Analytical comparison of pulses generated by locking three and five longitudinal modes in free-running class B lasers

We consider the coherent oscillation of five longitudinal modes, which leads to the coupling of modes in the frequency domain and generation of short pulses in the time domain. The aim is to audit the mechanism of mode locking in more detail by extending the analytical solution of the Maxwell-Bloch equations of motion from three to five mode states. The characteristics of pulses including height, repetition, and duration have been calculated for a five-mode class B laser, and the changes are compared with respect to the three-mode state. The effects of other parameters, such as the mean damping rate of cavity mirrors, the frequency detuning of cavity longitudinal modes, and the laser pumping rate have also been investigated. The central and adjacent modes supply the energy of pulses. The amplification gains of five oscillating modes, together with the contribution to forming pulses, are evaluated. It is finally demonstrated that the results satisfy the energy conservation law.