# Strong optical coupling combines isolated scatterers into dimer

## TL;DR

This paper investigates the transition from weak to strong optical coupling between two dielectric rods, identifying the critical distance for peak splitting in spectra through multiple analytical and numerical approaches.

## Contribution

It provides a comprehensive analysis of the critical distance for strong coupling in dielectric rod dimers using spectral, near-field, and eigenfrequency methods, including analytical approximations.

## Key findings

- Critical distance correlates with the tidal energy flux region around a rod.
- Spectral peak splitting indicates the strong coupling regime.
- Analytical formulas approximate the critical distance effectively.

## Abstract

We analyze the transition between different coupling regimes of two dielectric rods, which occurs at a critical distance between them. The hallmark of strong coupling regime is the peak splitting effect observed in spectra. Here we comprehensively evaluate the critical distance as a function of the rod permittivity using a number of different approaches. The scattering spectra of the two rods in dependence on the distance demonstrate the weak to strong coupling transition. We start the analysis by introducing a region of a tidal energy flux around a single isolated rod (the region is related to the near field) and demonstrate that its effective radius corresponds to the critical distance obtained from the scattering spectra. Next, we study the eigenfrequencies of the dimer as functions of distance by 'diagonalizing' the coupled multipole matrix. In order to find an analytical formula for the critical distance, we consider the problem under several approximations, which yield similar results.