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Our understanding of emission from a collection of emitters stronglyinteracting among them and also with other polarizable matter in proximity hasbeen approximated by independent emission from the emitters. This is primarilydue to our inability to evaluate the self-energy matrices and the collectiveeigenstates of emitters in heterogeneous ensembles. A method to evaluate theself-energy matrices that is not limited by the geometry and the materialcomposition is presented here to understand and exploit such collectiveexcitations. Numerical evaluations using this method are used to highlight thesignificant differences between independent and the collective modes ofemission in heterostructures. A set of n emitters driving each other and mother polarizable entities, where N=m+n, is used to represent the coupledsystem of a generalized geometry in a volume integral approach. Closed formrelations between the Green tensors of entity pairs in free space and theircorrespondents in a heterostructure are derived concisely. This is madepossible for general geometries because the global matrices consisting of allfree-space Green dyads are subject to conservation laws. The self-energy matrixof the emitters can then be assembled using the evaluated Green tensors of theheterostructure, but a decomposition of its components into their radiative andnon-radiative decay contributions is non-trivial. This is accomplished usingmatrix decomposition identities applied to the global matrices containing allfree-space dyads. The relations to compute the observables of the eigenstates(such as quantum efficiency, power/energy of emission, radiative andnon-radiative decay rates) are presented. We conclude with a note on extensionof this method to collective excitations that also include strong interactionswith a surface in the near-field.

Collective eigenstates of emission in an N-entity heterostructure and the evaluation of its Green tensors and self-energy components