Stability of CW Solutions of the FDML Laser

The problem of existense and stability of continuous wave (CW) solutions $R\exp(i\Lambda t)$ of a Fourier Domain Mode Locking laser model is studied. This model consists of two differential equations with delay. The delay is sufficiently large. It is nessesary for the existense of CW solutions of this model that parameters determining the "main part" of solution must lie on a certain curve ($\Gamma(\kappa,g_0)$). Sufficient conditions of stability of CW solutions for all sufficiently large values of delay are found. The location of stability regions on $\Gamma(\kappa,g_0)$ is studied. In the case of zero linewidth enhancement factor $\alpha$ for all values of parameters of the linear attenuation factor per cavity round trip $\kappa$ and the linear unsaturated gain parameter $g_0$ the number of stability regions and their boundaries on $\Gamma(\kappa,g_0)$ are found analytically. The comparison of location of stability regions on $\Gamma(\kappa,g_0)$ in tha case of zero $\alpha$ and nonzero $\alpha$ is made.