmetric glass-air structures: capillary fiber, tubular fiber in air and jacketed tubular fibers with optimised and non-optimized jacket separation. The curves refer to the fibers shown in the inset, where air regions are shown in white, the core radius is 15 μm and core tube thickness is 0.42 μm. (b) Calculated confinement loss vs radius r for capillary (circles), tubular (diamonds) and optimized jacketed tubular fiber (squares).
We calculate the optimum jacket distance zopt by combining a semi-analytical expression [3] for the effective index neff of the fundamental core mode with the quarter wave condition for this air layer, and obtain:
Here J01 is the argument that produces the first null of the zeroth order Bessel function. This shows that to a first approximation the optimum air gap is independent of wavelength. Numerical simulations of a fiber with the optimum air gap at three wavelengths [Fig. 2(a)] confirmed this and also showed the loss was nearly optimal over a broad range of z/r, between ~0.6 and ~0.8. Furthermore, we simulated an unsupported hexagonal core and found that Eq. (4) held where r is taken as the inradius of the hexagonal air core. We use the optimized (circular) jacketed tubular structure as a reference with which to compare other structures in the following section.
Fig. 2 Calculated loss at three wavelengths vs normalized air gap (z/r) for the structure shown in the insert.
2.2 Simulations of realistic structures
We now investigate with full vector FEM simulations two structures that may be fabricated by stacking 6 capillaries, and compare their confinement loss to that of the unfeasible jacketed tubular fiber examined in the previous section and with a negative curvature Kagome fiber. Introducing support struts inevitably breaks the circular core surround into a number of segments and provides other resonances to which light in the air guided core mode may couple [16]. Figure 3 shows the calculated loss for three realistic structures (S1, S2 and S3) having the same inradius of the air core (r = 15 µm) and same thickness of the glass core surround (t = 0.42 µm). Firstly a hexagonal core surround is supported by 6 radial struts (S1) and the jacket layer is placed at the optimized distance for the reference fiber zopt = 0.65r. The support struts are formed from the glass of two stacked capillaries but the hexagonal core surround from only one. Accordingly we make the width of the support struts equal to 2t. In respect of the radial struts and core shape this is broadly similar to the fiber reported in [12]. Secondly, we simulate a hexagram or Star of David structure (S2). In this structure capillaries fuse where they touch in a first-stage draw to cane, while during the second-stage pressurised draw, the thin walls of each capillary become stretched and further straightened. Thirdly, we simulate a 2 layer Kagome structure with a negative curvature core surround [S3]. The three structures are compared to the optimised jacketed tubular fiber discussed in the previous section. In this comparison we do not consider structures where the cladding comprises a number of contacting or non-contacting circular capillaries [15, 16]. For these structures we assume that fibers are a scaled but otherwise unmodified copy of the stacked preform. Thus, for operation at visible wavelengths or near 1 µm they become extremely challenging to fabricate because they require a core diameter of some tens of microns and a glass core surround thickness of typically 0.35 µm, which implies obtaining and stacking tubes with a ratio of inner to outer diameters of ~0.97 or greater.
Fig. 3 FEM calculations of the confinement loss of two fiber structures (S1 blue, S2 black) that may be fabricated from a stack of 6 capillaries, a 2 layer Kagome structure (S3 orange) and an optimized, jacketed tubular tube introduced in the previous section (red: FEM simulation; black dashed: semi-analytic matrix method). All fibers have the same core inradius r = 15 µm and thickness of the core surround t = 0.42 µm.
In contrast to the reference fiber, the loss curves of all three realistic structures show spectral oscillations. Fiber S1 shows the smallest oscillations and most closely follows the loss curve for the reference structure. Fiber S2 has stronger oscillations and the minimum loss is comparable to the negative curvature Kagome fiber (S3), which in the notation of [11] has curvature b = √2-1≈0.414. This suggests that negative core curvature may not be the only route to low loss in simple hollow core fibers and implies that the struts connecting the hexagonal core surround to the jacket layer play a positive role in loss, at least over some narrow spectral regions which outweighs the effect of the hexagram structure having non-optimal z/r of ~1. However the Kagome fiber is low loss compared to the reference fiber over a wider bandwidth.
3. Fabricated fibers
3.1 Fibers with azimuthally aligned nodes
In previous work we have shown that the loss of hexagram fibers could be greatly increased by local thickening of the glass (nodes) in the core surround at the intersection of support struts [20, 21]. Our initial hexagram fibers had loss at all wavelengths that exceeded the one we calculated for a reference jacketed tubular fiber of the same dimensions r,t. To some degree these nodes are an inevitable consequence of surface tension and the softened glass state during fiber draw. The effect of these nodes on loss was simulated by adding a fillet of glass to each intersection of an ideal hexagram structure with otherwise uniform strut thickness. Figure 4 shows the confinement loss of simulated hexagram fibers without nodes and with a fillet radius such that the nodes were similar to our fabricated fibers. These small departures from an ideal hexagram can increase loss by 2 orders of magnitude at some wavelengths. This is because the nodes act as suspended core fibers to which light from the air guided core mode may easily couple.
Fig. 4 Calculated confinement loss for hexagram fibers without thickened nodes (black curve) and with two sizes of thickened nodes (green and blue curves). The loss of a jacketed tubular fiber with optimised jacket separation is shown by the red curve. All fibers have r = 15 µm t = 0.42 µm as in Fig. 3.
In order to reduce the nodes and therefore coupling to them from light in the air core, we increased expansion during fiber draw to further stretch glass in the core surround and thereby reduced the transverse dimension of the nodes. Two fibers were drawn with elongated nodes and the loss of each one was compared to the calculated loss of a reference jacketed tubular fiber having the same core diameter and core surround thickness, as shown in Fig. 5. The loss was measured by cut back method, where we avoided direct excitation of glass modes by butt coupling the hexagram fiber to an endlessly single mode large mode area (ESM-LMA) fiber into which light from a supercontinuum source was focused. One fiber had a core diameter of 39 µm, t = 0.30 µm and azimuthally elongated nodes with width of 1.3t, while a second fiber had a core diameter of 77 µm, t = 0.48 µm and nodes with width of 1.2t. Their minimum loss was 0.9dB/m at 1.21 µm and 0.4dB/m at 2.17 µm, respectively. These values are lower loss than calculated for a reference fiber of comparable dimensions, but only in very narrow wavelength windows. We note that for ultrashort pulse applications the spectral width of the low loss window may be less than the pulse bandwidth. The loss spectrum of both fibers is highly structured and suggests that the nodes are still introducing many additional resonances which couple light out of the air guided mode. We are confident that these fast oscillations are real and not an artefact of supercontinuum noise for example, since repeated measurements with different lengths of fiber and also transmission measurements using an incandescent, incoherent white light source reproduced these spectral features. The high loss peaks at wavelengths given by Eq. (3) are outside the wavelength range of each graph.
Fig. 5 Measured loss for two fibers (top and bottom) with azimuthally elongated nodes compared to calculated confinement loss for a reference jacketed tubular fiber having the same dimensions r,t in each case. Electron micrographs of the hexagram region of each fiber and a higher magnification image of a node are also shown on the left. The mode image (top insert) was obtained from 2.1m of fibre over the spectrum below 1.1 µm
3.2 Fiber with radially aligned nodes
The fibers in the previous section were drawn with a uniform pressure in all the holes of the cane. When drawn to cane, the 6 stacked capillaries fuse where they touch each other and the enclosing jacket tube, creating 12 cladding holes. Six of these quasi-triangular holes have edges that form part of the core surround, while the remaining 6 have edges along the perimeter of the structured region. To improve upon the previous fibers we decided to draw fibers with radially rather than azimuthally aligned nodes. To do this, we connected the core hole and the perimeter holes to one source of pressure (P1) and the 6 holes with core edges to a second source of pressure (P2). Figure 6 provides an outline of the fabrication process. In the condition P2>P1 the nodes were tilted by 90° and became radially aligned without changing the overall hexagram shape of the cladding. However the direction of tilt at each corner of the core hexagon is not controlled; one may turn clockwise whilst its neighbor counter-clockwise. Consequently this technique generally also introduced some asymmetry to the core.
Fig. 6 Outline of the fabrication process (a) A stack of 6 capillaries. (b)An optical micrograph of a cane produced from the stack. (c) A cane is inserted inside a jacket tube and the cane is pressurized during fiber draw as described in the text. (d) Electron micrograph of a hexagram fiber with tilted nodes.
To demonstrate the control that can be achieved with this method on the node orientation we pulled fiber having a core diameter of ~54 µm at constant outer diameter, firstly with equal pressures (P1 = P2 = 26kPa) and then with P2 increased to 29.5kPa. The furnace temperature was 2000°C and the coated fiber tension was 120g which shows that it is possible to avoid the extreme fiber draw parameters used elsewhere to fabricate similar fibers [9]. This small overpressure was sufficient to tilt the nodes from being azimuthally to radially orientated. Figure 7 (a) compares the loss of each fiber measured by the cutback method and Fig. 7 (b) shows bend loss of the azimuthally aligned node fiber. In these measurements light from a supercontinuum source was injected into an ESM-LMA fiber which was butt coupled to the fiber under test. Use of a correctly aligned and butt-coupled ESM-LMA fiber avoids exciting modes of the glass and provides a spot size that changes little over the wavelength range of the measurement. A 50 µm core, 0.2NA fiber was used to collect light from the end of the hexagram fiber and delivered it to an optical spectrum analyzer (OSA). It is clear that tilting the nodes has eliminated many undesirable transmission features in the spectrum.
Fig. 7 (a) Measured loss of hexagram fiber with azimuthal nodes (black curve), hexagram fiber with non-optimized tilted nodes (blue curve), 2r ~54 µm, t~0.31 µm at bend radius 20 cm and calculated confinement loss for a jacketed tubular fiber (dashed curve) having the same r,t . (b) Bend loss relative to R = 20cm of the hexagram fiber with azimuthal nodes for bend radii from 10cm to 4cm.
We then adjusted the draw conditions to provide a fiber with a ~50 µm diameter core and adjusted P2 slightly so that the radially aligned nodes were less elongated and the core slightly less distorted. The widths across each of the sides of the hexagonal core were 48.8 µm, 50.7 µm and 52.2 µm, indicating some asymmetry remained. The core surround thickness was 0.31 µm. Again, we measured the loss of the fiber by the cutback method using the same excitation and output beam collection methods. Figure 8 shows the loss and bend loss characteristics of this fiber. During measurement the fiber condition was 10 coils of radius of 20 cm cut back to one coil. For bend loss the transmission spectrum was obtained whilst taking the final (10th) coil of R = 20cm and replacing it consecutively with 2 coils at R = 10cm, R = 8cm, 3 coils at R = 6.5cm and 5 coils at R = 4cm.
Fig. 8 (a) Measured loss of hexagram fiber (solid curve) with tilted nodes, 2r ~50 µm, t~0.31 µm at bend radius 20 cm and calculated confinement loss for a jacketed tubular fiber (dashed curve) having the same r,t . The mode image (insert) was obtained from fiber length ~13m. (b) Bend loss relative to R = 20cm of same fiber for bend radii from 10cm to 4cm.
This fiber has a sub 0.2 dB/m low loss window of bandwidth 200nm centered near 1140nm. The minimum loss falls to 0.13 dB/m near 1100 nm and is close to the calculated loss of a reference fiber having the same r,t . Within this window the loss of this simple, single cladding-ring fiber is comparable to the first published 7-cell hypocycloid-core, three-ring Kagome cladding HC-PCF having similar core size [10]. However the Kagome fiber has a wider bandwidth. For some longer wavelengths loss improves compared to the reference curve even if the absolute value is greater than the minimum. The bend loss characteristics show a short wavelength bend edge that moves to longer wavelengths as bend radius decreases. At wavelengths longer than the bend edge (except for R = 4 cm), loss decreases to values comparable to the experimental precision of the short fibre length under test. Also, at R = 4cm the bend loss is increased for all wavelengths. At R = 8cm the short wavelength edge falls at a shorter wavelength than the sub 0.2 dB/m window, making this fiber an interesting candidate for many applications at the commonly used laser wavelength of 1064nm.
We attributed the high loss of the hexagram fiber with azimuthally aligned nodes to mode coupling from the air guided core mode to glass modes. Even a structure with a uniform thickness glass ring supports many modes with slightly different effective indices due to the many possible azimuthal oscillations of the field [19]. Introducing thickened sections within the ring adds to the number of modes to which the air mode may couple. When the nodes are radially aligned we explain the loss improvement by suppressed mode coupling because the modes of the node are almost orthogonal to the air mode even when the effective indices are similar.
To confirm the role of node alignment we calculated confinement loss for structures with sharp radially aligned intersections and rounded radially aligned nodes having an added fillet of glass. In both cases the nodes were represented by a short length of glass web having thickness and length obtained from a high magnification electron micrograph of the fabricated fiber. For the rounded nodes we added a small fillet radius of glass to represent the rounding that occurs due to surface tension during fibre draw. The results together with the measured loss of the fiber are shown in Fig. 9. For wavelengths longer than ~1.1 μm rounding of the nodes makes little difference to loss. For wavelengths near 0.95 μm loss curves of the sharp and rounded node fibers diverge. Here the loss increase of the rounded node fiber is broadly similar to that of the measured fiber. The resolution of the OSA was 10 nm and wavelength increment 0.35 nm in the measurements shown in Figs. 7 and 8. This resolution cannot account for the comparative absence of spectral oscillations in the measured loss curve of the fiber in the range 1 μm to 1.4μm compared to the simulations of Fig. 9. Instead we attribute this to the asymmetries of the real fiber.
Fig. 9 Comparison between the calculated loss of fibers having radially aligned sharp intersections (red curve) and rounded radially aligned nodes (green curve). Both have 2r = 50 µm, t~0.31 µm. Measured loss of the fabricated fiber is shown by the blue curve. The inserts to the right of the graph are electron micrographs for the fabricated fiber and drawings for the simulated fibers at a different scale.
Finally we note that all the fibers reported herein with cores of width 50 µm or less and at a wavelength of 1.06 µm produced a Gaussian mode similar to the insert in Fig. 8(a) that was stable with fiber handling when excited with a well centred beam. The mode image in Fig. 8(a) was obtained from ~13 m of fiber whereas the image in Fig. 5 from 2.1 m. Only when the launch was highly offset did we observe a higher order LP31 like mode. We conclude in practise these fibers are effectively single mode. In contrast the imaged mode of fiber with azimuthally aligned nodes and core width 77 µm did not produce a stable mode at visible wavelengths suggesting there is an upper limit to core size for effectively single mode operation depending on wavelength.
4. Conclusions
We have shown that both the separation between the glass antiresonant ring and the outer jacket layer and the shape formed by the support struts have a strong influence on the ultimate loss that can be achieved in simple, single capillary ring hollow core fibers. The hexagram shape was found to provide a loss benefit at some wavelengths compared to a jacketed tubular reference structure. We have therefore fabricated and characterized several hexagram fibers and observed that when their nodes are elongated and aligned azimuthally their loss is much higher than that of an ideal hexagram fiber. However, aligning the nodes along the radial direction, which is possible in practice, mitigates the problem over much of the operating window making such fiber more attractive for ultrashort pulse propagation applications. We have presented a hollow hexagram fiber with loss comparable to a first generation negative core curvature, three ring Kagome fiber that also has tolerable bend loss, with effectively single mode operation.
Acknowledgments
This work was supported by UK EPSRC through grant EP/H02607X/1 (EPSRC Centre for Advanced Manufacturing in Photonics). FP and DJR gratefully acknowledge support from the Royal Society.
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