Transparency of the PT-symmetric complex potentials for coherent injection

TL;DR

This paper investigates the transparency phenomenon in PT-symmetric complex potentials, demonstrating analytically and numerically that perfect wave emission can occur across different symmetry-breaking regimes.

Contribution

It provides an analytical demonstration that PT-symmetric potentials can exhibit transparency regardless of symmetry-breaking status, supported by numerical evidence.

Findings

Transparency occurs for all energies in PT-symmetric potentials.

Analytical proof using the Scarf II potential.

Numerical support from other potentials.

Abstract

Two port s-matrix for a complex PT-symmetric potential may have uni-modular eigenvalues. If this happens for all energies, there occurs a perfect emission of waves at both ends. We call this phenomenon transparency which is distinctly different from coherent perfect absorption with or without lasing. Using the versatile PT-symmetric complex Scarf II (scattering) potential, we demonstrate analytically that the transparency can occur regardless of whether PT-symmetry is unbroken or broken or if there are only scattering states. In these three cases, for a given value of the strength of the real part; the strength of the imaginary part $|V_2|$ of the potential lies in $(0, V_{\alpha}), (V_{\alpha}, V_{\beta})$ and $(0,V_{\beta})$ respectively. Several other numerically solved potentials also support our findings.