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NEOCLASSICAL THEORY OF INTERACTION 77

reflection really means refraction obeying the Snell’s law [8]. It explains the factor 1/cos
describing the critical frequency.
Depending on ionosphere conditions the relatively regular communication and broadcast
commonly take place at frequencies below 27-30 MHz (shortwave band) and slightly above in
the years of solar maximum. We put “relatively regular” because of the state of ionosphere
fluctuates extensively and consistently. Besides, the quality of communication may be messed
up by the effect of multipath fading illustrated in Figure 2.5.3 when several copies of the same
signals travel by a number of not the same paths and come to the receiver with different
magnitude and phase. The shortwave signals can be detected at the distances of thousand
kilometers from the transmitter. The first transatlantic communication of such kind occurred in
1921 and was made by radio amateurs. By 1924 many amateurs were routinely making
transoceanic contacts at distances of 6,000 miles (~9,600 km) and more. Very sophisticated so-
called over-the-horizon radar based on similar principle is able to look for the targets located
far beyond the horizon at the range of hundreds and even thousands of kilometers.
2.5.4 Broadband Complex Constant () of Dielectrics

Physically, the main difference between metals and dielectrics is that the most of the electrons
in dielectrics are bound to molecules forming dipoles and cannot move freely. However, the
string model will stay, and thus we can apply (2.79) and (2.81) to dielectrics too with properly

Figure 2.5.4 Complex dielectric constant of clear water at 20°C

corrected the numerical parameters , , 0, and . It means that the permittivity of any

dielectric more or less depends on frequency and can be considered as a constant over some
restricted frequency band only. Such frequency dependence is called dispersion and generally
defined by the dielectric chemical structure. The plot in Figure 2.5.4 illustrates the broadband
dispersion effect in clear water. It can be roughly divided into four areas.

Blue area of low dispersion. The frequencies (from 0 Hz to 2 GHz) are far lower than 1/ ( is
the dipole damping time). Here () ≫ (), () = 81, as expected, and both parameters
′
′′
′

are practically independent on frequency. Explicitly, since at all these frequencies the dipole
rotations follow the external electrical field with relatively low dissipation and delay.
The yellow area of high dispersion. At higher frequencies, the external electric field intensity
rises and declines much faster. If so, the plenty of dipoles cannot keep up with the field
variations and stay almost motionless. As a result, the orientation polarization diminishes and
the real part () of dielectric constant drops. Simultaneously the imaginary part ()
′
′′