Optical properties of metals: Infrared emissivity in the anomalous skin effect spectral region

When the penetration depth of an electromagnetic wave in a metal is similar to the mean free path of the conduction electrons, the Drude classical theory is no longer satisfied and the skin effect becomes anomalous. Physical parameters of this theory for twelve metals were calculated and analyzed. The theory predicts an emissivity peak εpeak at room temperature in the mid-infrared for smooth surface metals that moves towards larger wavelengths as temperature decreases. Furthermore, the theory states that εpeak increases with the emission angle but its position, λpeak, is constant. Copper directional emissivity measurements as well as emissivity obtained using optical constants data confirm the predictions of the theory. Considering the relationship between the specularity parameter p and the sample roughness, it is concluded that p is not the simple parameter it is usually assumed to be. Quantitative comparison between experimental data and theoretical predictions shows that the specularity parameter can be equal to one for roughness values larger than those predicted. An exhaustive analysis of the experimental optical parameters shows signs of a reflectance broad peak in Cu, Al, Au, and Mo around the wavelength predicted by the theory for p = 1.