Optimum Refractive-Index Difference for Graded-Index Fibers Resulting From Concentration-Fluctuation Scattering

Since the use of graded-index optical-fiber waveguides can greatly reduce pulse dispersion, fibers with greater acceptance angles can be used to increase the power coupled from an incoherent source. The increase in acceptance angle is obtained by increasing the total index variation between the core and cladding, which is achieved by increasing the doping of the fiber. This paper shows that the increased loss of the fiber resulting from concentration-fluctuation scattering by the dopant eventually decreases the light at the output end of the fiber. Therefore, there is an optimum magnitude for the total index variation based on loss considerations alone. Analytic expressions are developed using a simplified theory of concentration-fluctuation scattering that assumes the dopant molecules are randomly distributed. These expressions are applied to doped-silica-based fibers, assuming typical values for the source intensity, fiber loss, and receiver sensitivity.