Principles of Electromagnetic Waves and Materials, 2nd Edition

2Electromagnetics of Simple Media: One-Dimensional Solution*

The mathematics needed to solve problems may be simplified if we are able to model the problem as one-dimensional. Sometimes a practical problem with the appropriate symmetries and dimensions will permit us to use one-dimensional models. A choice of the appropriate coordinate system will sometimes allow us to reduce the dimensionality of the problem. A few of such basic solutions will be listed next.

2.1Uniform Plane Waves in Sourceless Medium (ρ_V = 0, J_source = 0)

A simple lossy medium with the parameters ε_r, μ_r, and σ has the following one-dimensional (say z-coordinate) solutions in Cartesian coordinates:

(2.1)$$E_z=H_z=0,$$

(2.2)$$\mathrm{\eta }H=\widehat{z}\times E,$$

(2.3)$$E=E_{\text{t}}\left\{\begin{array}{c}\hfill {\text{e}}^{+\text{j}kz}\hfill \\ \hfill {\text{e}}^{-\text{j}kz}\hfill \end{array}\right\}.$$

In the above, the braces ...