Impact of Rough Building Material Surfaces on Reflection Coefficients from 5 GHz to 260 GHz

When an electromagnetic wave is reflected by a smooth and planar surface, its amplitude is decreased by the Fresnel reflection coefficients depending on the material permittivity, incidence angle and polarization. Recent work showed that the permittivity does not depend on the frequency from 2 to 260 GHz implying that the reflection gain is constant from 2 to 260 GHz for a given incidence angle and polarization. But Fresnel coefficients are only valid for materials with a smooth surface which is not always the case for building materials. Materials such as concrete or patterned glass may be rough or have a relief surface. This paper analyzes the reflection gain deviation from the Fresnel coefficients when material surfaces are not smooth and proposed a simplified model based on the Rayleigh-Rice or Beckmann- Kirchhoff theoretical approaches. The investigated frequencies ranged from 5 to 260 GHz.