Why does the complex dielectric coefficient imply absorption? The answer goes back to Maxwell’s equations, and the solution for propagating waves. Two elements of the solution are claimed here:
1) For a plane wave, the electromagnetic field propagates according to the form
Such waves propagate at a velocity
2) The velocity is
in vacuum.
Hence,
where we make use of the fact that the permeability
is generally equal to the vacuum value. Here
is the relative dielectric coefficient (not just the real component).
Note that if
is complex,
then so is the velocity, since it depends on the square root of
This raises a problem of interpretation, since it is not really meaningful for the wave velocity to be complex. Still, we can persist by returning to the definition of v, as the ratio of w and k. One of the two, at least, must be complex. For radar purposes, it is best to take the frequency as real—making k complex. This has the following effect on our equation above:
Our traveling wave is now multiplied by an exponentially decreasing term, which is just the absorption of the radar energy by water, or another absorbing element.
