  We investigate structural resonances in multi-element optical resonators and
provide a roadmap for 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.
