Abstract

Varying the refractive index of a thin film from one boundary to the other is a very appealing design approach for new types of coating with higher performance. An exact expression for the amplitude reflection coefficient of a single inhomogeneous layer has been given by Sossi in the particular case where there is no refractive-index discontinuity at the layer boundaries.¹ Nevertheless, the most efficient way to calculate the optical properties of a coating remains the matrix method where each layer is characterized by a 2 × 2 matrix. Although matrices have been listed in the literature for particular refractive-index profiles,² no general expression has ever been given. Until now, the only general way to deal with inhomogeneous layers has been to consider each layer as a stack of numerous homogeneous sublayers and to multiply all the corresponding matrices. We introduce a new matrix characterizing any type of inhomogeneous layer, which can easily be included in the traditional programs and allows the calculation of the optical properties of any stack of inhomogeneous and homogeneous layers.

© 1986 Optical Society of America