Abstract: In order to reduce the film layer number and improve the reflection efficiency, a multi-layer film transmissivity calculation method is proposed. For the plane wave function of one-dimensional time-independent Schrödinger Schrodinger equation solution, the relation formula of film surface including incident and transmission wave amplitudes are obtained respectively based on the boundary conditions of thin film. The two formulas are connected by transmission and reflection waves inside the film. The relation including the transmission wave amplitude of the film layer is obtained, and that of the multi-layer film is obtained. According to the relationship between energy factor and refractive index, the film thickness is selected according to the matching principle, and the amplitude relation is transformed into an equation to calculate the multi-layer film transmittance. Four kinds of optical media are used to make film system, and the equation is numerically simulated and compared. Results show that the proposed method is feasible and the degenerative critical point of coating reflection effect is found. When the film layer number is 8, the film system reflectivity reaches 99.69%. If the traditional film system is adopted, the film layer number must be 13 for reaching standard. It shows that the efficiency of the proposed method is about 38% higher than that of the traditional method. .

Key words: thin film optics, film system reflectivity, Schrödinger equation, numerical simulation