all researchers and engineers active in the broad eld of electromagnetics across the microwave, terahertz, and optical regimes of the spectrum. This book, the rst textbook on the eld, responds to a pressing need for a unied document as a support to this syllabus, and opens horizons for further developments of the field.
What is the point about metasurfaces? After all, their visual appearance is essentially similar to that of frequency- or polarization-selective surfaces and spatial light modulators, which have been known and extensively used for several decades. The point is. . . DIVERSITY. Metasurfaces represent generalizations of these devices, which are respectively restricted to ltering or polarizing and phase-only or magnitude-only wave manipulations. Metasurfaces indeed offer a universal platform for unlimited control of the magnitude, the phase, and the polarization of electromagnetic waves to meet transformation specications of virtually unlimited complexity. Moreover, in contrast ix to their voluminal counterparts, they feature a low prole that implies easier fabrication, lower loss, and, perhaps surprisingly, even greater functionality.
This diversity would be of little practical interest if it were not accompanied by a proper instrument to master it. Fortunately, such an instrument has progressively emerged and crystalized as a combination of bianisotropic surface susceptibility models and generalized sheet transition conditions, the former properly describing metasurfaces, whose subwavelength thickness prohibits Fabry–Perot resonances, as a sheet of equivalent surface polarization current densities, and the latter representing a generalized version of the conventional boundary conditions, via the addition of these currents to the induced sources. This global modeling approach allows to systematically manipulate the enormous number of possible combinations of the 36 degrees of freedom of bianisotropic metasurfaces, both in the analysis and characterization of existing metasurfaces and in the synthesis and design of metasurfaces according to specications. It constitutes, therefore, the backbone of the book, providing, in addition to its design power, deep insight into the physics of metasurfaces and quick information on their fundamental properties.
The book constitutes a coherent, comprehensive, self-consistent, and pedagogical framework that covers the essential theoretical aspects and practical design strategies of electromagnetic metasurfaces and their applications. It is designed to provide a solid understanding and efficient mastery of the eld to both students and researchers alike. To achieve this goal, we have organized this book in a logical fashion, with each chapter building up on the concepts established by the previous ones. Considering the plethora of publications in the eld, we naturally had to select out what we considered as the most important and relevant developments, hoping that the presented material would be x sufficient to provide comfortable access to all the non-explicitly treated topics.
Chapter 1 provides a general denition of metasurfaces as well as a historical perspective of their development. Chapter 2 describes the fundamental electromagnetic media properties pertaining to metasurfaces. It presents the general bianisotropic constitutive relations, reviews the concepts of temporal and spatial dispersion, and recalls the Lorentz and Poynting theorems. Chapter 3 extends these concepts to the metasurfaces, establishes their modeling principles in terms of bianisotropic surface susceptibilities and generalized sheet transition conditions, and extracts from this model several fundamental physical properties and limitations. Chapter 4 applies these modeling principles to the synthesis of linear time-invariant, time-varying and nonlinear metasurfaces, and illustrates them with several examples. Chapter 5 overviews four analysis schemes that may be used to simulate and predict the scattering response of metasurfaces. One of these methods is based on the Fourier propagation technique; two are based on nite-difference methods, one in the frequency domain and the other in the time domain; and the last method is an integral equation method, which is particularly well suited for 3D computations. Chapter 6 details several fabrication metasurface technologies that pertain to the different parts of the electromagnetic spectrum. It shows how dielectric and metallic scattering particles may be used to realize metasurfaces at both optical and microwave frequencies and demonstrates several techniques to tune the shape of the scattering particles to achieve desired responses. Finally, Chapter 7 discusses three representative metasurface applications, involving respectively the properties of angle independence, perfect matching, and diffractionless refraction, and constituting representative examples of state-of-the-art metasurfaces.
1 Introduction
Metasurfaces are subwavelenghtly thick electromagnetic structures that may be used to control the scattering of electromagnetic waves. Because of their subwavelength thickness, they may be considered as the two-dimensional counterparts of volumetric metamaterials. However, compared to metamaterials, metasurfaces offer the advantages of being less bulky, less lossy, and easier to fabricate in both the microwave and optical regimes.
This chapter presents a general description of metasurfaces and metamaterials and the types of electromagnetic transformations that they can realize. Section 1.1 provides a historical perspective on the origin and concept of metamaterials, while Section 1.2 discusses the emergence of metasurfaces along with their applications and synthesis strategies.
1.1 Metamaterials
The origin of the term metamaterial can be traced back to a 1999 DARPA1 Workshop [183], where it was introduced by Rodger M. Walser to describe artificial materials with electromagnetic properties beyond those conventionally found in nature [25, 29, 41, 165]. Obviously, the concept of artificial electromagnetic structure has existed long before the appearance of the term metamaterial. One of the most well-known and ancient examples of metamaterials is that of the Lycurgus cup, dating to the fourth century AD, which is a type of dichroic glass like those used in the conception of stained glass. Back then, the optical properties of glass were tuned by adding various types of metallic powders during its fabrication process but the lack of proper understanding of the interactions of light with matter meant that these processes were essentially made by trial and errors [145].
It is only much later, in the second part of the nineteenth century, that people became properly equipped to study and control the propagation of electromagnetic waves thanks to the newly established theory of electromagnetism of Maxwell [100]. Soon after, near the end of the nineteenth century, Bose introduced what was probably one of the first examples of artificial electromagnetic structures in the form of a polarization rotator made of twisted jute that was supposed to imitate the chiral response of some sugar solutions [20]. Similar types of chiral responses were also introduced by Lindman in the 1910s and 1920s using spiral-shaped resonating structures [94]. The concept of “artificial dielectrics” was then pioneered by Kock in the 1940s, which originally consisted in inserting metallic patches inside layered metal–dielectric media. Based on this principle, Kock realized the first-known artificial microwave delay lens [79]. During the same period, split-ring resonators were proposed by Schelkunoff and Friss as a mean of controlling the permeability of artificial materials [144].
Until the middle of the twentieth century, artificial electromagnetic structures were mostly used as a means of achieving desired values of permittivity, permeability, and chirality within reasonable ranges. It is only since then that more extreme material parameters started to be investigated. For instance, artificial materials with a refractive index less than unity were introduced by Brown in the 1950s [22] while, in the 1960s, Rotman associated
