Stability of passively mode-locked fiber lasers with fast saturable absorption

The stability of passively mode-locked fiber lasers with fast saturable absorption is examined by a direct numerical approach. The laser operation is described by use of a standard model, closely related to the Ginzburg–Landau equation, which is valid when the change of the laser pulse during one round trip through the laser is small. This equation is then linearized around an equilibrium solution, and the eigenmodes and eigenvalues of the linearized equation are determined numerically. This approach retains the advantage of previous analytical research of permitting one to explore a wide range of parameter space while also permitting one to avoid approximations in the stability calculation. The stability of a figure-eight loop laser with the amplifier in the external loop is then studied by use of this approach.