Abstract

Inhomogeneous films are difficult to produce, but they have potentially a number of advantages over the more classical coatings composed of multiple homogeneous layers. One of the few approaches available for the synthesis of such films is the Fourier transform method. It is fast and it can also yield homogeneous multilayers. Essentially, it is based on a Fourier transform relationship between the logarithmic derivatives 1/n dn/ dx of the refractive index profile, and a spectral function Q(σ) which depends on the desired spectral performance. A proper definition of Q(σ) is essential for accuracy. The analytical forms of Q(σ) proposed in the past are approximate, especially when the desired reflectance is high.¹ Sossi proposed an interesting approach where successive corrections ΔQ(σ) are added to Q(σ). A modified version, developed and programmed at the NRCC, is described. Examples illustrate the influence of several key parameters not addressed before and which have important practical implications. In particular, we show that the thickness of the films can be reduced considerably by defining appropriately the complex phase of Q(σ). This phase can also be used to modify the shape of the refractive index variations, without affecting the spectral performance.

© 1989 Optical Society of America