Analytic modelling of high-gain ytterbium-doped fibre amplifiers

A new theoretical approach for modelling the saturated single-pass gain in a three-level fibre amplifier is presented, relevant to the behaviour of rare-earth-doped silica fibres. This approach accounts for both two- and three-level schemes, and coupled spectral and power effects. A basic approximation considering an averaged value of the depleted pump over the length of the fibre allows us to obtain analytic expressions for input and output pump, amplified spontaneous emission (ASE) and signal power in the fibre. We show that, according to these assumptions, these expressions can be described with the help of a unique parameter S shown to be fully representative of the saturation in the medium. Continuing with this model and assuming homogeneous linewidth, we are able to predict spectral properties of the ASE. These expressions describe side-pumped fibres by adjusting some of the model parameters and the model is very useful to calculate cascaded amplifier architectures, including coupled ASE effects.