Kramers-Kronig potentials for the discrete Schr\"odinger equation
Abstract
In a seminal work, S.A.R. Horsley and collaborators [S.A.R. Horsley {\em et al.}, Nature Photon. {\bf 9}, 436 (2015)] have shown that, in the framework of non-Hermitian extensions of the Schr\"odinger and Helmholtz equations, a localized complex scattering potential with spatial distributions of the real and imaginary parts related to one another by the spatial Kramers-Kronig relations are reflectionless and even invisible under certain conditions. Here we consider the scattering properties of Kramers-Kronig potentials for the discrete version of the Schr\"odinger equation, which generally describes wave transport on a lattice. Contrary to the continuous Schr\"odinger equation, on a lattice a stationary Kramers-Kronig potential is reflective. However, it is shown that a slow drift can make the potential invisible under certain conditions.
Keywords
Cite
@article{arxiv.1709.09344,
title = {Kramers-Kronig potentials for the discrete Schr\"odinger equation},
author = {Stefano Longhi},
journal= {arXiv preprint arXiv:1709.09344},
year = {2017}
}
Comments
8 pages, 5 figures, to appear in Phys Rev A