  We develop a microscopic theory for the multimode polariton dispersion in
materials coupled to cavity radiation modes. Starting from a microscopic
light-matter Hamiltonian, we devise a general strategy for obtaining simple
matrix models of polariton dispersion curves based on the structure and spatial
location of multi-layered 2D materials inside the optical cavity. Our theory
exposes the connections between seemingly distinct models that have been
employed in the literature and resolves an ambiguity that has arisen concerning
the experimental description of the polaritonic band structure. We demonstrate
the applicability of our theoretical formalism by fabricating various
geometries of multi-layered perovskite materials coupled to cavities and
demonstrating that our theoretical predictions agree with the experimental
results presented here.
