Thermal microwave emission from an inhomogeneous half-space

Abstract

The phenomena of thermal electromagnetic radiation sources, electromagnetic propagation in both one and two dimensionally inhomogeneous media, and surface roughness effects on electromagnetic transmission have been analyzed and mathematically modeled. These analyses have been aimed toward aiding in microwave radiometery research, but the results are very general and should be useful to other applications in electromagnetic propagation. The thermal electromagnetic radiation described by Planck's radiation law and by the fluctuation dissipation theory have been analyzed and compared to each other. It has been shown that the fluctuation dissipation theory is apparently the correct model for general applications in inhomogeneous media. It has been shown that the thermal radiation source can be modeled as a sum of plane waves. Solutions have then been found for electromagnetic wave propagation in both one and two dimensionally inhomogeneous media with surface boundaries. These solutions are derived directly from Maxwell's equations in the form of power series. The propagation solutions are first derived for smooth surfaces and then for rough surfaces. A random small scale surface roughness model is developed which is applicable to surfaces with horizontal variations much less than a wavelength. Then a general two dimensional surface roughness model is developed. The solutions exhibit expected characteristics and appear to be useful for physical applications.