Radiative Properties of Gold Surfaces with One-Dimensional Microscale Gaussian Random Roughness

The radiative properties of engineering surfaces with microscale surface textures depend on the incident wavelength, optical properties, and temperature as well as the topography of the reflective surface. In the case of slightly rough surfaces, the traditional Kirchhoff theory on rough surface scattering may be applicable. In this study, a direct numerical solution of Maxwell’s equations was developed to understand scattering from weakly to very rough surfaces. The method is the finite-difference time-domain method. The problem of interest is a set of gold surfaces with Gaussian random roughness distributions. Highly accurate experimental data are available from the earlier work of Knotts and O’Donnell in 1994. Due to the negative real component of the complex dielectric constant at the infrared light source wavelengths of 1.152 and 3.392 μm, the convoluted integral was used to convert the frequency domain electrical properties to time-domain properties in order to obtain convergent solutions. The bi-directional reflectances for both normal and parallel polarizations were obtained and compared with experimental data. The predicted values and experimental results are in good agreement. The highly specular peak in the reflectivity was reproduced in the numerical simulations, and the increase of the parallel polarization bi-directional reflectance was found to be due to the effect of a variation in the optical constant from 1.152 to 3.392 μm.