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In this work, dispersion, nonlinearity, gain factor associated with the pumping pulse, attenuation, and others – can be incorporated into the general equation for signal propagation in optical fibers through a laser resonator where the type and modulation depth of the saturable absorber directly affect pulse shaping and energy extraction. The equation is solved using the split-step Fourier transform method (SSFM), which requires creating a time and frequency lattice, slicing the resonator into small distances, and iteratively solving the equation for each segment until the end of the resonator is reached. The results showed that the energy increases with the effect of the pumping energy, which is represented by the  g    o    factor. The pulse width initial  T    o    and  T  2  modulated depth represent the effects of the change method on the oscillation of the factors resulting in pulses. Heavily doped fibers can enhance gain but may also introduce quenching effects. Optimal doping balances gain and energy extraction without degrading beam quality.

Theoretical study of the factors affecting the pulse energy generated by erbium-doped optical fiber lasers