Restricted Hilbert transform for non-Hermitian management of fields

Non-Hermitian systems exploiting the synergy between gain and loss have recently become the focus of interest to discover novel physical phenomena. The spatial symmetry breaking in such systems allows tailoring the wave propagation at will. Inspired by such property, we propose a feasible approach based on local Hilbert transform to control the field flows in two- or higher dimensional non-Hermitian systems, restricting the complex refractive index within practical limits. We propose an iterative procedure to reduce the dimensionality of complex refractive index parameter space to two, one or zero dimensions. The proposed method provides a flexible way to systematically design locally PT-symmetric systems realizable with a limited collection of realistic materials.