In this work we present a numerical study of the solidification of crystalline fibers of titanium doped sapphire drawn by the micro-pulling down (µ-PD) growing technique. Our study emphasizes on the physical properties of the melting zone. The crystals of sapphire have many applications in lasers and in optoelectronics.  In  this  study  we  have established  a  numerical,  two-dimensional model  in  cylindrical  co-ordinates  with  an  axisymmetric  configuration  for  a  Newtonian  and incompressible  fluid,  of  a  laminar  flow  based  on  the  equations  which  are  mainly  those  of derived from of the physical conservation laws.  The flow, the thermal transfer and the mass transfer are modeled by the differential equations of conservation of the mass, of quantity of the movement, energy and the species.  This problem, which takes into account the convection-diffusion coupling, is discretized   using the Finite Volumes Method (FVM). Our model is in good agreement with experimental results. We have been able to show that the µ-PD method can gather the necessary conditions for optimization of the dopants concentration distribution  for  increasing  the  coupling  between  the  laser  wave  and  the  ions  of  the  doping agent  in  order  to  give  the  highest  possible  luminous  power  at  the  output  of  the  laser.  We found  that,  in  the  melt,  Marangoni  convection  is  dominant,  and  the  buoyancy  convection  is negligible.

1. POSTER: Numerical simulation of the crystal growth process of titanium doped sapphire fibers by the micro-pulling down technique, Microsoft Office Document, 1.8MB

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1. Segregation study of titanium ions in sapphire single crystal fibers grown by the µ-PD technique