Numerical modeling of free-running lasing in axisymmetric optical resonators

The problem of free-running lasing from axisymmetric optical resonators loaded with a saturable active medium is considered. The split-step spectral method based on the Fast Hankel transform over radius and Fast Fourier transform over angle was elaborated for free-space propagation step. Computational efficiency of this algorithm is demonstrated in comparison with traditional split-step algorithm using 2D FFT over transverse Cartesian coordinates in the case of weak angular honuniformity. The problem of stability of single-mode lasing in Fabry–Perot resonator with circular mirrors is studied numerically. The results are compared with the theory, developed in neglecting of nonlinear mode deformation. The study was performed for Rigrod medium and for fast-flow $\mathrm{CO}_2$ laser medium. The problem of stability of single-mode lasing from confocal unstable resonator formed by circular mirrors and loaded with locally saturable (Rigrod) medium is investigated.