A detailed study of axicon-based Bessel-Gauss resonator for the thin disk laser has been carried out. A paraxial ray analysis is performed to find the self-consistency condition to have stable periodic ray trajectory after one or two round trips. By using the Fox-Li method, it is possible to find the lowest mode shape and associated optical loss for an arbitrary optical resonator. Nevertheless, the mentioned routine is very time-consuming and therefore, we make use of a technique in order to convert the Huygens-Fresnel integral self-consistency equation into a matrix one and then find the eigenvalues and the eigenfields of the resonator. Here, special attention is paid to investigate the dependence of the transverse profile and the loss on the cavity length.
