Theoretical analysis of saturable absorbtion in passively mode-locked fiber lasers

We propose a general analytical method for estimation of the saturable absorber output energy as a function of the input energy. The method is based on a representation of the saturable absorber output energy as a series of powers of the recovery time. We also derive a simplified expression of the saturable absorber output energy that gives a good approximation for large input energies. The analytical results are verified by the numerical simulation. The results have been applied to the particular cases of an input function that include the Gaussian input pulse and the hyperbolic secant input pulse. We show that the analytical results can improve the prediction of the output energy in the fiber lasers.