Emissvity of metallic microcontoured surfaces

In this paper, we study the diffraction of electromagnetic radiation by a periodic micro-rough surface separating vacuum from a metal with a finite conductivity. We submit the integral method to the surface impedance boundary condition. Thus the numerical implementation is greatly reduced. We compare the numerical emissivities obtained by this approach to those we have calculated through the rigorous multilayer modal method. This enables us to show that the mentioned approximate method has two regions of validity: one corresponding to fairly flat surfaces and the other to very deep surfaces. It is well known that both the Kirchhoff approximation and the constant flat boundary impedance approximation are also valid for fairly flat surfaces. Our investigation aims also to establish whether these two approximate methods lead to the same results, and whether the integral method submitted to the surface impedance condition has a larger domain of validity. Concerning deep surfaces with a period smaller than the wavelength, we introduce the homogenization process in order to study its accuracy.Finally, this work permitted to identify three different regimes depending on the surface slopes: the simple scattering regime, the homogenization regime and the intermediate regime. For the latter, if the period is in the order of the wavelength, then we will show that the emissivity can be exalted.