Frequency spectra of transient electromagnetic pulses in a conducting medium

The energy density spectra of transient electromagnetic fields generated by a pulsed ideal dipole source in an infinite conducting medium have been investigated for various distances from the source. A characteristic frequency
\omega_{c}
, corresponding either to the peak of the spectrum or to its haft-width, is defined and shown to vary inversely as the square of distance at large distances. The behavior of
\omega_{c}
with distance is a measure of the behavior of the pulse energy. Thus, at large distances it appears that the attenuation factor associated with
\omega_{c}, \exp \{-r\sqrt{\omega_{c}\mu\sigma/2}\}
, is independent of
r
, due to the constancy of the product
r\sqrt{\omega_{c}}
. From this point of view, the transient fields do not decrease exponentially as
r
, but as inverse powers of
r
. This should not be construed as meaning that the transient possesses an advantage over CW. The attenuation for monochromatic components of the pulse is the same as for continuous waves of the same frequency and at large distances the energy put into the high frequency components is wasted. The phenomenon is illustrated by calculations that have been carried out for the case of pulses in sea water.