Non-Hermitian Light Management Based on Local Hilbert Transform

We demonstrate a novel idea of nonhermitian management of light based on a local Hilbert transform. Local Hilbert transform, a substantial modification of classical Hilbert transform allows to design non-Hermitian vector fields of arbitrary directionality, p⃗(r⃗), with desired shapes and topologies. We derive a local Hilbert transform to systematically build such potentials, by modifying background potentials (being either regular or random, extended or localized). In particular, we explore particular directionality fields, for instance in the form of a focus to create sinks for probe fields (which could help to increase absorption at the sink), or to generate vortices in the probe fields. Physically, the proposed mechanism provide a flexible new tool for dynamically shaping and precise control over probe fields leading to novel effects in nonlinear wave dynamics, and in particular in broad area microlasers.