Approximate analytical expressions for signal amplification in strongly pumped fibre amplifiers

Strongly pumped fibre amplifiers (e.g. Er³⁺ and Nd³⁺ doped fibres) have been analysed previously, yielding approximate but quite accurate analytical expressions for the pump and signal powers. These expressions are inefficient, however, for forward pumping, when the parameter q approaches unity (typical for single clad fibres). An alternative form of the expressions is presented, which is also useful in that region. Furthermore, the analysis is extended to include systems such as Yb³⁺ doped fibres, for which the pumping efficiency is reduced due to stimulated emission at the pump wavelength of λ_p