This paper gives an overview on the design process of modulated metasurface (MTS) antennas and focus on their performance in terms of efficiency and bandwidth. The basic concept behind MTS antennas is that the MTS imposes the impedance boundary conditions (IBCs) seen by a surface wave (SW) propagating on it. The MTS having a spatially modulated equivalent impedance transforms the SW into a leaky wave with controlled amplitude, phase and polarization. MTS antennas are hence highly customizable in terms of performances by simply changing the IBCs imposed by the MTS, without affecting the overall structure. The MTS can be configured for high gain (high aperture efficiency) with moderate bandwidth, for wide bandwidth with moderate aperture efficiency, or for a trade-off performance for bandwidth and aperture efficiency. The design process herein described relies on a generalized form of the Floquet wave theorem adiabatically applied to curvilinear locally periodic IBCs. Several technological solutions can be adopted to implement the IBCs defined by the synthesis process, from sub-wavelength patches printed on a grounded slab at microwave frequencies, to a bed of nails structure for millimeter waves: in any case, the resulting device has light weight and a low profile.

Generalized impedance boundary conditions are employed to simulate the effects of the parallel-stratified media on electromagnetic fields. Sommerfeld type integral contained in Hertz potential is expressed as the sum of two parts: zeroth order Hankel function and an absolutely convergent series expansion of spherical Hankel functions.

The radar cross section (RCS) of a dielectric-coated cylindrical cavity was measured and the measurements were compared with those calculated according to the iterative physical optics (IPO). The IPO analysis used the equivalent-impedance boundary condition (EIBC) based on transmission-line theory which takes into account the thickness of the coating. It was consequently found that this condition is much more effective than the ordinary-impedance boundary condition based on the intrinsic impedance of the material.

The boundary integral equation (BIE) on interior walls with surface impedance conditions is implemented to the iterative physical optics method and how to treat the singularities involved in the BIE of an impedance cavity is described. Singular integrals over a rectangular region can be represented by simple elementary functions.

An electromagnetic wave scattering by a material loaded rectangular trough on a ground plane is approximately analyzed by using standard impedance boundary condition (SIBC). The validity of the derived approximate solution is examined by comparing with the rigorous one not only for the oblique incidence but also for the variation of both the filled material's parameters and the trough dimension. An applicability condition has been derived here for this trough structure.