Analytical solutions to zeroth-order dispersion relations of a cylindrical metallic nanowire

TL;DR

This paper derives analytical solutions for the dispersion relations of cylindrical metallic nanowires near the Surface Plasmon frequency, explaining back bending due to Ohmic loss and proposing its use in measuring metallic losses.

Contribution

It provides approximate analytical solutions for the complex dispersion relations of metallic nanowires, clarifying the origin of back bending and suggesting a new measurement method for Ohmic loss.

Findings

Analytical solutions valid near Surface Plasmon frequency

Back bending explained by Ohmic loss

Back bending point useful for loss measurement

Abstract

Zeroth-order complex dispersion relations of a cylindrical metallic nanowire have been solved out analytically with approximate methods. The analytical solutions are valid for the sections of the dispersion relations whose frequencies are close to the Surface Plasmon frequency. The back bending of the Surface Plasmon-Polaritons(SPPs) can be well described by the analytical solutions, confirming that the back bending is originated from the metal Ohmic loss. The utility of the back bending point in the dispersion relation for the measurement of the metallic Ohimc loss has also been suggested.