Semi-analytic saturation theory of fiber optical parametric amplifiers

A semi-analytical theory for the gain saturation of parametric amplifiers is presented. The theory is both simple and intuitive, it is compared with experiments on a parametric amplifier, and a very good agreement is found. Furthermore, using theoretical results, a method to obtain saturation characteristics for parametric amplifiers that have features not easily reproduced by theory is presented. The obtained method finds saturation characteristics in a few steps, providing that the gain studied is above 15 dB, where the approximations upon which our simple expression is based are strictly valid. An exact solution of the gain saturation when the pump power is totally converted is also presented and compared with the simplified expression using previously obtained theoretical results.