Spectral singularity and deep multiple minima in the reflectivity in non-Hermitian (complex) Ginocchio potential

TL;DR

This paper investigates the spectral singularities and reflectivity minima in the non-Hermitian Ginocchio potential, revealing conditions for spectral singularities and the transformation of reflectionless points into deep minima.

Contribution

It demonstrates the existence of at most one spectral singularity and deep reflectivity minima in the complex Ginocchio potential, highlighting the effects of non-Hermiticity on optical properties.

Findings

Existence of at most one spectral singularity in the potential.

Deep multiple minima in reflectivity occur when the potential is non-Hermitian.

Co-existence of spectral singularity with deep reflectivity minima.

Abstract

We bring out the existence of at most one spectral singularity (SS) and deep multiple minima in the reflectivity of the non-Hermitian (complex) Ginocchio potential. We find a parameter dependent single spectral singularity in this potential provided the imaginary part is emissive (not absorptive). The reflectionlessness of the real Hermitian Ginocchio's potential at discrete positive energies gives way to deep multiple minima in reflectivity when this potential is perturbed and made non-Hermitian (complex). A novel co-existence of a SS with deep minima in reflectivity is also revealed wherein the first reflectivity zero of the Hermitian case changes to become a SS for the non-Hermitian case. {PACS: 03.65.Nk,11.30.Er,42.25.Bs}