Diffraction splitting of frequencies in a ring laser with a misaligned quadratically homogeneous active element

The diffraction splitting of frequencies of the opposite waves in a ring laser with a quadratically inhomogeneous active element is calculated for the case of weak diffraction. The dependences of the frequency splitting on the mode index, length of the active element, and its position along the resonator axis are determined. A study is made of the influence of misalignment of a quadratically inhomogeneous active element on the diffraction effects in ring lasers with resonators containing even and odd numbers of mirrors.