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Today, the number of services, which includes large information contents like high-definition movies, is rapidly increasing. The graded-index plastic optical fiber (GI-POF) has been proposed as a solution. The conventional fabrication method of GI-POF, however, is unsuitable for mass production. Therefore, we propose the dopant diffusion coextrusion process for fabricating high-bandwidth GI-POF. It has been generally thought that formation mechanism of refractive-index distribution in optical polymer materials by this process would be a Fick's diffusion with constant diffusion coefficient and, therefore, has a tailing part at the core-cladding boundary. Contrary to predictions, we succeed in fabricating GI-POF with an almost optimum-index distribution. It is made evident by experiments and simulation that the formation mechanism of GI-POF by this process is a Fick's diffusion with diffusion coefficient dependent on dopant concentration. These results indicate high possibility of fabrication of high-bandwidth fibers of a polymethyl methacrylate-diphenyl sulfide system by the dopant diffusion coextrusion process.