Table of Contents:
The microscopic equations of motion for THz light interacting with an electron hole plasma are presented. This system is presumed to be incoherent and an analogy is made between the holes of the plasma and the fixed positive ions at the heterojunction of a 2DEG system. An analytic solution to the system response leads to the correct Lindhard type of response for three dimensional electron gases interacting with a transverse THz field. This analysis also gives the %experimentally observed response for one- and two- dimensions, which is not predicted by longitudinal plasma frequencies. This transverse response is compared with a longitudinal dielectric function which is often found in literature concerning the interaction of THz light with 2DEGs. A comparison is made between the behaviour of the transversal response with electron density and the behaviour of a longitudinal plasmon response with density. A fully dynamic response is also computed, to examine the temporal evolution of the ``transverse plasmon'' response. This work clearly illustrates when and why a longitudinal plasmon approach does not reproduce experimental results concerning THz spectroscopy of electron gases, a source of sizeable current interest in both physics and nanotechnology communities.