Abstract
Novel physical phenomena arising from the interplay between gain and loss is beyond the recent focus on Non-Hermitian systems. The spatial symmetry breaking in such systems may lead to an arbitrarily control of the flow of light. We present an approach to design Non-Hermitian systems on demand, with desired shapes and topologies based on a modification of the classical Hilbert transform. The procedure allows restricting the dimensionality of the complex index parameter space, keeping the physical properties within practical limits and realizable with a finite collection of materials.