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Microstructured optical fibre drawing with active channel pressurisation

  • Michael J. Chen (a1), Yvonne M. Stokes (a1), Peter Buchak (a2), Darren G. Crowdy (a2) and Heike Ebendorff-Heidepriem (a3)...

Abstract

The use of channel pressurisation in drawing microstructured optical fibres (MOFs) potentially allows for fine control of the internal structure of the fibre. By applying extra pressure inside the channels it is possible to counteract the effect of surface tension which would otherwise act to close the channels in the fibre as it is drawn. This paper extends the modelling approach of Stokes et al. (J. Fluid Mech., vol. 755, 2014, pp. 176–203) to include channel pressurisation. This approach treats the problem as two submodels for the flow, one in the axial direction along the fibre and another in the plane perpendicular to that direction. In the absence of channel pressurisation these models decoupled and were solved independently; we show that they become fully coupled when the internal channels are pressurised. The fundamental case of a fibre with an annular cross-section (containing one central channel) will be examined in detail. In doing this we consider both a forward problem to determine the shape of fibre from a known preform and an inverse problem to design a preform such that when drawn it will give a desired fibre geometry. Criteria on the pressure corresponding to fibre explosion and closure of the channel will be given that represent an improvement over similar criteria in the literature. A comparison between our model and a recent experiment is presented to demonstrate the effectiveness of the modelling approach. We make use of some recent work by Buchak et al. (J. Fluid Mech., vol. 778, 2015, pp. 5–38) to examine more complicated fibre geometries, where the cross-sectional shape of the internal channels is assumed to be elliptical and multiple channels are present. The examples presented here demonstrate the versatility of our modelling approach, where the subtleties of the interaction between surface tension and pressurisation can be revealed even for complex patterns of cross-sectional channels.

Copyright

Corresponding author

Email address for correspondence: michael.chen@adelaide.edu.au

References

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Boyd, K., Ebendorff-Heidepriem, H., Monro, T. M. & Munch, J. 2012 Surface tension and viscosity measurement of optical glasses using a scanning $\text{CO}_{2}$ laser. Opt. Mater. Express 2 (8), 11011110.
Buchak, P. & Crowdy, D. G.2014 Fluid dynamics of MOF fabrication: elliptical cross-sections. Available at: http://wwwf.imperial.ac.uk/∼dgcrowdy/.
Buchak, P., Crowdy, D. G., Stokes, Y. M. & Ebendorff-Heidepriem, H. 2015 Elliptical pore regularisation of the inverse problem for microstructured optical fibre fabrication. J. Fluid Mech. 778, 538.
Chen, Y. & Birks, T. A. 2013 Predicting hole sizes after fibre drawing without knowing the viscosity. Opt. Mater. Express 3 (3), 346356.
Crowdy, D. G. 2004 An elliptical-pore model of late-stage planar viscous sintering. J. Fluid Mech. 501, 251277.
Cummings, L. J. & Howell, P. D. 1999 On the evolution of non-axisymmetric viscous fibres with surface tension, inertia and gravity. J. Fluid Mech. 389, 361389.
Dewynne, J. N., Howell, P. D. & Wilmott, P. 1994 Slender viscous fibres with inertia and gravity. Q. J. Mech. Appl. Maths 47 (4), 541555.
Dewynne, J. N., Ockendon, J. R. & Wilmott, P. 1992 A systematic derivation of the leading-order equations for extensional flows in slender geometries. J. Fluid Mech. 244, 323338.
Fitt, A. D., Furusawa, K., Monro, T. M., Please, C. P. & Richardson, D. J. 2002 The mathematical modelling of capillary drawing for holey fibre manufacture. J. Engng Maths 43, 201227.
Griffiths, I. M. & Howell, P. D. 2007 The surface-tension-driven evolution of a two-dimensional annular viscous tube. J. Fluid Mech. 593, 181208.
Griffiths, I. M. & Howell, P. D. 2008 Mathematical modelling of non-axisymmetric capillary tube drawing. J. Fluid Mech. 605, 181206.
Kostecki, R., Ebendorff-Heidepriem, H., Warren-Smith, S. C. & Monro, T. M. 2014 Predicting the drawing conditions for microstructured optical fiber fabrication. Opt. Mater. Express 4, 2940.
Monro, T. M. & Ebendorff-Heidepriem, H. 2006 Progress in microstructured optical fibers. Annu. Rev. Mater. Res. 36, 467495.
Monro, T. M., Warren-Smith, S., Schartner, E. P., François, A., Heng, S., Ebendorff-Heidepriem, H. & Afshar, S. 2010 Sensing with suspended-core optical fibre. Opt. Fiber Technol. 16 (6), 343356.
Ruan, Y., Schartner, E. P., Ebendorff-Heidepriem, H., Hoffmann, P. & Monro, T.M. 2007 Detection of quantum-dot labeled proteins using soft glass microstructured optical fibers. Opt. Express 15 (26), 1781917826.
Stokes, Y. M., Buchak, P., Crowdy, D. G. & Ebendorff-Heidepriem, H. 2014 Drawing of micro-structured fibres: circular and non-circular tubes. J. Fluid Mech. 755, 176203.
Stokes, Y. M., Tuck, E. O. & Schwartz, L. W. 2000 Extensional fall of a very viscous fluid drop. Q. J. Mech. Appl. Maths 53, 565582.
Taroni, M., Breward, C. J. W., Cummings, L. J. & Griffiths, I. M. 2013 Asymptotic solutions of glass temperature profiles during steady optical fibre drawing. J. Engng Maths 80, 120.
Voyce, C. J., Fitt, A. D., Hayes, J. R. & Monro, T. M. 2009 Mathematical modeling of the self-pressurizing mechanism for microstructured fiber drawing. J. Lightwave Technol. 27 (7), 871878.
Wilson, S. D. R. 1988 The slow dripping of a viscous fluid. J. Fluid Mech. 190, 561570.
Wylie, J. J., Huang, H. & Miura, R. M. 2011 Stretching of viscous threads at low Reynolds numbers. J. Fluid Mech. 683, 212234.
Yarin, A. L. 1993 Free Liquid Jets and Films: Hydrodynamics and Rheology. Longman Scientific & Technical and Wiley & Sons.
Yarin, A. L., Gospodinov, P. & Roussinov, V. I. 1994 Stability loss and sensitivity in hollow fiber drawing. Phys. Fluids 6, 14541463.
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