Abstract: The present invention provides a method for forming a transparent optical element, such as an optical fiber, having a graded index of refraction. One preferred practice of the invention employs a hollow tube formed of an amorphous fluoropolymer and fills the tube with a liquid dopant material having an index of refraction that is different than that of the fluoropolymer. The heating of the filled tube for a sufficient duration causes the diffusion of the dopant material through the fluoropolymer, thereby producing a graded distribution of the dopant and hence a graded refractive index.