This paper develops a quasi-analytical and self-consistent model to compute the polarizabilities of split ring resonators (SRRs). An experimental setup is also proposed for measuring the magnetic polarizability of these structures. Experimental data are provided and compared with theoretical results computed following the proposed model. By using a local field approach, the model is applied to the obtaining of the dispersion characteristics of discrete negative magnetic permeability and left-handed metamaterials. Two types of SRRs, namely, the so-called edge coupled- and broadside coupled- SRRs, have been considered. A comparative analysis of these two structures has been carried out in connection with their suitability for the design of metamaterials. Advantages and disadvantages of both structures are discussed.

At microwave frequencies, hollow metallic waveguides behave in certain aspects as a “one-dimensional plasma.” This feature will be advantageously used for simulating the propagation of electromagnetic (EM) waves in left-handed metamaterials provided the hollow waveguide is periodically loaded with split ring resonators. It will be shown that EM transmission in this structure is feasible within a certain frequency band even if the transverse dimensions of the waveguide are much smaller than the associated free-space wavelength. This effect can be qualitatively and quantitatively explained by the left-handed metamaterial theory, thus providing a new experimental validation for such a theory.

Metasurfaces are thin two-dimensional metamaterial layers that allow or inhibit the propagation of electromagnetic waves in desired directions. For example, metasurfaces have been demonstrated to produce unusual scattering properties of incident plane waves or to guide and modulate surface waves to obtain desired radiation properties. These properties have been employed, for example, to create innovative wireless receivers and transmitters. In addition, metasurfaces have recently been proposed to confine electromagnetic waves, thereby avoiding undesired leakage of energy and increasing the overall efficiency of electromagnetic instruments and devices. The main advantages of metasurfaces with respect to the existing conventional technology include their low cost, low level of absorption in comparison with bulky metamaterials, and easy integration due to their thin profile. Due to these advantages, they are promising candidates for real-world solutions to overcome the challenges posed by the next generation of transmitters and receivers of future high-rate communication systems that require highly precise and efficient antennas, sensors, active components, filters, and integrated technologies. This Roadmap is aimed at binding together the experiences of prominent researchers in the field of metasurfaces, from which explanations for the physics behind the extraordinary properties of these structures shall be provided from viewpoints of diverse theoretical backgrounds. Other goals of this endeavour are to underline the advantages and limitations of metasurfaces, as well as to lay out guidelines for their use in present and future electromagnetic devices. This Roadmap is divided into five sections: 1. Metasurface based antennas. In the last few years, metasurfaces have shown possibilities for advanced manipulations of electromagnetic waves, opening new frontiers in the design of antennas. In this section, the authors explain how metasurfaces can be employed to tailor the radiation properties of antennas, their remarkable advantages in comparison with conventional antennas, and the future challenges to be solved. 2. Optical metasurfaces. Although many of the present demonstrators operate in the microwave regime, due either to the reduced cost of manufacturing and testing or to satisfy the interest of the communications or aerospace industries, part of the potential use of metasurfaces is found in the optical regime. In this section, the authors summarize the classical applications and explain new possibilities for optical metasurfaces, such as the generation of superoscillatory fields and energy harvesters. 3. Reconfigurable and active metasurfaces. Dynamic metasurfaces are promising new platforms for 5G communications, remote sensing and radar applications. By the insertion of active elements, metasurfaces can break the fundamental limitations of passive and static systems. In this section, we have contributions that describe the challenges and potential uses of active components in metasurfaces, including new studies on non-Foster, parity-time symmetric, and non-reciprocal metasurfaces. 4. Metasurfaces with higher symmetries. Recent studies have demonstrated that the properties of metasurfaces are influenced by the symmetries of their constituent elements. Therefore, by controlling the properties of these constitutive elements and their arrangement, one can control the way in which the waves interact with the metasurface. In this section, the authors analyze the possibilities of combining more than one layer of metasurface, creating a higher symmetry, increasing the operational bandwidth of flat lenses, or producing cost-effective electromagnetic bandgaps. 5. Numerical and analytical modelling of metasurfaces. In most occasions, metasurfaces are electrically large objects, which cannot be simulated with conventional software. Modelling tools that allow the engineering of the metasurface properties to get the desired response are essential in the design of practical electromagnetic devices. This section includes the recent advances and future challenges in three groups of techniques that are broadly used to analyze and synthesize metasurfaces: circuit models, analytical solutions and computational methods.

Extraordinary optical transmission of light or electromagnetic waves through metal plates periodically perforated with subwavelength holes has been exhaustively analyzed in the last ten years. The study of this phenomenon has attracted the attention of many scientists working in the fields of optics and condensed matter physics. This confluence of scientists has given rise to different theories, some of them controversial. The first theoretical explanation was based on the excitation of surface plasmons along the metal-air interfaces. However, since periodically perforated dielectric (and perfect conductor) slabs also exhibit extraordinary transmission, diffraction by a periodic array of scatterers was later considered as the underlying physical phenomenon. From a microwave engineering point of view, periodic structures exhibiting extraordinary optical transmission are very closely related to frequency-selective surfaces. In this paper, we use simple concepts from the theory of frequency-selective surfaces, waveguides, and transmission lines to explain extraordinary transmission for both thin and thick periodically perforated perfect conductor screens. It will be shown that a simple transmission-line equivalent circuit satisfactorily accounts for extraordinary transmission, explaining all of the details of the observed transmission spectra, and easily gives predictions on many features of the phenomenon. Although the equivalent circuit is developed for perfect conductor screens, its extension to dielectric perforated slabs and/or penetrable conductors at optical frequencies is almost straightforward. Our circuit model also predicts extraordinary transmission in nonperiodic systems for which this phenomenon has not yet been reported.

Here, we report on the transmissivity of electromagnetic waves through a stack of monolayer graphene sheets separated by dielectric slabs at low-terahertz frequencies. It is observed that the multilayer structure possesses band-gap properties and supports a series of bandpass and band-stop regions, similar to the cases of stacked metallic meshes separated by dielectric slabs at microwave/THz frequencies and a metal-dielectric stack at optical frequencies. The transmission resonances in the bandpass region are identified as coupled Fabry-P\'erot resonances associated with the individual cavities of dielectric slabs loaded with graphene sheets. It is also noticed that these resonances lie within a certain characteristic frequency band, independent of the number of layers in the graphene-dielectric stack. The study is carried out using a simple analytical transfer-matrix approach or, equivalently, a circuit-theory model, resulting in the exact solution for the multiple dielectric/graphene sheet surface-conductivity model. Also, an independent verification of the observed phenomena is obtained with commercial numerical simulations.

This paper is focused on the application of complementary split-ring resonators (CSRRs) to the suppression of the common (even) mode in microstrip differential transmission lines. By periodically and symmetrically etching CSRRs in the ground plane of microstrip differential lines, the common mode can be efficiently suppressed over a wide band whereas the differential signals are not affected. Throughout the paper, we present and discuss the principle for the selective common-mode suppression, the circuit model of the structure (including the models under even- and odd-mode excitation), the strategies for bandwidth enhancement of the rejected common mode, and a methodology for common-mode filter design. On the basis of the dispersion relation for the common mode, it is shown that the maximum achievable rejection bandwidth can be estimated. Finally, theory is validated by designing and measuring a differential line and a balanced bandpass filter with common-mode suppression, where double-slit CSRRs (DS-CSRRs) are used in order to enhance the common-mode rejection bandwidth. Due to the presence of DS-CSRRs, the balanced filter exhibits more than 40 dB of common-mode rejection within a 34% bandwidth around the filter pass band.