Optical fibers are made of glass with different refractive indices in the (inner) core and the (outer) cladding regions. The difference in refractive index arises due to a rapid transition in the concentration of a dopant across the boundary between these two regions. Fibers are normally drawn from a heated glass preform, and the different dopant concentrations in the two regions will change due to dopant diffusion and convective transport induced by the flow. In this paper, we analyze a mathematical model for the dynamics of dopant concentration changes during the fiber drawing process. Using a long-wave approximation, we show that the governing equations can be reduced to a simple diffusion equation. As a result, we are able to identify key dimensionless parameters that contribute to the diffusion process. We also derive asymptotic solutions for the temperature, cross-sectional area, and effective diffusion coefficient when there are strong temperature dependencies in the viscosity a...
Huaxiong Huang, Robert M. Miura, Jonathan J. Wylie