Abstract-A general method, based on susceptibility tensors, is proposed for the synthesis of metasurfaces transforming arbitrary incident waves into arbitrary reflected and transmitted waves. The proposed method exhibits two advantages: 1) it is inherently vectorial, and therefore better suited for full vectorial (beyond paraxial) electromagnetic problems, 2) it provides closedform solutions, and is therefore extremely fast. Incidentally, the method reveals that a metasurface is fundamentally capable to transform up to four independent wave triplets (incident, reflected and refracted waves). In addition, the paper provides the closed-form expressions relating the synthesized susceptibilities and the scattering parameters simulated within periodic boundary conditions, which allows one to design the scattering particles realizing the desired susceptibilities. The versatility of the method is illustrated by examples of metasurfaces achieving the following transformations: generalized refraction, reciprocal and non-reciprocal polarization rotation, Bessel vortex beam generation, and orbital angular momentum multiplexing.

We aim at providing a global perspective on electromagnetic nonreciprocity and clarifying confusions that arose in recent developments of the field. We provide a general definition of nonreciprocity and classify nonreciprocal systems according to their linear time-invariant (LTI), linear time-variant (LTV), or nonlinear natures. The theory of nonreciprocal systems is established on the foundation formed by the concepts of time reversal, time-reversal symmetry, time-reversal symmetry breaking, and related Onsager-Casimir relations. Special attention is given to LTI systems, the most-common nonreciprocal systems, for which a generalized form of the Lorentz reciprocity theorem is derived. The delicate issue of loss in nonreciprocal systems is demystified and the so-called thermodynamics paradox is resolved from energyconservation considerations. An overview of the fundamental characteristics and applications of LTI, LTV, and nonlinear nonreciprocal systems is given with the help of pedagogical examples. Finally, asymmetric structures with fallacious nonreciprocal appearances are debunked.

Abstract:The paper overviews our recent work on the synthesis of metasurfaces and related concepts and applications. The synthesis is based on generalized sheet transition conditions (GSTCs) with a bianisotropic surface susceptibility tensor model of the metasurface structure. We first place metasurfaces in a proper historical context and describe the GSTC technique with some fundamental susceptibility tensor considerations. On this basis, we next provide an in-depth development of our susceptibility-GSTC synthesis technique. Finally, we present five recent metasurface concepts and applications, which cover the topics of birefringent transformations, bianisotropic refraction, light emission enhancement, remote spatial processing, and nonlinear second-harmonic generation.

We introduce a nonreciprocal nongyrotropic magnetless metasurface. In contrast to previous nonreciprocal structures, this metasurface does not require a biasing magnet, and is therefore lightweight and amenable to integrated circuit fabrication. Moreover, it does not induce Faraday rotation, and hence does not alter the polarization of waves, which is a desirable feature in many nonreciprocal devices. The metasurface is designed according to a Surface-Circuit-Surface (SCS) architecture and leverages the inherent unidirectionality of transistors for breaking time reversal symmetry. Interesting features include transmission gain as well as broad operating bandwidth and angular sector operation. It is finally shown that the metasurface is bianisotropic in nature, with nonreciprocity due to the electric-magnetic coupling parameters, and structurally equivalent to a moving uniaxial metasurface

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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.

The paper presents partial overview of the mathematical synthesis and the physical realization of metasurfaces, and related illustrative examples. The synthesis consists in determining the exact tensorial surface susceptibility functions of the metasurface, based on generalized sheet transition conditions, while the realization deals with both metallic and dielectric scattering particle structures. The examples demonstrate the capabilities of the synthesis and realization techniques, thereby showing the plethora of possible metasurface field transmission and subsequent applications. The first example is the design of two diffraction engineering birefringent metasurfaces performing polarization beam splitting and orbital angular momentum multiplexing, respectively. Next, we discuss the concept of the "transistor" metasurface, which is an electromagnetic linear switch based on destructive interferences. Then, we introduce a non-reciprocal non-gyrotropic metasurface using a pick-up circuit radiator (PCR) architecture. Finally, the implementation of all-dielectric metasurfaces for spatial dispersion engineering is discussed.