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General discussion

We look for piane wave Solutions of the form e-y-r, in which y is the complex vector y = a + jp (9.4)

It will be recalled from the previous discussion that there exist planes of constant amplitudę (la) and planes of constant phase (lp). It may be shown that in the lossless medium case (i.e. when o = 0) that a • p = 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 a and p to be at right angles; in generał they can be at some other angle.

In many important cases, however, a and p 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.