Passive mode-locking upon limitation of the spectral width of a laser emission

An analysis is presented of passive locking of modes in lasers with an additional intracavity element that limits the spectral width of a laser emission due to frequency dispersion of an order higher than quadratic. It is found that spectral limitation of this type may give rise to a multiple-pulse regime of passive mode-locking. The laser mode of operation established after a transient process, in this case, appears to be multistable, with the number of pulses per axial period being dependent on the initial conditions of the lasing. It is shown that the dependence of the number of pulses on the pump power is of hysteretic character. The theoretical analysis and numerical simulation are carried out using an equation close to the Ginzburg-Landau equation. Specifically, the nonlinear losses and nonlinear refractive index are supposed to be inertia-less and proportional to the light intensity; the frequency dispersion of the gain and the refractive index are approximated by a quadratic dependence; and the frequency-dependent losses related to the additional spectral limitation of the laser emission are determined by fourth-order frequency dispersion. The possibility of using the characteristic features of mode-locking predicted for control of regimes of formation and propagation of ultrashort light pulses is discussed.