3: Wave Propagation in General Media

• 3.1: Poynting’s Theorem
• 3.2: Poynting Vector
• 3.3: Wave Equations for Lossy Regions
We wish to upgrade the wave equations for electromagnetic propagation in lossless and source-free media  to account for the possibility of loss. First, let’s be clear on what we mean by “loss.” Specifically, we mean the possibility of conversion of energy from the propagating wave into current, and subsequently to heat. This mechanism is described by Ohm’s law.
• 3.4: Complex Permittivity
• 3.5: Loss Tangent
• 3.6: Plane Waves in Lossy Regions
• 3.7: Wave Power in a Lossy Medium
In this section, we consider the power associated with waves propagating in materials which are potentially lossy; i.e., having conductivity σ significantly greater than zero. T
• 3.8: Decibel Scale for Power Ratio
In many disciplines within electrical engineering, it is common to evaluate the ratios of powers and power densities that differ by many orders of magnitude. These ratios could be expressed in scientific notation, but it is more common to use the logarithmic decibel (dB) scale in such applications.
• 3.9: Attenuation Rate
Attenuation rate is a convenient way to quantify loss in general media, including transmission lines, using the decibel scale.
• 3.10: Poor Conductors
A poor conductor is a material for which conductivity is low, yet sufficient to exhibit significant loss. To be clear, the loss we refer to here is the conversion of the electric field to current through Ohm’s law.
• 3.11: Good Conductors
A good conductor is a material which behaves in most respects as a perfect conductor, yet exhibits significant loss. Now, we have to be very careful: The term “loss” applied to the concept of a “conductor” means something quite different from the term “loss” applied to other types of materials. Let us take a moment to disambiguate this term.
• 3.12: Skin Depth
The electric and magnetic fields of a wave are diminished as the wave propagates through lossy media.

Thumbnail: Gaussian quantum wave packet superposition in 1D. (CC BY-SA 4.0 International; David Kirkby via Wikipedia)