Fundamentals of Electromagnetics - RF/Microwave Interaction with Biological Tissues - page 41

this case, the magnitude of D W cannot be determined, and spectroscopy is
impossible.
Neighboring oscillators interchange energy by collisions. Lorentz deduced
a theory of line broadening which is a good approximation for the case that
neither the resonance frequency nor the field frequency is very small and that
line broadening is not too great, which covers most typical spectra [20]. His
results can be closely approximated by introducing a damping term in the
equation of the oscillator which yields the very simple solution of a second-
order differential equation with a damping term, the simplest formal descrip-
tion of resonance absorption. The behavior of the complex dielectric constant
as a function of frequency is quite different for resonance and relaxation, as
may be seen from Figures 1.1 and 1.2.
The absorption spectra of crystalline solids are at short wavelengths due to
electronic transitions within atoms or molecules and at longer wavelengths
due to vibrations of the crystal as a whole [5]. The lattice vibrations are either
optical or acoustic. Together they constitute the thermal vibrations whereby
the atoms and ions, for example, within the crystal achieve thermal equilib-
rium. The acoustic vibrations do not involve a change of the polarization and
do not interact with EM fields. The optical vibrations correspond to oscilla-
tory displacements of charges.
The most important optical vibration in a simple ionic crystal such as KCl
may be visualized as a movement of K and Cl ions in opposition to each other,
as in the case of a dipole whose length is oscillating. The frequency of this
vibration in the alkali halides is of the order of 10 THz, in the IR spectrum.
Investigating the broadening of the IR spectra of crystalline solids is a diffi-
cult subject, although first-order approximations can be obtained rather easily.
The transition from resonant to nonresonant absorption, that is, relaxation,
has been studied in gases by increasing damping, hence line broadening.
It has also been approached for solids. When the resonant frequency
decreases, however, optical measurements become increasingly difficult and
very complex techniques have to be used. For a wavelength of about 1 mm,
which corresponds to 300 GHz in a vacuum, the optical techniques of the
far-IR overlap with microwave techniques.

1.6.3 Cole-Cole Display

The data provided by dielectric measurements can be presented in different
ways. One classical representation is in plotting the real and imaginary parts
of the permittivity as functions of frequency, most frequently as functions of
log 10 w. The disadvantage, however, is that these two plots are then presented
independently of each other while their frequency behaviors are linked
through the general theoretical considerations. These were developed in
Section 1.3.1 where it was shown that each part can be calculated from the
variation of the other part over the whole frequency range, as indicated by the
Kramer and Kronig equation (1.12) [6].