Abstract

A semi-analytic model of the amplification process is presented for Raman amplifiers made with graded-index multimode fibers. When the pump beam remains much more intense than the signal being amplified, it evolves in a self-similar fashion and recovers its initial width periodically. Using this feature, the width of the amplified signal is found to satisfy an equation whose form is similar to that of a damped harmonic oscillator. We use this equation to discuss the spatial beam narrowing occurring inside a Raman amplifier. In addition to oscillating with a period ${\sim}{1}\;\text{mm}$, the beam also narrows down during its amplification inside a graded-index fiber on a length scale ${\sim}{1}\;\text{m}$. The main advantage of our simplified approach is that it provides an analytic expression for the damping distance of width oscillations that shows clearly the role played by various physical parameters.

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