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M etamaterials are artificial structures that can be designed to exhibit specific electromagnetic properties not commonly found in nature. Recently, metamaterials with simultaneously negative permittivity (ε) and permeability (µ), more commonly referred to as left-handed (LH) materials, have received substantial attention in the scientific and engineering communities. Science magazine even named LH materials (LHMs) as one of the top ten scientific breakthroughs of 2003 [1]. The unique properties of LHMs have allowed novel applications, concepts, and devices to be developed. In this article, the fundamental electromagnetic properties of LHMs and the physical realization of these materials are reviewed based on a general transmission line (TL) approach. The general TL approach provides insight into the physical phenomena of LHMs and provides an efficient design tool for LH applications. LHMs are considered to be a more general model of composite right/left hand (CRLH) structures, which also include right-handed (RH) effects that occur naturally in practical LHMs. Characterization, design, and implementation of one-dimensional (1-D) and two-dimensional (2-D) CRLH TLs are examined. In addition, novel microwave devices based on CRLH TLs and their applications are presented.

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.

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Breaking time-reversal symmetry enables the realization of non-reciprocal devices, such as isolators and circulators, of fundamental importance in microwave and photonic communication systems. This effect is almost exclusively achieved today through magneto-optical phenomena, which are incompatible with integrated technology because of the required large magnetic bias. However, this is not the only option to break reciprocity. The Onsager-Casimir principle states that any odd vector under time reversal, such as electric current and linear momentum, can also produce a non-reciprocal response. These recently analysed alternatives typically work over a limited portion of the electromagnetic spectrum and/or are often characterized by weak effects, requiring large volumes of operation. Here we show that these limitations may be overcome by angular momentum-biased metamaterials, in which a properly tailored spatiotemporal modulation is azimuthally applied to subwavelength Fano-resonant inclusions, producing largely enhanced non-reciprocal response at the subwavelength scale, in principle applicable from radio to optical frequencies.

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