Numerical study of the spiking instability caused by modulation frequency detuning in an actively mode-locked solid-state laser

We have studied both analytically and numerically the transient active mode locking in the case of a modulation frequency detuning. Analytical results for pulse width and position, extending previous works, are obtained within the frame of the stationary theory by assuming that a short pulse restores its shape after each round trip. Numerical evaluation leads to relaxation oscillations and change of the short-pulse shape. The results of both approaches agree with each other only for small detunings, when laser is operated in the steady state. For larger detunings the laser dynamics change dramatically, and the three operation modes observed earlier in experiments were demonstrated numerically: sequences of damped relaxation oscillations, deep periodic spiking and chaotic spiking. The periodic spiking can be used to increase the intensity of mode-locked pulses.