Recurrence Formulae for the Reflectance And Transmittance of Multilayer Films with Applications

Abstract

Formulae are developed which, by repeated application, give the changes in amplitude and phase when light passes normally through any number of layers of homogeneous absorbing or transparent materials. These formulae are suitable for numerical computation and provide a direct route to the analytical expressions for the reflectance and transmittance in particular cases. Special attention is given to the case in which the layers are a quarter wave or multiples of a quarter wave in thickness.