Evaluation of the effect of mirror shape distortions on the optical quality of radiation in unstable resonators

Subject of study. The subject of this study was an unstable telescopic optical resonator. Aim of study. This study aimed to investigate the quantification of small-scale mirror inhomogeneities, particularly in unstable resonators, and their effect on the M2 parameter, Strehl number, and radiation divergence angle. Method. This study conducted the numerical modeling of a structure with a small-scale inhomogeneity of mirrors as a homogeneous normal random field given by an exponential-cosine correlation function, with the further modeling of an unstable resonator in a geometric approximation using mirrors as "phase screens" and the subsequent determination of the characteristics of the radiation optical quality from the radiation pattern. A method for the analytical calculation of the radiation optical quality obtained after the unstable resonator with intracavity phase inhomogeneities is also proposed. Main results. This study considers the effect of mirror shape distortions on the optical quality of radiation in unstable resonators. The influence of the level and characteristic type of distortions on the M2 parameter, Strehl number, and radiation divergence angle is investigated. The nature of the dependence of these optical quality indicators on the resonator magnification coefficient, correlation radius, and the standard deviation of the mirror surface shape is shown. The calculated ratios for the estimation of the upper and lower limits of the range of changes in optical quality indicators depending on the parameters of the resonator and the specific type of mirror distortion are proposed. Practical significance. The results of the numerical simulation of the unstable resonator are compared with the quantitative estimates obtained based on the proposed calculation ratios. Based on the analysis of the results, practical recommendations and conclusions are formulated, considering the influence of mirror shape distortions on the optical quality of radiation when designing the resonator.