Abstract: The optical resonator is a key component in modern optical systems, and the study of its stability has significant theoretical and practical importance.This paper analyzes the stability of optical resonators using the eigenspectrum of the round-trip matrix, revealing the intrinsic relationship between stability and the distribution of eigenvalues and the number of eigenvectors.We establish clear and definitive stability criteria by introducing the g parameter and stability diagram.The stability analysis method is further extended from empty resonators to non-empty resonators, broadening the applicability of these criteria.This analytical approach is mathematically rigorous and provides intuitive insights into the physical nature of resonator stability, offering strong theoretical guidance for optical resonator design and optimization.

Key words: optical resonator, stability analysis, matrix eigenspectrum, g parameter, stability diagram