Interplay between Fano resonance and $\mathcal{PT} $ symmetry in non-Hermitian discrete systems

TL;DR

This paper investigates how PT-symmetric complex potentials influence transport properties and Fano resonances in non-Hermitian discrete systems, revealing phenomena like perfect transmission and reflection changes, with potential applications in optical waveguides.

Contribution

It provides an analytical study of the interplay between Fano resonance and PT symmetry in non-Hermitian systems, highlighting effects on transport properties.

Findings

PT-symmetric imaginary potentials induce perfect transmission and reflection changes.

Rich behaviors observed at resonant frequencies due to PT symmetry.

Potential realization in optical waveguide experiments.

Abstract

We study the effect of PT-symmetric complex potentials on the transport properties of non-Hermitian systems, which consist of an infinite linear chain and two side-coupled defect points with PT-symmetric complex on-site potentials. By analytically solving the scattering problem of two typical models, which display standard Fano resonances in the absence of non-Hermitian terms, we find that the PT-symmetric imaginary potentials can lead to some pronounced effects on transport properties of our systems, including changes from the perfect reflection to perfect transmission, and rich behaviors for the absence or existence of the prefect reflection at one and two resonant frequencies. Our study can help us to understand the interplay between the Fano resonance and PT symmetry in non-Hermitian discrete systems, which may be realizable in optical waveguide experiments.