Non-Hermitian curved space via inverted wave equation

Directly solving graded materials from amplitude and phase was a method developed following transformation optics (TO), which provided reflectionless media for an incidence wave. However, this inverting method gives Hermitian media thus not applicable to non-Hermitian (NH) photonics. In this Letter we then design NH media offering more freedom to manipulate waves of no reflection. Our picture of curved-space powered with gain and loss, is exemplified by three types: amplitude controlling, phase conversion, and direction shunting. These examples showcase precise wave manipulation in a surprisingly simple manner, which goes beyond convectional TOs and is implementable in nonreciprocal photonic platform.