Electromagnetic diffusion in anisotropic media



[1] I present a plane-wave analysis of anisotropic electromagnetic media at the low-frequency range, where the displacement currents can be neglected and the field is diffusive. Anisotropy is due to the conductivity tensor and the magnetic permeability is a scalar quantity. The analysis includes the energy balance (Umov-Poynting theorem) and provides expressions of measurable quantities such as the phase and energy velocities, the attenuation factor, and the skin depth as a function of frequency and propagation direction. The balance of energy allows the identification of the stored and dissipated energy densities, which are related to the magnetic energy and the conductive part of the electric energy. For a real conductivity tensor, the stored energy equals the dissipated energy. I also establish fundamental relations, e.g., the scalar product between the slowness vector and the power-flow vector is equal to the energy density. For uniform plane waves, the phase velocity is the projection of the energy velocity vector onto the propagation direction and a similar relation is obtained by replacing the energy velocity with a velocity related to the dissipated energy. I have also obtained the Green function for an azimuthally isotropic medium (transverse isotropy), which is used to calculate transient fields.