The Reflection and Transmission of a Multi-layer Film

Abstract

From the recurrence formula of Weinstein a matrix equation is derived connecting the amplitudes of electric vector of light in the k-th layer with those in the p-th layer of a multi-layer film. The elements of the matrix are expressed as functions of the reflection and transmission of the intermediate film between the media k and p. From this equation, formulas are derived for the transmission and reflection of an arbitrary multi-layer filter as functions of the thickness of the spacing layer. The results are found out to be of the same form as Abelé’s equations derived by the consideration of the multiple reflections in the spacing layer. By these equations, the physical meaning of the complicated phase factor of Vašicek’s equation is made clear and some new relations of the intensity and phase of the transmitted and reflected light are obtained.