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A flexible method of manufacturing polymer elements at the extremity of both single mode and multimode optical fibers is reported. The procedure consists in depositing a drop of liquid photopolymerizable formulation on the cleaved fiber and using the light emerging from the fiber to induce polymerization process. After exposure and rinsing with methanol, a polymer tip is firmly attached to the fiber as an extension of the fiber core. When this process is applied to a multimode fiber, the fabricated polymer element can be the 3D mold of a pre-selected linearly polarized (LP) mode of the fiber.A numerical calculation (consisting on a beam propagation method (BPM) in a medium whose refractive index is time-varying) has shown that our method is based on a gradual growth, just above the fiber core, of an optical waveguide in the liquid formulation. At the end of this paper, potential uses of the obtained tipped-fibers are hinted. [Copyright &y& Elsevier]