Effective Mode Description for Macroscopic Fabry P\'{e}rot Cavities

Abstract

We introduce an effective modes formalism to describe how the quasi-continuum of photonic modes in an optical cavity effectively behaves in the strong light-matter coupling regime of cavity quantum electrodynamics. By expressing these effective modes, we are able to show that the mode volumes of these effective modes are independent of the physical area of the Fabry-P\'erot cavity mirrors. Further, our theoretical framework shows that the photonic density of state for a Fabry-P\'erot exhibits a sharp peak at the normal incidence and is quality factor dependent. These results provide a possible explanation for the recently discovered experimental phenomenon in vibrational polaritons, where chemical reactivities can only be modified if the molecules are coupled in resonance to the normal-incidence mode in a Fabry-P\'erot cavity.