General theory of a moving Fabry-Perot interferometer and its application to the Pound-Drever-Hall technique

In a follow-up effort to our prior report on the optical transmission of a moving Fabry-Perot interferometer \cite{Pyvovar}, this work seeks to establish a general framework that describes the transmission and reflection properties of a Fabry-Perot interferometer when key components in its operation system, including the light source, the detector and the interferometer itself, have relative motions against each other along their common optical axis. Our analysis indicates that these movements result in various new factors in the transmission and reflection coefficients, which all find their roots in the Doppler effect. As a demonstration of its potential application, the new theory is applied to the Pound-Drever-Hall frequency-locking technique. It is shown that velocity-induced frequency modulations are effectively added to the laser frequency due to the motions, and such excess frequency noise can be impactful in certain applications.