Parameters of the model

In the numerical calculations, we assume a generic setup for a Kerr-lens mode-locked laser to employ a longitudinally-pumped active medium, an arbitrary dispersion-compensating scheme, which together with the active medium provides the flat second-order dispersion, and an instantaneous $n_2$-based self-amplitude modulation mechanism. This generic scheme is suitable to model practically all the published experimental studies of the multipulsing in Kerr-lens mode-locked lasers in different active media [1,13,14,26,19,20,22,23]. While our main interest stays with the case of the Cr:ZnSe laser [26], we also consider the Kerr-lens mode-locked Ti:Sapphire laser to verify our model. For the latter, we take the well-documented experiment in Ref. [13] for modelling. It is also important that for both experiments all the setup parameters are available. Table summarizes the relevant material parameters of Cr:ZnSe and Ti:Sapphire, intrinsic to the chosen materials. In Table , $x$, $w_0$, $T_{cav}$, and $\alpha _{max}$ represent the experimental parameters, which are used to obtain the modelling parameters $\beta$, $t_f$, $\epsilon$, and $P_{max}$. Intensities are calculated using the expression for the mode area inside the active medium, taking into account the astigmatism of the Brewster-oriented crystal. Additionally, the $t_f$ parameter includes the spectral dependence of both, the gain and the loss due to the output coupler. In the simulations, we consider the parameters in the Table as fixed, while varying $P$, $\rho$, GDD, $\gamma$, and $\sigma$. In the experiment this corresponds to the pump power tuning, the exchange of the output coupler, the variation of the distance between the prisms and of their insertion, the slit width adjustment, and the stability zone and the lateral crystal position scans, respectively. If the Kerr-lens mode locking is based on the so-called "soft-aperture", then $\gamma$ and $\sigma$ parameters are simultaneously changed by scanning through the stability zone, and the adjustment of the crystal position and of the pump focusing lens. The simulations are performed at the grid with 2$^{13}$ points (102 ps time window) over 6 $\times$ 10$^{4}$ transits corresponding to 0.6 ms of the real time, which guarantees the convergence to the steady-state or, physically, the mode locking self-start. The model validity for the field evolution located within the time window $\ll$ T$_{cav}$ is justified by the control simulations on the grid with 2$^{19}$ points (6.6 ns time window) for the arbitrary chosen parameters as well as by the transition to the grid with the $t_f/2\sqrt{ln2}$ step. The solutions with deviations of the peak intensity within 1% during the last 5000 transits are considered as steady-state. The small intensity single spike is chosen as the initial condition for ab initio simulations.

Hosted by www.Geocities.ws