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

Abstract

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.

Wave-front Transformation with Gradient Metasurfaces

“…We show in the following that this picture is inherently approximate, as it does not consider the relevance of impedance matching in the scattering process [29]. Changing the refraction angle from normal to oblique implies a different ratio of the transverse components of electric and magnetic fields on the surface, which in turn requires that the local transmission coefficient t should be different for local tangential electric and magnetic fields.…”

“…(5) also allows us to go beyond the maximum efficiencies attainable from multimode Huygens metasurfaces [29,42]. Multimode metasurfaces rely on the presence of one or more additional scattering modes to ensure surface passivity, and they may suffer from low efficiencies and a large number of evanescent modes close to the metasurface, particularly at large deflection angles.…”

Floquet-Bloch analysis of refracting Huygens metasurfaces

“…In a sense, the current elements act as Huygens sources, producing a unidirectional response that cancels the incident field and introduces the transmitted field, in the spirit of the Huygens principle [24,25]; accordingly, these reduced-reflection structures were named Huygens metasurfaces [20]. * ariel.epstein@utoronto.ca † gelefth@waves.utoronto.ca Since the proposition of this concept, Huygens metasurfaces (HMSs) demonstrating a variety of wave-front manipulation capabilities have been designed [26][27][28][29][30]. Nonetheless, relying on the equivalence principle for the design means that the functionality of the HMS is predictable only for the designated excitation field, especially if the implementation is passive.…”

“…In addition, despite the aforementioned difficulty in predicting the HMS response when the excitation field differs from the design specifications, experiments conducted on refracting Huygens metasurfaces indicate that the HMS retains its functionality even if the incident beam deviates from the designated direction by as much as 40 • [20,27]. This evidence remains to be explained, particularly in view of our recent observation that passive lossless HMSs induce reflected fields to equalize the total wave impedance at the incident facet to that of the transmitted (refracted) plane wave; the absolute propagation direction of the transmitted wave is explicitly incorporated into the design scheme [21,29]. Another unresolved question arises from these demonstrations, as it turns out that the required sheet reactance modulation reaches infinite values and has infinite spatial bandwidth and hence cannot be realized in practice.…”

Surface Impedance Synthesis Using Parallel Planar Electric Metasurfaces

“…Both of them are important and necessary to achieve full control on EM wave propagation [23,24]. The electric surface impedance is usually implemented by ultra-thin metallic patterns [4,14,17,18,[25][26][27], whereas the magnetic surface impedance is usually implemented by the metallic loops [7,23,24,28].…”