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.

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We show that the public experiment held in Venice by Tamburini et al and reported in 2012 New J. Phys. 14 033001 can be regarded as a particular implementation of multiple-input-multiple-output (MIMO) communications and, therefore, has no advantages over established techniques. Moreover, we explain that the use of a 'vortex' mode (orbital angular momentum = 1) at one of the transmit antennas is not necessary to encode different channels since only different patterns-or similarly different pointing angles-of the transmit antennas are required. Finally, we identify why this MIMO transmission allowed the decoding of two signals, despite being line-of-sight. This is due to the large separation between the receiving antennas, which places the transmit antennas in the near-field Fresnel region of the receiving 'array'. This severely limits the application of this technique in practice, since, for a fixed separation between receiving antennas, the detectable signal power from any additional vortex mode decays at least as 1/r 4 .

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An overview about mutual coupling analysis in antenna arrays is given. The relationships between array impedance matrix and embedded element patterns, including beam coupling factors, are reviewed while considering general‐type antennas; approximations resulting from single‐mode assumptions are pointed out. For regular arrays, a common Fourier‐based formalism is employed, with the array scanning method as a key tool, to explain various phenomena and analysis methods. Relationships between finite and infinite arrays are described at the physical level, as well as from the point of view of numerical analysis, considering mainly the method of moments. Noise coupling is also briefly reviewed.