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We present a semianalytical 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: 1) local power conservation and 2) local impedance equalization. Expressing the fields via their plane-wave spectrum and harnessing the slowly-varying envelope approximation, we obtain semianalytical formulae for the scattered fields, and prescribe the surface reactance required for the metasurface implementation. The resulting 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 semianalytical 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.

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