# Modal Approach to the Theory of Energy Transfer Mediated by a Metallic Nanosphere

## TL;DR

This paper presents a modal approach to analytically calculate the enhancement of energy transfer mediated by a metallic nanosphere, providing insights into the system's response for various molecular orientations.

## Contribution

It introduces a straightforward modal method for calculating energy transfer enhancement around a nanosphere using spectral properties of the electrostatic operator.

## Key findings

- Analytical expressions for the Green's function are derived.
- The method accommodates any molecular orientation.
- Numerical results illustrate the enhancement effects.

## Abstract

Theoretically, the presence of a metallic nanoparticle enhances the intermolecular energy transfer. We calculate this enhancement factor with a modal approach pertaining analytical results in the case of a nanosphere. We calculate the Green's function of the system relaying on the spectral properties of the electrostatic operator, fully known for spherical geometry. In contrast to other treatments, the present calculations are straightforward for any molecular orientation giving modal information about the response of the system. Numerical calculations and further discussions are also provided.