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The authors solve a model which describes a nested fiber Raman cavity using Bragg reflectors by taking into account all interactions between forward and backward traveling waves. They apply the model to the cases in which a laser source at 1117 nm pumps a two-step Raman cascade leading to a 1240-nm output or a five-step cascade leading to a 1480-nm output. In order to insert into the calculations realistic fiber parameters, they have performed measurements of both Raman gain and linear losses for a few optical fibers. They derive from the numerical analysis the optimum fiber length and output coupling, and calculate, for the optimum configuration, the dependence of the output power on the pump power. The model describes with good accuracy the published experimental results.