Graded-index (GRIN) fibers are often used for making high-power Raman amplifiers. We employ numerical and semi-analytical techniques to model such amplifiers and include not only the signal’s amplification and pump’s depletion but also various nonlinear interactions between the signal and pump beams and the self-imaging effects within the GRIN fiber. We solve the coupled nonlinear equations of the pump and signal beams numerically. We also employ the variational technique to obtain simpler equations that can be solved much faster than the full model and still agree with it in most cases of practical interest. We discuss the evolution dynamics of the pump and signal beams, along with a novel process of energy exchange between the two beams because of self-imaging inside the GRIN fiber. The dependence of the signal’s amplification on various input parameters is analyzed in detail to optimize the device’s design and enhance the signal’s amplification for a given pump power and fiber length. Based on our analysis, we establish a resonant condition for the maximum energy transfer from the pump to the signal being amplified. We further show that the periodic self-imaging of the pump and signal beams inside a GRIN fiber leads to higher output powers compared to step-index fibers.
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