An optical fiber can include a glass core that is multimode at a selected wavelength and that comprises an index of refraction and a diameter D.sub.core, a glass cladding disposed about said glass core, said glass cladding comprising an outer diameter D.sub.cladding and a first index of refraction that is less than said index of refraction of said core, and a second cladding disposed about said glass cladding, said second cladding comprising an optically cured polymer, said polymer comprising an index of refraction that is less than said first index of refraction. In certain embodiments, the fiber can include various other features. For example, [D.sub.cladding/D.sub.core].sup.2 can be no greater than 1.5; the polymer can have a modulus of no greater than 100 MPa; the core can include means for affecting the power distribution amongst modes propagated by the core, such as by having a non circular outer perimeter; the core can support at least 100 modes at the selected wavelength; D.sub.core can be at least 250 microns; the fiber can include a region disposed about the second cladding, and the region can comprise a polymer comprising an index of refraction that is greater than the index of refraction of said core. The fiber can be used, for example, for delivering light having the selected wavelength to or from a work object.