A new method to find full complex roots of a complex dispersion equation for light propagation

TL;DR

This paper introduces a novel numerical approach for accurately finding all complex roots of dispersion equations, demonstrated on metallic nanowires to analyze light propagation and plasmonic modes.

Contribution

The paper presents a new numerical method capable of efficiently computing all complex roots of dispersion equations, including analytical verification, for advanced photonic applications.

Findings

Successfully computes complex dispersion curves of SPPs and bulk modes.

Provides an approximate analytical solution for validation.

Enables comprehensive analysis of light propagation in nanostructures.

Abstract

A new numerical method is presented to find full complex roots of a complex dispersion equation. For the application of the solution, the complex dispersion equation of a cylindrical metallic nanowire is investigated. By using this method, locus of Brewster angle, complex dispersion curves of Surface Plasmon Polaritons (SPPs) and complex bulk modes can be obtained in once calculation. Approximate analytical solution to the complex dispersion equation has also been derived to verify our method.