Designing lasing and perfectly absorbing potentials
Abstract
Existence of a spectral singularity (SS) in the spectrum of {a Schr\"{o}dinger operator with} a non-Hermitian potential requires exact matching of parameters of the potential. We provide a necessary and sufficient condition for a potential to have a SS at a given wavelength. It is shown that potentials with SSs at prescribed wavelengths can be obtained by a simple and effective procedure. In particular, the developed approach allows one to obtain potentials with several SSs and with SSs of the second order, as well as potentials obeying a given symmetry, say, symmetric potentials. Also, the problem can be solved when it is required to obtain a potential obeying a given symmetry, say, symmetric potential. We illustrate all these opportunities with examples. We also describe splitting of a second-order SSs under change of the potential parameters, and discuss possibilities of experimental observation of SSs of different orders.
Cite
@article{arxiv.1812.05499,
title = {Designing lasing and perfectly absorbing potentials},
author = {Vladimir V. Konotop and Evgeny Lakshtanov and Boris Vainberg},
journal= {arXiv preprint arXiv:1812.05499},
year = {2019}
}
Comments
10 pages, 4 figures