Spectral singularity and reflectionlessness in non-Hermitian (complex) Ginocchio potential

Abstract

Recently, interest in scattering from complex non-Hermitian potentials has been renewed both theoretically and experimentally. When a potential becomes complex, several new features arise which may not be predicted. In this regard, we study the non-Hermitian version of the exactly solvable, versatile Ginocchio potential. We find that when it is non-Hermitian and non-absorptive there exists, at most, one spectral singularity (SS). The well-known reflectionlessness of this potential gives way to deep minima in reflectivity. We find the co-existence of an SS with deep oscillations in reflectivity. Remarkably, the complex PT-symmetric version of this potential does not entail any SS. In this case, the reflectionlessness at discrete energies persists with the handedness of reflectivity and non-unitarity. In the new parlance this would be called the invisibility of an optical potential but in this case, uniquely, it is from both sides, left and right. © 2012 IOP Publishing Ltd.