  Coordinate transformations are a versatile tool to mould the flow of light,
enabling a host of astonishing phenomena such as optical cloaking with
metamaterials. Moving away from the usual restriction that links isotropic
materials with conformal transformations, we show how non-conformal distortions
of optical space are intimately connected to the complex refractive index
distribution of an isotropic non-Hermitian medium. Remarkably, this insight can
be used to circumvent the material requirement of working with refractive
indices below unity, which limits the applications of transformation optics. We
apply our approach to design a broadband unidirectional dielectric cloak, which
relies on non-conformal coordinate transformations to tailor the nonHermitian
refractive index profile around a cloaked object. Our insights bridge the
fields of two-dimensional transformation optics and non-Hermitian photonics.
