Optical Properties of a Class of Inhomogeneous Thin Films

Thin films with a gradient of the refractive index in the direction z perpendicular to the film surface may be produced by varying the ratio of the evaporation rates of two sources, operated simultaneously and containing different substances. An analytical expression for the refractive index n=n(z) is derived by using certain assumptions about the optical properties of binary dielectric mixtures and assuming that the rates are linear functions of time. The reflectance of such films as function of the wave-number is calculated, supposing that the indices of the two substances are 2· 3 and 4·1. In particular, the heights and positions of the first three reflectance maxima and minima are studied and compared with those of homogeneous films with refractive index equal to the mean value of the index of the inhomogeneous films. It is shown that an inhomogeneous film has lower minima than the corresponding homogeneous film. The maxima are sometimes lower, sometimes higher. The positions are sometimes shifted towards lower, sometimes towards higher wave-numbers.