Hole Deformation Behaviour in Drawing Microstructured Optical Fibres Shicheng Xue1 , 2 3 Maryanne Large , Geoff Barton , Roger Tanner1, Richard Lwin3, Leon Poladian4 1 School of Aerospace, Mechanical and Mechatronics Engineering, University of Sydney, Sydney, NSW, Australia, Phone: (612) 93512305, Fax: (612) 93517060 , firstname.lastname@example.org 2 Optical Fibre Technology Centre, 3 Department of Chemical Engineering, 4 School of Mathematics and Statistics, University of Sydney, Sydney, NSW, Australia Abstract Rheological modelling and numerical simulations are used to demonstrate that hole deformation in drawing microstructured optical fibres depends critically on both material properties and fibre draw conditions. Introduction: Optical effects in microstructured optical fibres (MOFs) can be tailored by changing the hole pattern [1,2]. However as there may be substantial deformation of the hole structure during the draw process it is important to be able to understand and predict the nature of this deformation. It has been experimentally observed  and numerically predicted  that in drawing MOFs, a range of hole deformation can occur including: hole collapse (the hole is partially or totally closed); hole expansion (hole diameter is increased relative to the outer fibre diameter); hole enlargement (hole diameter is absolutely increased relative to its original size); and hole shape changes (original circular shape is deformed). Such deformations may lead to a significant alteration of the fibre’s optical properties relative to the initial design, although there are occasions where such deformation can be exploited . In order to find means of minimizing or exploiting hole deformation, it is necessary to understand its underlying mechanisms. Ultimately it is hoped that this understanding will allow us to design the perform most appropriate to a final required fibre. This is not however an easy task. As the deforming system is a three-dimensional Newtonian (for silica fibres) or viscoelastic (for polymer fibres) fluid flow problem involving free surfaces in a non- isothermal environment, it is not feasible to seek analytical solutions. However with the development of computational fluid dynamics, it is now possible to analyze this system numerically, thus predicting the possible deformation behaviour in hole structure in drawing MOFs of different materials under different drawing conditions. In this work, the POLYFLOW package  was used to simulate the continuous isothermal drawing of MOFs for the case where the material is Newtonian. Process parameters: Currently both silica and polymethylmethacrylate (PMMA) MOFs are fabricated fabricated by continuously feeding (at a speed Vi) a preform of radius Ri into a furnace ( of Parameters PMMA Silica Length L and wall temperature Tw) where it is Ri (mm) 5 10 heated to the material softening point Ts (for Rf (mm) 240x10-3 62.5x10-3 silica fibres) or glass transition temperature Tg Tw (K) 473 2300 (for polymer fibres) and drawn down to a fibre L (mm) 20-40 40-50 of radius Rf under an applied draw tension. In Vi (mm/min) 2.3 3.0 the process, as the gravitational force is Vf (m/min) 1.0 120 negligible, only two external forces are involved (Pa.s) 5 10 ~10 7 5 10 ~10 6 - the draw tension and surface tension forces. (N/m) 0.032 0.3 The relative importance of these forces can be Ts or Tg (K) 393 1900 characterized by the capillary number 0.125~0.25 0.2~0.25 Ca Vi / where and are the viscosity 2 4 Dr 10 10 and surface tension coefficient of the material, 2 4 Ca 10 ~10 101~102 respectively. Dimensionless parameters are useful in describing the draw process, as they Table 1:Typical material and drawing parameters allow generalised results to be obtained that are applicable to quite different material and draw condition combinations. To characterize the overall deformation of an extended preform, two additional dimensionless parameters are of particular importance. These are the draw ratio Dr V f / Vi and the aspect ratio Ri / L . Typical material and drawing parameters for PMMA and silica MOFs are listed in Table 1, where appropriate a range of values is given, since the absolute values may vary over the temperature range experienced by the extending preform. Note that the magnitude of Ca for silica and PMMA can differ by orders of magnitude. The effect of a differing Ca has been predicted by Xue et al.  when drawing annular hollow fibres with in the range 0.125 to 0.25. It was shown that both hole expansion and hole collapse can occur. Thus in cases where a preform contains multiple holes, particularly when these are in close proximity to one another, then different deformation behaviour in the hole structure is to be expected during the drawing process due to the interaction between holes. Numerical simulations and discussion: Simulations were carried out for the drawing of MOFs from preforms having two illustrative cross-sectional hole structures as shown in Fig.1. In the five-hole structure case (Fig.1(a)), four small ‘satellite’ holes are symmetrically located around a large centric circular hole with the dimensionless spacing (normalised against Ri) between hole centres being 0.4. The dimensionless radii (normalised against Ri) for the small and large holes are 0.05 and 0.3, respectively. In the ‘Panda’ hole structure (Fig.1 (b)), two large holes ( = 0.3) are symmetrically located beside a small centric hole ( = 0.05) again with = 0.4. The two preforms are drawn down at a fixed Dr = 100 with a fixed feed speed Vi = 2.5 mm/min but for two different neck-down lengths ( = 0.25 and 0.125) and for two different Ca values (25 and 200) the latter representing silica and polymer fibres, respectively. (a) (b) Fig.1: Initial cross-sectional hole structures in (a) five-hole, and (b) Panda preforms (b) (b) (a) Fig.2:Pairs of images showing the final hole structures in fibres drawn down form the preform of five-hole structure with =0.25 at (a) Ca=200, and (b) Ca=25. (a) (b) Fig.3:Pairs of images showing the final hole structures in fibres drawn down form the preform of Panda hole structure with =0.25 at (a) Ca=200, and (b) Ca=25 (a) (b) a) Fig.4:Pairs of images showing the final hole structures in fibres drawn down from the preform of (a) five-hole, and (b) Panda hole structure with =0.125 at Ca=25 In Fig.2, the predicted final hole structures in the fibres drawn down using a short neck-down region (=0.25) and the preforms having the five-hole structure but for two different materials (in terms of Ca) are presented. Here the fibre cross-sections (left hand figure of the pair) have been enlarged to match the initial preform so that we can more easily see the relative size and shape changes of the holes. Also in order to view the dramatic shape changes in the small holes, the area around the small hole (right-hand one for the five-hole structure) has been enlarged (right hand figure of the pair). For the Ca=200 case (i.e., polymer), surface tension effects can be ignored and hole expansion occurs for both the large central hole and the four satellite holes. As a result, material between the central hole boundary and the outer fibre boundary is compressed. Any hole in this zone will therefore be squeezed in the radial direction while its own expansion will cause azimuthal elongation. The result of this interaction between holes is thus that the four small satellite holes become ovoid with their major axis parallel to the surface of the large hole. For the Ca=20 case (i.e., silica), hole collapse occurs for the satellite holes due to strong surface tension effects. Some hole expansion occurs for the large central hole, although it is much less than for the Ca=200 case. Due to expansion of the centric hole and the large surface tension forces acting around the small holes, material between these different sized holes will be ‘pulled’ towards the smaller holes. As in the polymer case, the small hole finds itself squeezed in the radial direction. However its shape change is not as dramatic as for polymer as there is no azimuthal expansion of these small holes. Similar deformation behaviour is to be expected if the positions of small and large holes are reversed as shown in Fig. 3. The predicted hole structures in the fibre drawn down from the Panda preform under the same conditions used in Fig.2 are presented. Here for the polymer (Ca=200) (Fig. 3 (a)), dramatic hole expansion leads to an ovoid shaped small hole. For the silica fibre (Ca=25) (Fig. 3(b)) however, there is only a slight collapse of the small hole and much less expansion of the large hole – a combination that results in only modest hole deformation If the same fibres are drawn down over a longer neck-down region (=0.125) with the same material and at a fixed Dr, a much smaller draw tension is required, so the surface tension effects are relatively more pronounced. As shown in Fig.4, for the Ca =25 case, hole collapse occurs in all holes for both types of hole structures. Material between adjacent holes is ‘stretched’ with the result that surface tension forces are partially balanced in the direction of any neighbouring hole. Consequently the hole collapse is less severe in this direction compared to that where there is no neighbouring hole. The net outcome due to this interaction between holes is that both the small and large holes become non- circular. Note that the small hole becomes quite ovoid in shape with its major axis (where there is less hole collapse) being along the line where there is a neighbouring hole. Calculations have also performed under different draw ratios. The results show that increasing draw ratio, like decreasing neck-down length, has the function of reducing surface tension effects, which is in line with the analysis . Conclusions: Totally different hole deformation behaviour can be expected when drawing MOFs of different materials (in terms of their viscosity and surface tension characteristics) and under different conditions (in terms of length of neck-down region and draw ratio). The way in which hole shape changes occur is determined by the ways in which the individual hole changes its relative size. With the fact of that the hole shape changes are due to the compressive force formed around an expanding hole and the stretching force formed around a shrinking hole, in principle, hole shape changes due to hole interaction can be reduced by using hole depressurization for the expanding holes and hole pressurization for the shrinking holes. References 1 T.A., Birks et al, Opt. Lett., 22, pp 961-963, (1997). 2 M. A. van Eijkelenborg, et al., Opt. Exp, 9, pp.319-327, (2001). 3 M. Large, et al., 30th Euro. Conf. on Optical Communication, Stockholm, Sweden. Sept. (2004). 4 S. C. Xue, et al., J. Lightwave Technol, Accepted, April (2005). 5 N A Issa, et al., Opt Lett, 29, pp. 1336-1338, (2004). 6 POLYFLOW User’s Manual, ver. 3.10, Fluent Inc., Sep. (2003). 7 S.C. Xue et al., Int.Conf.Polymer Optical Fibres, Nurnberg, Germany, Sept. (2004).
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