Introduction

Over the past 10 years, metamaterials have been the subject of a very extensive interest, as attested by numerous publications in both highly focused and wider public journals. On the one hand, the scientific attention finds its origin in the universal character of metamaterials. Indeed, this general concept can be applied to any physics domain involving the propagation of waves. On the other hand, metamaterials are relevant to everyday life and feed the imagination, especially with applications related to invisibility.

The project of this book was initiated during a thematic school organized by the network GDR ONDES 2451, supported by the French national organization CNRS (Centre National de la Recherche Scientifique) at Oléron from 29 May to 1 June 2012. The purpose of this event was to analyze the impact of the metamaterial approach in various fields of wave research and technologies. As a prospect, starting from an overview of the main research steps, we would like to propose metamaterials as a tool available to scientists and engineers working on the various domains related to the propagation of electromagnetic and acoustic waves. Before discussing the evolution of the metamaterial activity, let us define the metamaterial concept.

A metamaterial is an artificial structure whose dimensions are much smaller than the wavelength of interacting signals. If this condition is satisfied, the metamaterial can be considered as an average media. This media can then be modeled by effective constitutive parameters. For instance, for the domain of electromagnetic waves, a metamaterial is characterized by its effective permittivity eff and permeability This permittivity and permeability in turn describe the response of the metamaterial to electric excitation and magnetic fields, respectively. Following this principle, metamaterials appear like a new degree of freedom in the design of materials because their properties do not only rely on their basic compounds but also on the way these compounds are structured, namely the dimensions and the shape of the inclusions. Depending on these parameters, we can target unusual values of eff and µeff, which give rise to outstanding physical properties like, for instance, the negative refraction if both eff and µeff are negative. In the same manner, we can design the metamaterial structure in order to target very high or, on the contrary, near zero values of the permittivity and permeability.

One limit of this general concept lies in the definition of the metamaterial itself. Indeed, if the structure dimensions are required to be much smaller than the working wavelength, a given metamaterial loses its properties when the frequency is increased. This is due to the fact that the inclusions behave as scatterers when their dimensions are close to the incident signal wavelength. Therefore, the structured nature of a metamaterial is the first limitation of its working bandwidth.

The way to synthesize specific values of constitutive parameters is another source of frequency dispersion. Let us consider the case of electromagnetic material. These structures take their properties, especially artificial magnetism, from resonating inclusions. Because of this resonant behavior, the response of the artificial media to an electromagnetic excitation field strongly depends on frequency. Then, refractive index, for instance, can be negative over a very limited bandwidth.

This frequency dispersion comes along with anisotropy which is related to the arrangement of the structured media. Therefore, the response of a metamaterial to an incident wave depends on its incidence angle and polarization.

Because of these intrinsic dispersions, we can understand that metamaterials remain far behind the dream of an ideal media combining outstanding properties without any frequency, an incidence angle and polarization limitations. Nevertheless, as attested by the following bibliometric data, metamaterials have attracted an increasing interest for more than 10 years with an unquestionable impact on various domains of wave science and engineering.

Figure I.1 illustrates the general evolution of the metamaterial publications since the proposal of the concept at the beginning of the 21st Century. Let us recall that the term “metamaterial” was introduced in 2000 following two former articles by J.B. Pendry heralding the idea of a manufactured material with both negative permittivity and permeability. In the first article, Pendry [PEN 96] showed that the plasma frequency of a metallic medium, which marks the limit between its negative and positive permittivity regimes, can be tuned by means of an adequate structuration. Indeed, whereas the plasma frequency of a bulk metal equals several thousand terahertz, a metallic wire array under the approximation of a homogeneous medium is characterized by a lower plasma frequency, whose value depends on the main geometric dimensions of the array, namely the periodicity and filling factor. This allows for a tuning of the plasma frequency from the bulk metal value down to the lowest frequency range of the electromagnetic spectrum. This article led the way for negative permittivity engineering. In the second article, Pendry [PEN 99] proposed to use arrays of metallic inclusions, each behaving as a resonant current loop, in order to synthesize an effective permeability medium. One of the most exciting properties of such structures is the possibility to target negative values of the permeability close to the fundamental current loop resonance. This article, which marks the beginning of artificial magnetism, opened the way of permeability engineering.

Figure I.1. Evolution of the metamaterials related publications from 2000 to 2012, established from the SCOPUS database

The natural result of these two major contributions is the definition of an artificial material combining negative effective permittivity and permeability over the same frequency band, allowing for the experimental demonstration of negative refraction predicted by V. Veselago back in 1968 [VES 68]. This demonstration was achieved by D.R. Smith et al. in 2001 [SHE 01]. These major theoretical and experimental contributions mark the beginning of metamaterial development, initially motivated by the new prospects of left-handed electromagnetism which were introduced as a mirror image of the right-handed electromagnetism describing the orientation of wave, electric field and magnetic field vectors in positive media, meaning a media where the constitutive parameters and µ are both positive. Left-handed electromagnetism means that if negative values of and µ are considered, the direction of the wave vector is reversed.

In order to further understand the exponential increase of metamaterial-related works observed over the last 10 years, we can analyze the global distribution of publications over several research and application fields. This distribution is depicted in Figure I.2. The selected fields are not exhaustive but they bring a structuring sight on metamaterial short history.

Figure I.2. Distribution of the metamaterials related publications from 2000 to present, established from the SCOPUS database

As a direct prospect of the former publications on left-handed electromagnetism, the first activities were mainly devoted to the synthesis of a negative refractive index medium. This includes both fundamental contributions and efforts toward applications. The left-handed electromagnetism idea has a strong impact on several laws of wave physics. Among them, we can cite the reversal of the Snell–Descartes law, the reversal of the Doppler effect and the reversal of Cherenkov effect [VES 68]. A lot of early articles are related to negative refraction, firstly because negative refraction allows the focus of an electromagnetic signal by means of a flat lens which appears like a new degree of freedom. Following Smith’s first demonstration [SHE 01], many other experimental works have been conducted mainly at microwave frequencies [HUA 04, CHE 05, LHE 08]. Furthermore, negative refraction studies were motivated by the dream of a perfect lens, i.e. a lens able to overcome the diffraction limit responsible for a maximum resolution of roughly half a wavelength. This new possibility was pointed out by Pendry in 2000 [PEN 00], who explained that a negative index media would be able to amplify evanescent waves, thus opening the way to unlimited resolution.

Fundamentally, this article has been the subject of many discussions. Despite these controversies, resolutions under the diffraction limit have been demonstrated, experimentally, from microwaves to optics [GRB 04, FAN 05, FAB 08].

However, we can note in Figure I.2 that the negative refraction and lens curves, initially superimposed and following a linear increase from 2002, are diverging from 2008. This behavior supports several interpretations. First, it should be noted that the synthesis of double negative media implies very important design and technological challenges, especially in optics. Moreover, if we target imaginary applications, the frequency dispersion and anisotropy, mentioned before, are two major issues. These required properties are much more restrictive in the case of the perfect lens proposed by Pendry which is based on an index value equal to –1. Moreover, if we consider the impedance matching condition, which is necessary to minimize the reflection at the edges of the focusing device, both the permittivity ε and...