Green's Function Analysis of Spontaneous Emission in Planar Fabry-Pérot Resonators

A dyadic Green's function formalism is used to model spontaneous emission in planar Fabry-Pérot (FP) resonators composed of multiple dielectric layers. Following the conventional approach, the electric field and dyadic Green's function are expanded in terms of in-plane waves by exploiting translational symmetry in the transverse plane, and a transfer-matrix method is employed to compute the tensor components  , , and , and corresponding to TE and TM polarization channels. The Purcell factor is obtained from the imaginary part of the Green's function at the emitter position. The analysis shows that TM modes yield a broad and moderate enhancement ~0.13-0.14 at  ( is the cavity thickness) while TE modes exhibit sharp resonant peaks due to strong coupling to high-Q cavity resonances. The method captures both confined and radiative modes without requiring explicit mode expansion and can be readily extended to include gain, dispersion, or realistic material losses. This framework provides a rigorous foundation for studying strong light-matter coupling in two-dimensional materials and facilitates future investigations of exciton-polariton formation in moiré superlattice structures, where TMDC-based quantum emitters interact with engineered photonic environments.