Wave emission and absorption at spectral singularities

TL;DR

This paper investigates the dynamics of spectral singularities in a coupled resonator array, demonstrating wave emission with gain and absorption with loss, and exploring the coalescence of these states in PT-symmetric systems at exceptional points.

Contribution

It introduces a detailed analysis of spectral singularities in coupled resonator systems, highlighting their behavior as wave emitters and absorbers, and examines their coalescence in PT-symmetric configurations.

Findings

Gain resonator acts as a wave emitter at spectral singularities.

Lossy resonator functions as a wave absorber at spectral singularities.

PT-symmetric system exhibits exceptional point behavior with a 2x2 Jordan block.

Abstract

We studied the critical dynamics of spectral singularities. The system investigated is a coupled resonator array with a side-coupled loss (gain) resonator. For a gain resonator, the system acts as a wave emitter at spectral singularities. The reflection probability increased linearly over time. The rate of increase is proportional to the width of the incident wave packet, which served as the spectral singularity observer in the experiment. For a lossy resonator, the system acts as a wave absorber. The emission and absorption states at spectral singularities coalesce in a finite parity-time (PT ) symmetric system that combined by the gain and loss structures cut from corrresponding scattering systems at spectral singularities; in this case, the PT -symmetric system is at an exceptional point with a 2 * 2 Jordan block. The dynamics of the PT -symmetric system exhibit the characteristic of exceptional points and spectral singularities.