We present a 3D method to numerically design a realizable metasurface, which transforms a given incident field into a radiated field that satisfies mask-type (inequality) constraints. The method is based on an integral equation formulation, with local impedance boundary condition (IBC) approximation. The procedure yields the spatial distribution of the impedance, yet the process involves the synthesis of the equivalent current only. This current is constrained to correspond to a realizable surface impedance, i.e., passive, lossless, and with reactance values bounded by practical realizability limits. The current-based design avoids any solution of the forward problem, and the impedance is obtained from the synthesized current only at the end of the process. The procedure is gradient-based, with the gradient expressed in closed form. This allows handling large metasurfaces, with full spatial variability of the impedance in two dimensions. The method requires no a priori information, and all relevant operations in the iterative process can be evaluated with O ( N log N ) complexity. Application examples concentrate on the case of on-surface excitation and far-field pattern specifications; they show designs of circular and rectangular metasurface antennas of 20 wavelengths in size, with pencil- and shaped-beam patterns, and for both circular and linear polarization.

Entire-domain, spectral basis functions have witnessed recent interest in the integral-equation analysis of large Metasurface antennas modeled via homogenized Impedance Boundary Conditions.We present a formulation employing classical Galerkin test via Rao-Wilton-Glisson functions, yet assembled to represent entire-domain div-conforming basis functions for the shape of interest (e.g. circular/coaxial Waveguide modes). On the one hand, the rationale is that entire-domain, spectral basis functions afford a significant economy in the number of necessary unknowns; on the other hand, being expressed as combination of Rao-Wilton-Glisson functions, reaction integrals are computed with optimum cost via fast methods. This is applied to reduce the cost of the optimization process used to design Metasurface antennas based on spatially modulated reactance profiles. The authors support the method proposed, presenting criteria to define the entire domain functions, considering the overall numerical complexity in an optimization framework, and providing convergence analysis and numerical results for holographic leaky-wave antennas, relevant in the Metasurface context.

Beam-scanning antennas are employed in a wide range of applications, such as in satellite communications and 5G networks. Current commercial solutions rely mostly on electronically reconfigurable phased arrays, which require complex feeding networks and are affected by high losses, high costs, and are often power-hungry. In this paper, a novel beam scanning architecture employing a pair of planar metasurfaces, for use in thin reconfigurable antennas, is presented and experimentally demonstrated. The structure consisted of a radiative passive (non-reconfigurable) modulated metasurface, and a second metasurface that controls beam pointing, operating as a variable-impedance ground plane. Unlike other existing approaches, surface impedance variation was obtained by on-plane varactor diodes, no vias and a single voltage bias. This paper presents a design procedure based on an approximate theoretical model and simulation verification; a prototype of the designed antenna was fabricated for operation in X band, and a good agreement between measured results and simulations was observed. In the presented simple embodiment of the concept, the angular scanning range was limited to ${10}^{°}$; this limitation is discussed in view of future applications.

Line-waves are one-dimensional modes propagating at the interface between two planar complementary surfaces, characterized by tight transversal confinement of the field. Despite their unique guiding properties, their use in real microwave devices is still in the early stages, lacking a comprehensive design procedure and comparative analysis with conventional guiding structures. To fill this gap, here we report a simple and straightforward workflow for designing waveguides supporting 1D modes propagation. The design is based on the analytical relations existing between the surface impedance of the propagating modes and the sheet impedance of the metasurfaces, which allow quick retrieval of the geometrical parameters of the complementary metasurfaces sustaining the line-wave propagation. This approach is used to design several waveguiding layouts and compare their transmission performance through full-wave simulations accounting for dielectric and ohmic losses. Finally, experimental results for some selected designs in the microwave regime are provided, and a thoughtful comparison between a line-wave waveguide and an equivalent microstrip transmission line is carried out to assess the suitability of these devices for efficient high-frequency waveguiding.

This paper offers an efficient numerical approach to optimizing the design of large circular planar Metasurfaces (MTSs) antennas based on specially varying impedance profiles. Div-conforming spectral basis functions on the whole antenna are defined. The goal is to reduce the number of unknowns, to lead to a well-conditioned system, and to speed up the multiple solutions needed by an automatic optimization code. We consider the overall numerical complexity of the scheme and show its advantages in optimization applications.

We present a 3D method to numerically design a realizable metasurface, which transforms a given incident field into a radiated field that satisfies mask-type (inequality) constraints. The method is based on an integral equation formulation, with local impedance boundary condition (IBC) approximation. The procedure yields the spatial distribution of the impedance, yet the process involves the synthesis of the equivalent current only. This current is constrained to correspond to a realizable surface impedance, i.e., passive, lossless, and with reactance values bounded by practical realizability limits. The current-based design avoids any solution of the forward problem, and the impedance is obtained from the synthesized current only at the end of the process. The procedure is gradient-based, with the gradient expressed in closed form. This allows handling large metasurfaces, with full spatial variability of the impedance in two dimensions. The method requires no a priori information, and all relevant operations in the iterative process can be evaluated with O ( N log N ) complexity. Application examples concentrate on the case of on-surface excitation and far-field pattern specifications; they show designs of circular and rectangular metasurface antennas of 20 wavelengths in size, with pencil- and shaped-beam patterns, and for both circular and linear polarization.