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

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, 2359Rev. B 19, (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 Förster Resonant Energy Transfer (FRET) rate enhancement, 1 arXiv:1912.05415v1 [physics.comp-ph] 11 Dec 2019showing 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.

Strong multipolar transition enhancement with graphene nanoislands

“…For future exploration, GENOME also allows the determination of the Green's function for more complex structures, such as a scatterer on a substrate, 29 non-uniform scatterers, 46 cluster of scatterers and finite periodic structures. 38 For experimental observation the investigation of these designs is important for the coupling of produced photons to the far-field. As an example, combining the near-field results (e.g.…”

“…However, more complex structures need to be evaluated numerically, with high computational cost. 38 Equation 5 is also resource demanding since the integration is performed over 6 dimensions (r and r ′ ). In order to resolve these two issues, we resort to GENOME, 29 with the advantage that one modal computation allows the knowledge of the complete spatial Green's function.…”

“…This formulation suits well the determination of spontaneous emission rates since the emission frequency is determined by the emitter. The modes E m (r) of the scatterer are solved with a commercial finite-element based software (COMSOL Multiphysics) 38 and the Green's function becomes…”

An efficient solver for the generalized normal modes of non-uniform open optical resonators

“…Similar procedures also exist for the hypbridization of modes of individual resonators to obtain modes of clusters. 29,33 The target modes are expanded into the modes of a simpler open resonator. We formulate this re-expansion method to be able to obtain the modes of any finite resonator, but in this paper we shall apply it only to resonators with smoothly varying permittivity profiles where no new discontinuities are introduced.…”

“…32 For modes of a general geometry we adapted the eigenfrequency solvers of COMSOL, a FEM-based software package, to produce eigenpermittivity modes. 24,33 Despite the rapid implementation and ease of use, the COMSOL implementation nevertheless suffered from many of the aforementioned issues.…”