Electromagnetic wave propagation through a slab of a dispersive medium

TL;DR

This paper introduces a method to analyze electromagnetic wave propagation through a dispersive medium slab, capturing transient and steady-state responses, including precursors and resonance effects, with implications for understanding wave behavior in complex materials.

Contribution

A novel analytical approach for electromagnetic wave propagation in dispersive media that accurately captures transient phenomena and resonance effects without branch-cut complications.

Findings

Retrieved Sommerfeld and Brillouin precursors.

Identified poles responsible for transient responses.

Analyzed effects of interface reflections on wave propagation.

Abstract

A method is proposed for the analysis of the propagation of electromagnetic waves through a homogeneous slab of a medium with Drude-Lorentz dispersion behavior, and excited by a causal sinusoidal source. An expression of the time dependent field, free from branch-cuts in the plane of complex frequencies, is established. This method provides the complete temporal response in both the steady-state and transient regimes in terms of discrete poles contributions. The Sommerfeld and Brillouin precursors are retrieved and the corresponding set of poles are identified. In addition, the contribution in the transient field of the resonance frequency in the Drude-Lorentz model is exhybited, and the effect of reflections resulting from the refractive index mismatch at the interfaces of the slab are analyzed.