  Manufacturing end-of-fiber optical components able to realize optical
functions ranging from a simple lens to more complex functions such as mode
selective components is a decisive but \emph{a priori} complex task owing to
the fiber core dimensions. Effective low cost methods allowing to grow polymer
components by free-radical photopolymerization using the light coming out of
the fiber have recently been reported. A novel phenomenological model of the
photopolymerization process underlying is here given and used to simulate the
polymer component growth in a three dimensional time-resolved manner. The
simulations results are thus used to understand and optimize the component
growth conditions, focusing particularly on the role of oxygen either present
in the atmosphere or dissolved in the solution.
