Jamming anomaly in $\mathcal{PT}$-symmetric systems

TL;DR

This paper investigates the jamming anomaly in $ ext{PT}$-symmetric optical systems, revealing how energy flux behaves unexpectedly at higher gain-loss amplitudes and its relation to spectral phenomena like exceptional points.

Contribution

It identifies and explains the jamming anomaly in $ ext{PT}$-symmetric systems, linking it to spectral transitions such as exceptional points and eigenvalue immersion.

Findings

Energy flux initially increases with gain-loss amplitude

At larger amplitudes, flux decreases despite increasing amplitude

Jamming anomaly signals spectral transitions like exceptional points

Abstract

The Schr\"odinger equation with a $\mathcal{PT}$-symmetric potential is used to model an optical structure consisting of an element with gain coupled to an element with loss. At low gain-loss amplitudes $\gamma$, raising the amplitude results in the energy flux from the active to the leaky element being boosted. We study the anomalous behaviour occurring for larger $\gamma$, where the increase of the amplitude produces a drop of the flux across the gain-loss interface. We show that this jamming anomaly is either a precursor of the exceptional point, where two real eigenvalues coalesce and acquire imaginary parts, or precedes the eigenvalue's immersion in the continuous spectrum.