Need for Abrupt Transitions in Index of Refraction in the Soft X-ray Spectral Region

Gradual transitions in index of refraction from layer to layer, as in rugate coatings, can be advantageous. When absorption or the k-value is negligible, it can be shown that the first order reflection band is not significantly changed from when the transition between layers is “square” even to the case where it is sinusoidal. In most visible spectrum cases, the difference between the indices of the layers is almost exclusively in the real part of the refractive index, and it is that difference which causes Fresnel reflection at the interfaces. In the EUV/Soft X-ray region, the real parts of the indices are near unity, and therefore more layer pairs are required to achieve high reflection because of the low reflection at each interface. In these cases where one of the materials has a relatively high k-value, it can be shown that slow transitions in index from layer to layer are detrimental to the reflection desired. Even when interface roughness and interlayer diffusion are ignored per se, it can be shown that the layers with the highest k-values need to be as thin as possible to reduce absorption losses. This leads to sharp transitions between layers because the most absorbing material components are compressed into the smallest thicknesses practical.