# Coupled Mode Theory of Microtoroidal Resonators with a One-dimensional Waveguide

## TL;DR

This paper analyzes how light transmission through multiple microtoroidal resonators coupled to a 1D waveguide varies with the number of resonators and mutual-mode coupling, revealing exponential decay of minimum transmission and FWHM scaling.

## Contribution

It provides a theoretical framework for understanding transmission and mode-splitting in coupled microtoroidal resonators with a 1D waveguide, including effects of mutual-mode coupling.

## Key findings

- Minimum transmission vanishes exponentially with the number of resonators at small mutual-mode coupling.
- FWHM scales proportionally to the square root of the number of resonators.
- Increased resonators reduce mode-splitting at high mutual-mode coupling.

## Abstract

We study the transmission of light through a system consisting of an arbitrary number $N$ of microtoroidal resonators coupled to a one-dimensional (1D) waveguide. The transmission $T$ through such a system and its full-width at half-maximum (FWHM) are calculated for various values of $N$ and mutual-mode coupling coefficients. We found that at small mutual-mode coupling, the minimum transmission vanishes exponentially with $N$ while the FWHM is proportional to $\sqrt{N}$. At big mutual-mode coupling, as the number of resonators increases, the mode-splitting is reduced. Our findings contribute to better understanding of novel interfaces between quantum emitters and resonant photonic structures for quantum information processing.