Abstract: Fresnel integral equations of the transverse multimode are solved by the numerical integration method in the cylinder coordinate. Under the initial conditions of the uniform and random distribution given respectively for the complex light-field amplitude, TEM_n0 modes of the confocal and stable cavities with circular mirrors of spherical surfaces as well as the plane cavity with circular mirrors are computed and analized. Computational results indicate that the numerical results of single mode for spherical cavity coincide with the analytical results. The results of the multimode not only conform to the behavior of the multimode space distribution, but also show that those of the fundamental mode dominate.

Key words: Fresnel integral equation, transverse multimode, stable cavity with circular mirrors of spherical surfaces, virtual confocal unstable cavity with circular of spherical surfaces