Plane Waves in Isotropic Media
In order to clarify the basic physical features of plane waves, it is useful to transform, according to the usual Steinmetz procedure, complex field vectors into the corresponding time-domain vectors. The more restrictive the requirements one places on the fields, the easier to prove the completeness of plane waves. A procedure which makes use of the Fourier transform automatically provides a quantitative criterion, to decide when a single plane wave is acceptable, at least as an approximation. Plane waves lend themselves to the description of how electro magnetic fields behave at a sharpe discontinuity in the parameters of the medium. The validity of the results one gets there in terms of single plane waves has to be checked with the criterion. Plane waves in unbounded isotropic media suffer from a number of very severe limitations, which make them inadequate to model some basic phenomena.