General discussion - wykład

General discussion We look for plane wave solutions of the form e−γ·r, in which γ is the complex vector
γ = α + jβ (9.4)
It will be recalled from the previous discussion that there exist planes of constant
amplitude (⊥ α) and planes of constant phase (⊥ β). It may be shown that in the
lossless medium case (i.e. when σ = 0) that α · β = 0. Thus in a lossless medium either
there is no attenuation or the attenuation is at right angles to the propagation. A proof
of this result appears in Reference 2.
We did not have occasion to discuss any such waves in the lossless case but would have
encountered them if we looked carefully at the waves in medium 2 when total internal
reflection of electromagnetic energy obliquely incident on a dielectric interface occurs in
medium 1.
In the case which we pursue here of a lossy medium, there is no need for α and β to
be at right angles; in general they can be at some other angle.
In many important cases, however, α and β happen to be parallel and we look now
for solutions of that type. Thus we will look for waves whose direction of propagation and
direction of attenuation are the same.
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