Dispersion Relation of a Surface Wave at a Rough Metal-Air Interface

TL;DR

This paper derives a new dispersion relation for surface waves at a rough metal-air interface, accounting for surface impedance due to finite conductivity and roughness, addressing discrepancies in terahertz wave propagation data.

Contribution

It introduces a dispersion relation considering both roughness and finite conductivity, improving understanding of surface wave behavior at metal-air interfaces.

Findings

Reconciles experimental data with theoretical models in the terahertz range

Shows the significance of combined impedance effects on surface wave propagation

Provides a new framework for analyzing surface waves on rough metals

Abstract

We derived a dispersion relation of a surface wave at a rough metal-air interface. In contrast to previous publications, we assumed that an intrinsic surface impedance due to a finite electric conductivity of the metal can be of the same order as the roughness-induced impedance. We then applied our results to the analysis of a long-standing problem of the discrepancy between the experimental data on the propagation of surface waves in the terahertz range of frequencies and the classical Drude theory.