Optical surface waves over metallo-dielectric nanostructures: Sommerfeld integrals revisited

TL;DR

This paper provides an exact asymptotic solution for the diffraction of a dipole over a metallo-dielectric interface, clarifying the behavior of surface waves including surface plasmon polaritons and radiative waves.

Contribution

It revisits Sommerfeld integrals to derive a closed-form solution for surface wave diffraction over complex interfaces, enhancing understanding of near- and far-field behaviors.

Findings

Analytic expressions accurately describe surface wave components.

Validation confirms the model's agreement with experimental data.

The solution covers the entire propagation range from near to asymptotic.

Abstract

The asymptotic closed-form solution to the fundamental diffraction problem of a linear horizontal Hertzian dipole radiating over the metallo-dielectric interface is provided. For observation points just above the interface, we confirm that the total surface near-field is the sum of two components: a long-range surface plasmon polariton and a short-range radiative cylindrical wave. The relative phases, amplitudes and damping functions of each component are quantitatively elucidated through simple analytic expressions for the entire range of propagation: near and asymptotic. Validation of the analytic solution is performed by comparing the predictions of a dipolar model with recently published data