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This paper considers the problem of forward Raman scattering process in a single transverse mode fiber. Both pump wave depletion and spontaneous scattering are considered in the analysis. Analytic solutions of the governing differential equations are obtained. We examine the conditions under which a nondepleted pump approximation is valid. Expressions are derived for the maximum fiber loss and the minimum fiber length which allow significant pump to Stokes wave conversion. It is shown that for a given fiber length there is an optimal pumping power, or at a given pump power there is an optimal fiber length that yields maximum first-order Stokes power output. Good agreement with published experimental results in the threshold power prediction is obtained.