The operational parameters including the polarization controlling and the pump power in a nonlinear polarization rotation-based passively mode-locked fiber laser are studied in this paper.The carrier rate equations of the activated erbium-doped fiber are first employed together with the nonlinear Shro¨dinger equations to reveal the relation between the operational parameters and the output state of the passively mode-locked fiber laser.The numerical and experimental results demonstrate that the output state of the mode-locked laser varies with the polarization controlling and the pump power.The periodicity of the polarization controlling is observed.With given pump power,there exists a set of polarization controlling under which the ultra-short pulse can be generated.With given polarization controlling,the mode-locked state can be maintained generally except for some particular values of pump power.Three shapes of the output optical spectra from the fiber cavity can be identified when the pump power changes.The results in this paper provide a comprehensive insight into the operation of the nonlinear polarization rotation-based passively mode-locked fiber laser.
