Spatial beam narrowing in multimode graded-index fiber amplifiers: an analytic approach

Doped and optically pumped graded-index (GRIN) fibers can be used to amplify an optical beam such that its spatial quality is improved at the output end of the fiber compared with that of the unamplified beam. We develop a simple model of the amplification process in such GRIN fiber amplifiers and show that the resulting equations can be solved analytically with suitable approximations. The solution shows that the width of the amplifying beam oscillates but also becomes narrower because of the radial dependence of the optical gain. The main advantage of our simplified approach is that it provides an analytic expression for the damping distance of beam-width oscillations that shows clearly the role played by various physical parameters.