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									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 , shicheng@aeromech.usyd.edu.au
              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 [3] and numerically predicted [4] 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 [5]. 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 [6] 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. [4] 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 [4].
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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