  New high-gradient accelerating RF cavities are nowadays developed in several
national laboratories for high-energy physics applications. Ultra high
gradients, up to the order of GV/m, can be achieved by using ultra compact
accelerating structures in the sub-THz regime. Nevertheless, the experimental
setup for measuring the main RF parameters for such compact structures is not
trivial and can easily produce errors due to lack of accuracy. Moreover,
Radio-Frequency (RF) simulations for these types of cavities can require a
large amount of computational time. In particular, one of the main RF
parameters that needs to be evaluated and measured for the accelerating
structures is the reflection coefficient. In order to obtain a fast and
accurate analytical estimation, we have developed the electromagnetic theory
for the calculation of the coupling of a resonant cavity with an RF waveguide.
This theory is based on the Bethe's small aperture polarization approach, also
developed by Collin's. In this paper, we give an exact analytical expression of
the reflection coefficient as function of the physics parameters of the
cavity-waveguide system, which can be applied to any geometry, material and
frequency.
