We show that the use of the electromagnetic inverse source framework offers great flexibility in the design of metasurfaces. In particular, this approach is advantageous for antenna design applications where the goal is often to satisfy a set of performance criteria such as half power beamwidths and null directions, rather than satisfying a fully-known complex field. In addition, the inverse source formulation allows the metasurface and the region over which the desired field specifications are provided to be of arbitrary shape. Some of the main challenges in solving this inverse source problem, such as formulating and optimizing a nonlinear cost functional, are addressed. Lastly, some two-dimensional (2D) and three-dimensional (3D) simulated examples are presented to demonstrate the method, followed by a discussion of the method's current limitations.

Metasurfaces represent one of the most vibrant fields of modern science and technology. A metasurface is a complex electromagnetic structure, that is typically deeply subwavelength in thickness, electrically large in transverse size and composed of subwavelength scattering particles with extremely small features; it may generally be bianisotropic, spacevarying and time-varying, nonlinear, curved and multiphysics. With such complexity, the design of a metasurface requires a holistic approach, involving synergistic synthesis and analysis operations, based on a solid model. The Generalized Sheet Transition Conditions (GSTCs), combined with bianisotropic surface susceptibility functions, provide such a model, and allow now for the design of sophisticated metasurfaces, which still represented a major challenge a couple of years ago. This paper presents this problematic, focusing on the computational analysis of metasurfaces via the GSTC-susceptibility approach. It shows that this analysis plays a crucial role in the holistic design of metasurfaces, and overviews recently reported related frequency-domain (FDFD, SD-IE, FEM) and time-domain (FDTD) computational techniques.

Abstract-We introduce a rigorous and simple method for analyzing metasurfaces, modeled as zero-thickness electromagnetic sheets, in Finite Difference (FD) techniques. The method consists in describing the spatial discontinuity induced by the metasurface as a virtual structure, located between nodal rows of the Yee grid, using a finite difference version of Generalized Sheet Transition Conditions (GSTCs). In contrast to previously reported approaches, the proposed method can handle sheets exhibiting both electric and magnetic discontinuities, and represents therefore a fundamental contribution in computational electromagnetics. It is presented here in the framework of the FD Frequency Domain (FDFD) method but also applies to the FD Time Domain (FDTD) scheme. The theory is supported by five illustrative examples.Index Terms-Metasurface, electromagnetic sheet, spatial discontinuity, generalized sheet transition conditions (GSTCs), finite difference frequency domain (FDFD), finite difference time domain (FDTD), diffraction orders.

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The bianisotropic susceptibility Generalized Sheet Transition Conditions (GSTCs) synthesis method is extended from planar to spherical metasurfaces. Properties specific to the non-zero intrinsic curvature of the spherical shape are highlighted and different types of corresponding transformations are described. Finally, the susceptibility-GSTC method and exotic properties of spherical metasurfaces are validated and illustrated with three examples: illusion transformation, ring focusing and birefringence.