Phase time and transmission probability in the traversal of a PT-symmetric potential: the case of an electromagnetic waveguide

TL;DR

This paper investigates the transmission and timing properties of electromagnetic waves in a PT-symmetric waveguide with gain and loss media, revealing giant amplification, spectral singularities, and unusual delay times.

Contribution

It provides a detailed analysis of transmission probabilities, spectral singularities, and transit times in PT-symmetric waveguides, highlighting novel phenomena like giant amplification and negative delay times.

Findings

Giant amplification of signals at specific wavelengths.

Vanishing transit times in opaque barriers, akin to Hartman effect.

Negative delay times indicating non-local effects.

Abstract

We study the unconventional transmission properties of a wave-packet through a PT-symmetric potential region, as describing actual electromagnetic wave propagation along a waveguide filled with gain and loss media. The non-trivial behavior of the transmission probability manifests in the giant amplification of the incident electromagnetic signal of given wavelengths for well-defined configurations, depending on the gain/loss contrast. Maximum transmission peaks are related to spectral singularities and a strict correlation exists between the "resonant" wavelengths and the gain/loss contrast. The transit times are as well calculated, showing their surprising vanishing in the opaque barrier limit, independently of the gain/loss contrast, which is reminiscent of some sort of Hartman effect. Also, non-local effects manifest in the presence of negative delay times for given configurations, while a correlation is apparent between maximum delay times and transmission probability peaks, though appreciably depending on the gain/loss contrast.