Passive Lossless Huygens Metasurfaces for Conversion of Arbitrary Source Field to Directive Radiation

TL;DR

This paper introduces a semi-analytical method for designing passive lossless Huygens metasurfaces that convert arbitrary source fields into directive radiation, based on local power conservation and impedance equalization, verified by simulations.

Contribution

It develops a semi-analytical formulation for designing passive lossless HMSs for arbitrary sources, incorporating physical conditions for wavefront manipulation and providing a practical design procedure.

Findings

Semi-analytical formulas for scattered fields and surface reactance

Design procedure based on local power conservation and impedance equalization

Verification through finite-element simulations for various source configurations

Abstract

We present a semi-analytical formulation of the interaction between a given source field and a scalar Huygens metasurface (HMS), a recently introduced promising concept for wavefront manipulation based on a sheet of orthogonal electric and magnetic dipoles. Utilizing the equivalent surface impedance representation of these metasurfaces, we establish that an arbitrary source field can be converted into directive radiation via a passive lossless HMS if two physical conditions are met: local power conservation and local impedance equalization. Expressing the fields via their plane-wave spectrum and harnessing the slowly-varying envelope approximation we obtain semi-analytical formulae for the scattered fields, and prescribe the surface reactance required for the metasurface implementation. The resultant design procedure indicates that the local impedance equalization induces a Fresnel-like reflection, while local power conservation forms a radiating virtual aperture which follows the total excitation field magnitude. The semi-analytical predictions are verified by finite-element simulations of HMSs designed for different source configurations. Besides serving as a flexible design procedure for HMS radiators, the proposed formulation also provides a robust mechanism to incorporate a variety of source configurations into general HMS models, as well as physical insight on the conditions enabling purely reactive implementation of this novel type of metasurfaces.