# Wave propagation in randomly perturbed weakly coupled waveguides

## TL;DR

This paper analyzes how random interface perturbations in coupled waveguides cause power leakage and blurring of power transfer, with implications for waveguide design and signal integrity.

## Contribution

It provides a detailed mode amplitude analysis quantifying power transfer and leakage effects due to interface randomness in coupled waveguides.

## Key findings

- Random interface fluctuations cause significant power leakage at large distances.
- Power transfer becomes blurred and eventually reaches equipartition due to scattering.
- The analysis quantifies the impact of small interface perturbations on waveguide performance.

## Abstract

We present an analysis of wave propagation in a two step-index, parallel waveguide system. The goal is to quantify the effect of scattering at randomly perturbed interfaces between the guiding layers of high index of refraction and the host medium. The analysis is based on the expansion of the solution of the wave equation in a complete set of guided, radiation and evanescent modes with amplitudes that are random fields, due to scattering. We obtain a detailed characterization of these amplitudes and thus quantify the transfer of power between the two waveguides in terms of their separation distance. The results show that, no matter how small the fluctuations of the interfaces are, they have significant effect at sufficiently large distance of propagation, which manifests in two ways: The first effect is well known and consists of power leakage from the guided modes to the radiation ones. The second effect consists of blurring of the periodic transfer of power between the waveguides and the eventual equipartition of power. Its quantification is the main practical result of the paper.