Thermodynamic Consideration of Electromagnetic Cavity Resonators

If a cavity resonator has a "simple shape" and is filled with a homogeneous, isotropic medium, to calculate its resonant frequencies and mode functions is a straightforward task in principle. However, it is sometimes of interest to determine the oscillatory properties of a cavity that differs by a small amount in one or more of its physical characteristics from a cavity the oscillatory properties of which are known. For example, the calculation of resonant frequency shift accompanying the introduction a small foreign body into the cavity's volume is necessary in certain measurement techniques.