Non-Hermitian curved space via inverted wave equation

Abstract

Directly determining graded materials from prescribed wave amplitude and phase is an inverse-design method developed following transformation optics (TO), which enables reflectionless propagation for an incidence wave. However, exiting formulations of this inverted method yields Hermitian media and are thus not applicable to non-Hermitian (NH) photonics. In this Letter, we extend this method to NH media, thereby offering more freedom for manipulating waves of no reflection. Our picture of curved-space powered with spatially distributed gain and loss, is exemplified by three types: amplitude control, phase conversion, and direction shunting. These examples showcase precise wave manipulation in a surprisingly simple manner, which is implementable in photonic platform using similar techniques employed in TO.

arXiv comment7 pages, 4 figs