The invention concerns monomode or multimode optical fibers provided with a lens with an end taper, obtained by selective photopolymerization of a formulation, and with improved performances through the use of novel parameters and technical processes enabling production of polymer tapers with optimized characteristic required for a wide range of applications. The monomode or multimode optical fibers can, for certain specific applications, be equipped with a metallized polymer taper except for a nanometric opening for sensing or emitting light or a polymer taper whereof the formulation contains fluorescent particles. The novel fibers are essential components in various fields such as telecommunications (high performance connectors) or instrumentation (optical radiation comparator probes for scanning optical microscopy and near-field optical microscopy).