The service life of the electrolyte material is a key factor in the operational stability of the flow cell. In this paper，based on the Debye vector integral theory and the diffraction integral theory，the theoretical simulation experiment of the propagation characteristics of the convergent beam at the dielectric interface of the flow cell is carried out. The propagation model of the convergent beam refracting through the dielectric interface is established by MATLAB programing，the intensity distribution of the fluid cell is calculated，and the experimental device for measuring the refractive index of the end mirror is developed. The propagation behavior of the convergent beam refracted by the dielectric interface is studied，and the variation curves of reflection coefficient of the light wave are obtained，and the possible factors affecting the excitation affecting the excitation efficiency of the output beam quality are analyzed in detail. It provides a theoretical basis for the study of dye laser output efficiency and service life of electrolyte materials.