# Complex-k modes of plasmonic chain waveguides

## TL;DR

This paper investigates complex-k modes in plasmonic chain waveguides using a 3D finite-element solver, comparing materials like gold and silver, and exploring hybrid systems, to understand propagation characteristics and optimize waveguide performance.

## Contribution

It introduces a versatile numerical method to analyze complex modes in plasmonic chains, compares different materials, and examines hybrid configurations for improved waveguiding.

## Key findings

- Gold and silver chain waveguides have distinct propagation losses.
- Hybrid gold-silver chains show complex energy transfer behaviors.
- Reducing propagation loss involves geometry and material optimization.

## Abstract

Nanoparticle chain waveguide based on negative-epsilon material is investigated through a generic 3D finite-element Bloch-mode solver which derives complex propagation constant ($k$). Our study starts from waveguides made of non-dispersive material, which not only singles out "waveguide dispersion" but also motivates search of new materials to achieve guidance at unconventional wavelengths. Performances of gold or silver chain waveguides are then evaluated; a concise comparison of these two types of chain waveguides has been previously missing. Beyond these singly-plasmonic chain waveguides, we examine a hetero-plasmonic chain system with interlacing gold and silver particles, inspired by a recent proposal; the claimed enhanced energy transfer between gold particles appears to be a one-sided view of its hybridized waveguiding behavior --- energy transfer between silver particles worsens. Enabled by the versatile numerical method, we also discuss effects of inter-particle spacing, background medium, and presence of a substrate. Our extensive analyses show that the general route for reducing propagation loss of e.g. a gold chain waveguide is to lower chain-mode frequency with a proper geometry (e.g. smaller particle spacing) and background material setting (e.g. high-permittivity background or even foreign nanoparticles). In addition, the possibility of building mid-infrared chain waveguides using doped silicon is commented based on numerical simulation.