Approximate solution of diffraction integral equation of resonator

Abstract

Utilizing the diffraction integral equation and the principle of slow amplitude approximation, we obtain a novel approximate solution of the transverse mode including the cavity parameters a (a is the section size of the resonator) and g = 1-L/R (L is the cavity length, R is the radius of curvature of the cavity). With this approximate solution, we can explore the influence of the resonator parameters a and g on the transverse mode. The theoretical analysis demonstrates that a and g have a certain influence on the shape and quality of the transverse mode, and selecting the appropriate a and g can effectively improve the quality of the transverse pattern. Moreover, laser experiments are conducted to validate analysis conclusion.