Time for pulse traversal through slabs of dispersive and negative ($\epsilon$, $\mu$) materials

TL;DR

This paper investigates electromagnetic pulse traversal times through dispersive, dissipative slabs with negative permittivity and permeability, revealing effects of bandwidth, dissipation, and resonances on delay times, including negative and superluminal phenomena.

Contribution

It provides a detailed analysis of traversal and delay times in negative $ extit{( ext{epsilon}, ext{mu})}$ materials, considering dissipation, bandwidth, and mode coupling, with new insights into superluminal and resonant effects.

Findings

Large dissipation can cause negative traversal times near resonances.

Bandwidth broadening ensures positive, subluminal traversal times.

Coupling to plasmon polariton modes results in large delay times.

Abstract

The traversal times for an electromagnetic pulse traversing a slab of dispersive and dissipative material with negative dielectric permittivity ($\epsilon$) and magnetic permeability ($\mu$) have been calculated by using the average flow of electromagnetic energy in the medium. The effects of bandwidth of the pulse and dissipation in the medium have been investigated. While both large bandwidth and large dissipation have similar effects in smoothening out the resonant features that appear due to Fabry-P\'{e}rot resonances, large dissipation can result in very small or even negative traversal times near the resonant frequencies. We have also investigated the traversal times and Wigner delay times for obliquely incident pulses and evanescent pulses. The coupling to slab plasmon polariton modes in frequency ranges with negative $\epsilon$ or $\mu$ is shown to result in large traversal times at the resonant conditions. We also find that the group velocity mainly contributes to the delay times for pulse propagating across a slab with n=-1. We have checked that the traversal times are positive and subluminal for pulses with sufficiently large bandwidths.