Matrix expression for 2-D misalignment sensitivity of complex astigmatic resonator

In order to analyze the general astigmatism of laser resonator cavities,the general analytical formula of misalignment sensitivity for complex astigmatic resonator cavities with several optical components has been derived by adopting augmented 8×8 misaligned matrix and symbol operation functions of MATLAB.This formula is applicable to the complex astigmatic cavity including several optical components with general astigmatic characteristics,and it can be used to analyze quantitatively the misalignment sensitivity of these resonator cavities in x-O-z plane and y-O-z plane.Calculation results indicate that mode distributions in the complex astigmatic cavity and the misalignment sensitivities of the complex astigmatic cavity have coupling in x-O-z plane and y-O-z plane.These results afford some references for the design and analysis of complex astigmatic cavities.