Analytical technique for calculation of mirror surface parameters in “HEX-DARR” resonator for lasers with a ring active medium

Within the geometrical optics approximation, we consider a class of mirrors (with surfaces formed by rotating second-order curves) which enables an extension of the range of possible beam conversions in optical systems. The formulas used in the calculations are quite simple. Based on this approach, we worked out and presented a complete analytical algorithm for calculation of the mirror surface parameters in a “HEX-DARR” resonator. To check the algorithm, a numerical calculation of an optical system is carried out for a specific set of initial data. The results obtained confirm the accuracy of the equations derived and the efficiency of the algorithm.