where is the refractive index. Any divergence of the polarization field is associated with a bound charge density
whereas any time variation generates a polarization current whose density is
Consider an electromagnetic wave propagating through a quasi-neutral, linear, dielectric medium. Assuming a common time variation of the wave fields, demonstrate from Maxwell's equations that
and , and .
Show that the WKB solutions take the form
and , and .
Show that the WKB solutions take the form
where .
or, equivalently,
(Hint: This is a form of Abel inversion. See Budden 1985.)
where , , and are positive constants, then for , and
for . Here, is a Gamma function (Abramowitz and Stegun 1965a).
from the transmitter. Demonstrate that if then for some values of the previous equation is satisfied by three different values of . In other words, wave packets can travel from the transmitter to the receiver via one of three different paths. Show that the critical case corresponds to and .