Traversal of pulses through negative ($\varepsilon$, $\mu$) materials

TL;DR

This paper investigates electromagnetic pulse traversal times through negative $oldsymbol{ extit{ extbf{(ε, μ)}}}$ media, revealing effects like negative delay times, the Hartman effect, and the influence of dissipation and resonances on pulse delay.

Contribution

It provides a detailed analysis of pulse traversal times in dispersive negative index media, including effects of dissipation, resonances, and oblique incidence, with new insights into negative and superluminal delays.

Findings

Negative total delay times for evanescent waves in infinite media.

Reshaping delay dominates total delay in negative refractive index media.

Large dissipation can cause very small or negative traversal times near resonances.

Abstract

We study the traversal times of electromagnetic pulses across dispersive media with negative dielectric permittivity ($\varepsilon$) and magnetic permeability ($\mu$) parameters. First we investigate the transport of optical pulses through an electrical plasma and a negative refractive index medium (NRM) of infinite and semi-infinite extents where no resonant effects come into play. The total delay time of the pulse constitutes of the group delay time and the reshaping delay time as analyzed by Peatross et al \cite{peatross}. For evanescent waves, even with broadband width, the total delay time is negative for an infinite medium whereas it is positive for the semi-infinite case. Evidence of the Hartman effect is seen for small propagation distance compared to the free space pulse length. The reshaping delay mostly dominates the total delay time in NRM whereas it vanishes when $\varepsilon(\omega)=\mu(\omega)$. Next we present results on the propagation times through a dispersive slab. 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 investigate the traversal and the Wigner delay times for obliquely incident pulses. The coupling of evanescent waves to slab plasmon polariton modes results in large traversal times at the resonant conditions. We also find that the group velocity mainly contributes to the delay time for pulse propagating across a slab with refractive index (n) = -1. The traversal times are positive and subluminal for pulses with sufficiently large bandwidths.