Method for producing optical fibers and resulting fibers

A method for producing optical fibers having a variation of refractive index in the cross-sectional direction of the fibers, which comprises producing concentric circular sheath-core composite fibers composed of at least one polymer selected from the group consisting of polystyrene, polymethyl methacrylate, polycarbonate and styrene-methyl methacrylate copolymer as the core component and a film-forming polymer having a solubility parameter as defined in the specification of less than 20% and a swelling parameter as defined in the specification of 10-50% as the sheath component, the cross-sectional area ratio of core/sheath being 50/50-95/5, immersing said composite fiber into a solution of a monomer in a solvent, at a temperature of from room temperature to 100.degree. C, for from 1 minute to 15 hours, so that said monomer penetrates through said sheath into said core while said sheath acts as a protective film for said core, said monomer being such that a polymer thereof has a refractive index of at least 0.01 lower than the refractive index of the core and a photo transmission coefficient as defined in the specification of up to 5, and then polymerizing the introduced monomer whereby to transform the core so that its refractive index decreases in a gradient manner from the center of the core to the periphery of the core and the difference between the refractive index at the center of the core and the refractive index at the periphery of the core is at least 0.005.