Overcoming the bottleneck for quantum computations of complex nanophotonic structures: Purcell and Förster resonant energy transfer calculations using a rigorous mode-hybridization method

A calculation of the photonic Green's tensor of a structure is at the heart of many photonic problems, but for nontrivial nanostructures, it is typically a prohibitively time-consuming task. Recently, a general normal-mode expansion (GENOME) was implemented to construct the Green's tensor from eigenpermittivity modes. Here, we employ GENOME to study the response of a cluster of nanoparticles. To this end, we use the rigorous mode-hybridization theory derived earlier by D. J. Bergman [Phys. Rev. B 19, 2359 (1979)], which constructs the Green's tensor of a cluster of nanoparticles from the sole knowledge of the modes of the isolated constituent. The method is applied to a scatterer with a nontrivial shape (namely, a pair of elliptical wires) within a fully electrodynamic setting and for the computation of the Purcell enhancement and F\"orster resonant energy transfer rate enhancement, showing good agreement with direct simulations. The procedure is general, is trivial to implement using standard electromagnetic software, and holds for arbitrary shapes and number of scatterers forming the cluster. Moreover, it is orders of magnitude faster than conventional direct simulations for applications requiring the spatial variation of the Green's tensor, promising wide use in quantum technologies, free-electron light sources, and heat transfer, among others.