Light–matter interactions in multi-element resonators

We investigate light–matter interactions in multi-element optical resonators and provide a roadmap for the identification of structural resonances and the description of the interaction of single extended cavity modes with quantum emitters or mechanical resonators. Using a first principle approach based on the transfer matrix formalism we analyze, both numerically and analytically, the static and dynamical properties of three- and four-mirror cavities. We investigate in particular conditions under which the confinement of the field in specific subcavities allows for enhanced light–matter interactions in the context of cavity quantum electrodynamics and cavity optomechanics. (paper)