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Numerical analysis of the heat transfer within photonic crystal fibre preforms

Photonic crystal fibres consist of a number of air capillaries surrounding by either a solid or an air core. The airhole distribution allows the control of the fibre properties such as dispersion, birefringence and nonlinearities. For the manufacturing of these fibres, a preform with the required hole pattern is heated in a furnace and drawn down in a drawing tower, being essential that the air-structure of the preform be retained in the final fibre. The holes in the preform affect the heat conduction during the heating process and may result in surface tension forces and distorsion of the structure. A numerical simulation of the heat transfer during the preform heating is presented. Both finite element and volume element methods were developed for the two-dimensional axisymmetric linear heat equation with nonlinear boundary conditions accounting for the radiative heat transfer at the external surface by means of the Stefan-Boltzmann law. The heating time required to reach a uniform temperature distribution within the preform was determined for several hole distributions including high numerical aperture fibres. The main result is that the microstructured preform heats up faster or slower than the solid one, depending heavily on both the preform's air void fraction and distance of the exterior hole ring to the boundary. A detailed explanation of these facts is given. Since the outer part of the preform reaches the fibre draw temperature before the central part, a distorsion of the hole structure of the resulting fibre can result, therefore, a careful optimization of the heating process is a due requirement in photonic crystal fibre fabrication in order to avoid any such asymmetries.