Overcoming the bottleneck for quantum computations of complex nanophotonic structures: Purcell and FRET calculations using a rigorous mode hybridization method

TL;DR

This paper introduces a fast, general method for calculating the Green's tensor in complex nanophotonic structures, enabling efficient analysis of Purcell and FRET effects in arbitrarily shaped nanoparticle clusters.

Contribution

It applies a rigorous mode hybridization theory combined with GENOME to efficiently compute Green's tensors for complex nanostructures, including non-trivial shapes, with high accuracy and speed.

Findings

Method accurately predicts Purcell enhancement.

Method accurately predicts FRET rate enhancement.

Significantly faster than direct simulation methods.

Abstract

A calculation of the photonic Green's tensor of a structure is at the heart of many photonic problems, but for non-trivial 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 the 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, for the first time, to a scatterer with a non-trivial shape (namely, a pair of elliptical wires) within a fully electrodynamic setting, and for the computation of the Purcell enhancement and F\"{o}rster Resonant Energy Transfer (FRET) rate enhancement, showing a good agreement with direct simulations. The procedure is general, 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 a wide use in quantum technologies, free-electron light sources and heat transfer, among others.