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We propose a new approach of optical field management based on a local Hilbert transform, where the nonHermitian potentials generating arbitrary vector fields of directionality, (p) over right arrow((r) over right arrow), with desired shapes and topologies are designed. We derive a local Hilbert transform to build systematically 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, to generate vortices in the probe fields, and others. Physically, the proposed directionality fields provide a flexible new mechanism for dynamically shaping and precise control over probe fields leading to novel effects in wave dynamics., IEEE Photon Soc, IEEE, Univ Politehnica Bucharest, APEX Technologies, Photonics, OptoSigma, neaspec, Schaefer, Inst Lacznosci Panstwowy Inst Badawczy, NATO SPS Research grant [SPS 985048]; Spanish Ministerio de Ciencia e InnovacionInstituto de Salud Carlos IIISpanish Government; European Union FEDEREuropean Commission [FIS2015-65998-C2-1-P]; AMRDEC [W911NF-16-2-0069], We acknowledge financial support from NATO SPS Research grant (SPS 985048), from Spanish Ministerio de Ciencia e Innovacion, and European Union FEDER through project FIS2015-65998-C2-1-P, and from AMRDEC via project W911NF-16-2-0069.

We propose a new approach of optical field management based on a local Hilbert transform, where the nonHermitian potentials generating arbitrary vector fields of directionality, (p) over right arrow((r) over right arrow), with desired shapes and topologies are designed. We derive a local Hilbert transform to build systematically 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, to generate vortices in the probe fields, and others. Physically, the proposed directionality fields provide a flexible new mechanism for dynamically shaping and precise control over probe fields leading to novel effects in wave dynamics., IEEE Photon Soc, IEEE, Univ Politehnica Bucharest, APEX Technologies, Photonics, OptoSigma, neaspec, Schaefer, Inst Lacznosci Panstwowy Inst Badawczy, NATO SPS Research grant [SPS 985048]; Spanish Ministerio de Ciencia e InnovacionInstituto de Salud Carlos IIISpanish Government; European Union FEDEREuropean Commission [FIS2015-65998-C2-1-P]; AMRDEC [W911NF-16-2-0069], We acknowledge financial support from NATO SPS Research grant (SPS 985048), from Spanish Ministerio de Ciencia e Innovacion, and European Union FEDER through project FIS2015-65998-C2-1-P, and from AMRDEC via project W911NF-16-2-0069.

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., Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructura, Postprint (published version)

We propose a new approach of optical field management based on a local Hilbert transform, where the non-Hermitian potentials generating arbitrary vector fields of directionality p(\vec r), with desired shapes and topologies are designed. We derive a local Hilbert transform to build systematically 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, to generate vortices in the probe fields, and others. Physically, the proposed directionality fields provide a flexible new mechanism for dynamically shaping and precise control over probe fields leading to novel effects in wave dynamics. © 2018 IEEE., Peer Reviewed, Postprint (published version)