Diffractive eigenmode calculations in unstable optical resonators with gain medium

An eigenmode problem in laser unstable resonator with nonhomogeneous medium is considered. The proposed class of numerical algorithms for linear eigenproblem allows us to find efficiently several low-loss modes. The using gain and refractive index distributions were produced by solution of self-consistent lasing problem. The calculations were performed for Rigrod model and $\mathrm{CO}_2$ flow laser model.