Restricted Hilbert Transform for Non-Hermitian Management of Fields

Non-Hermitian systems exploiting the synergy between the properties of closed-conservative systems and open-dissipative (gain-loss) systems have recently become the playground to uncover unusual physical phenomena. Indeed, the spatial symmetry breaking in such systems allows tailoring of the wave propagation at will. Inspired by such a property, we propose a feasible approach based on local Hilbert transform to control the field flows in two- or higher-dimensional non-Hermitian systems. Moreover, we invent an iterative procedure to reduce the dimensionality of complex refractive-index parameter space to two, one, or zero dimensions, restricting the complex refractive index within practical limits. The proposal provides a flexible way to systematically design locally non-Hermitian systems realizable with a limited collection of realistic materials.