Calculation of propagation constants in particulate matter is an important aspect of wave
propagation analysis in engineering disciplines such as satellite comnlunication, geophysical
exploration, radio astronomy and material science. It is important to understand why different
propagation constants produced by different theories are not applicable to a particular problem.
Homogenization of the random media using effective medium theories yields the effective
propagation constants by effacing the particulate, microscopic nature of the medium. The
Maxwell-Gamet and Bruggeman effective medium theories are widely used but their limitations
are not always well understood.
In this thesis, some of the more complex homogenization theories will only be partially
derived or heuristically constructed in order to avoid unnecessary mathematical complexity
which does not yield additional physical insight. The intent of this thesis is to elucidate the
nature of effective medium theories, discuss the theories' approximations and gain a better
global understanding of wave propagation equations. The focus will be on the Maxwell-Garnet
and Bruggeman theories because they yield simple relationships and therefore serve as anchors
in a sea of myriad approximations.
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