  We experimentally and theoretically investigate the microwave transmission
line shape of the cavity-magnon-polariton (CMP) created by inserting a low
damping magnetic insulator into a high quality 3D microwave cavity. While fixed
field measurements are found to have the expected Lorentzian characteristic, at
fixed frequencies the field swept line shape is in general asymmetric. Such
fixed frequency measurements demonstrate that microwave transmission can be
used to access magnetic characteristics of the CMP, such as the field line
width $\Delta H$. By developing an effective oscillator model of the microwave
transmission we show that these line shape features are general characteristics
of harmonic coupling. At the same time, at the classical level the underlying
physical mechanism of the CMP is electrodynamic phase correlation and a second
model based on this principle also accurately reproduces the experimental line
shape features. In order to understand the microscopic origin of the effective
coupled oscillator model and to allow for future studies of CMP phenomena to
extend into the quantum regime, we develop a third, microscopic description,
based on a Green's function formalism. Using this method we calculate the
transmission spectra and find good agreement with the experimental results.
