Abstract-This paper describes in detail different formulations of the inverse-source problem, whereby equivalent sources and/or fields are to be computed on an arbitrary 3-D closed surface from the knowledge of complex vector electric field data at a specified (exterior) surface. The starting point is the analysis of the formulation in terms of the Equivalence Principle, of the possible choices for the internal fields, and of their practical impact. Love's (zero interior field) equivalence is the only equivalence form that yields currents directly related to the fields on the reconstruction surface; its enforcement results in a pair of coupled integral equations. Formulations resulting in a single integral equation are also analyzed. The first is the single-equation, two-current formulation which is most common in current literature, in which no interior field condition is enforced. The single-current (electric or magnetic) formulation deriving from continuity enforcement of one field is also introduced and analyzed. Single-equation formulations result in a simpler implementation and a lower computational load than the dual-equation formulation, but numerical tests with synthetic data support the benefits of the latter. The spectrum of the involved (discretized) operators clearly shows a relation with the theoretical Degrees of Freedom (DoF) of the measured field for the dual-equation formulation that guarantees extraction of these DoF; this is absent in the single-equation formulation. Examples confirm that singleequation formulations do not yield Love's currents, as observed both with comparison with reference data and via energetic considerations. The presentation is concluded with a test on measured data which shows the stability and usefulness of the dual-equation formulation in a situation of practical relevance.

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A self-complementary metasurface is studied in this paper. The metasurface is a 2-D periodical arrangement of unit cells formed by a metallic printed split ring resonator and its complementary counterpart. It is demonstrated that this structure behaves like a very selective band-pass filter for a certain linear polarization while band-stop filtering is achieved for the orthogonal polarization over the same frequency range. This idea opens the door to a new class of frequency selective surfaces made of connected and unconnected elements, whose filtering properties are mechanically tunable from band-pass to band-stop by rotating the surface or the polarization.

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The projection operator is a basic building block in the application of the alternating projections method to antenna synthesis. In general it is a non-linear operator that is repeatedly applied in the course of a single synthesis process, thus having a considerable impact on the convergence properties of the resulting algorithm. A novel approach to the computation of these projections is presented which exploits a simple definition of the relevant spaces (particularly that of radiated fields). Characterization of field mask specification as scale-invariant under this definition adds a further degree of freedom, namely reference level, which impacts on the (sensitive to scaling) projector. In order to compute the optimum reference level, an iterative procedure is proposed which is simple to implement, easily integrable in standard alternating projection routines, and adds negligible computational burden. Numerical tests confirm an improved performance with respect to the fixed-scaling projection operator in terms of convergence rate and robustness against the initial guess, supporting our approach as a valid aid in overcoming the drawbacks of the alternating projections-based antenna synthesis.