Some Basic Considerations on the Reflectance of Smooth Metal Surfaces: Fresnel’s Formula and More

We review the general properties of optical reflection spectra recorded from smooth solid surfaces from the infrared up to the X-ray spectral regions. Emphasis is placed on metal surfaces. By introducing a parallelism between a simple classical oscillator model treatment and surface reflection of light, general features of normal incidence reflection spectra are derived in a qualitative manner. This rather tutorial approach as relevant for an ideal metal surface is complemented by a broad elaboration of analytical features of realistic reflection spectra. The discussed topics include manageable dispersion formulas, the Kramers-Kronig method, oblique light incidence effects with an emphasis on Azzam’s analytical relations between the Fresnel’s coefficients, as well as special spectroscopic configurations involving reflection measurements at grazing light incidence. Further emphasis is placed on Infrared Reflection Absorption Spectroscopy IRAS, the Berreman effect, as well as X-ray reflectometry XRR. This way, we provide a synthesis of basic textbook material with advanced experimental and theoretical skills useful in the analytical work of an optical coating practitioner.