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We apply the concept of quasicrystals to metamaterials and experimentally demonstrate metasurfaces with isotropic properties and high resonance strength. By comparing quasicrystalline, periodic, and amorphous metasurfaces we quantify the impact of symmetry on their properties. This is achieved by studying the eigenpolarizations’ ellipticity and circular dichroism induced by mutual coupling of the meta-atoms. The advantage of the quasicrystalline in comparison to a periodic arrangement originates from the ability to reach a higher rotational symmetry in k space, therefore opening a route towards isotropic metasurfaces.

The availability of novel technologies that enable the fabrication of bulk metamaterials made it necessary to develop a theoretical language to discuss their properties appropriately. Here we use the fundamental Bloch mode approximation to explore bulk properties of metamaterials that operate at terahertz frequencies. We demonstrate that this approximation is valid in the case of terahertz meta-foil metamaterials. While relying on theoretical and experimental results, we show that the fundamental Bloch mode approximation can explain minuscule details that are unique to the bulk metamaterial. Various applications such as cylindrical lenses, terahertz cloaks, and sensors will benefit from our analysis.

International audience; The appropriate description of light scattering (transmission/reflection) at a bulky artificial medium, consisting of a sequence of functional metamaterial and natural material films, represents a major challenge in current theoretical nano-optics. Because in many relevant cases, in particular, in the optical domain, a metamaterial must not be described by an effective permittivity and permeability the usual Fresnel formalism cannot be applied. A reliable alternative consists in using a Bloch mode formalism known, e.g., from the theory of photonic crystals. It permits to split this complex issue into two more elementary ones, namely the study of light propagation in an infinitely extended metamaterial and the analysis of light scattering at interfaces between adjacent meta and natural materials. The first problem is routinely solved by calculating the relevant Bloch modes and theirdispersion relations. The second task is more involved and represents the subject of the present study. It consists in using the general Bloch mode orthogonality to derive rigorous expressions for the reflection and transmission coefficients at an interface between two three-dimensional absorptive periodic media for arbitrary incidence. A considerable simplification can be achieved if only the fundamental Bloch modes of both media govern the scattering properties at the interface. If this approximation is valid,which depends on the longitudinalmetamaterial period, the periodic metamaterial may be termed homogeneous. Only in this case the disentanglement of the fundamental modes of both media can be performed and the reflection/transmission coefficients can be expressed in terms of two impedances, each depending solely on the properties of the fundamental mode of the respectivemedium. In order to complement the picture, we apply the present formalism to the quite general problem ofreflection/transmission at a metamaterial film sandwiched between a dissimilar metamaterial. This situation asks for a devoted treatment where multiple modes have to be taken into account.

Metamaterials consist of a periodic or aperiodic arrangement of so-called meta-atoms. Usually their optical properties are derived from the collective response of this ensemble. However, it is highly desirable to deduce them from the scattering properties of individual meta-atoms because frequently the periodic arrangement has a spurious effect on the desired functionality. Moreover, understanding the scattering properties of individual meta-atoms permits introducing guidelines for their design and predicting effective properties of amorphous metamaterials. To achieve this we introduce a genuine approach to quantify the properties of individual meta-atoms. To this end we evaluate spectrally resolved the composition of the rigorously calculated scattered field in terms of contributions of electromagnetic multipoles, such as electric and magnetic dipoles, quadrupoles and, in principle, arbitrary higher order moments. Beyond its direct application to metamaterial's design and characterization, the approach will be significant in the entire field of nanooptics as, for example, for optical nanoantennas.

Although optical metamaterials that show artificial magnetism are mesoscopic systems, they are frequently described in terms of effective material parameters. But due to intrinsic nonlocal (or spatially dispersive) effects it may be anticipated that this approach is usually only a crude approximation and is physically meaningless. In order to study the limitations regarding the assignment of effective material parameters, we present a technique to retrieve the frequency-dependent elements of the effective permittivity and permeability tensors for arbitrary angles of incidence and apply the method exemplarily to the fishnet metamaterial. It turns out that for the fishnet metamaterial, genuine effective material parameters can only be introduced if quite stringent constraints are imposed on the wavelength/unit cell size ratio. Unfortunately they are only met far away from the resonances that induce a magnetic response required for many envisioned applications of such a fishnet metamaterial. Our work clearly indicates that the mesoscopic nature and the related spatial dispersion of contemporary optical metamaterials that show artificial magnetism prohibits the meaningful introduction of conventional effective material parameters.

We show for the first time that a planar metamaterial, an array of coupled metal split-ring resonators with a unit cell lacking mirror symmetry, exhibits asymmetric transmission of terahertz radiation (0.25-2.5 THz) propagating through it in opposite directions. This intriguing effect, that is compatible with Lorentz reciprocity and time-reversal, depends on a directional difference in conversion efficiency of the incident circularly polarized wave into one of opposite handedness, that is only possible in lossy low-symmetry planar chiral metamaterials. We show that asymmetric transmission is linked to excitation of enantiomerically sensitive plasmons, these are induced charge-field excitations that depend on the mutual handedness of incident wave and metamaterial pattern. Various bands of positive, negative and zero phase and group velocities have been identified indicating the opportunity to develop polarization sensitive negative index and slow light media based on such metamaterials., Comment: 5 pages, 6 figures (various minor improvements throughout)

We experimentally and numerically study the propagation of light through amorphous metamaterials. For this purpose we introduce a precisely controllable degree of positional disorder into a perfectly periodic system, transforming it to a partially disordered and ultimately an amorphous metamaterial. The observable spectral features occurring upon this transition and the impact of coherent interactions among neighboring unit cells are revealed. Backed by numerical simulations, the effective properties of the metamaterials are retrieved, most notably for the amorphous one. The most important finding with respect to negative index materials is that their magnetic properties are not affected by an arbitrarily high degree of disorder. This work enables the quantitative evaluation of effective properties of amorphous metamaterials fabricated by bottom-up approaches.

In the past several years, optical metamaterials (MMs) have attracted a considerable deal of interest because it may be anticipated that their properties can be shaped to an unprecedented extent relieving optics from some of its natural limitations. An inevitable first step toward this goal is the evaluation of the optical properties of specifically designed MMs. To date, apart from identifying chiral properties of very specific configurations, this is primarily done in retrieving an effective refractive index---mostly---only for normal incidence. On this basis suggestions for a perfect lens, exploiting this negative refractive index have been put forward by taking advantage of geometrical optics arguments. We show that this approach is pointless for realistic MMs. Instead we prove that the dispersion relation of normal modes in these MMs provides all the required information. Most of the relevant optical parameters, such as refraction and diffraction coefficients, can be derived from this relation. Imaging properties follow straightforwardly from that data. This general approach holds for any optical material, in particular, for all MMs in question. As an example, we apply it to the fishnet structure: one of the most prominent and best studied design approaches to date. We show that both refraction and diffraction properties are strongly spatially and temporally dispersive and they can even change sign. In detail, we study the effect of these peculiarities on imaging and refraction of finite beams. In particular, we discuss both the effect of the specific dispersion relation and the losses on the imaging properties. All our physical predictions are backed by rigorous numerical calculations and the agreement is almost perfect. Ultimately the main conclusion to be drawn is that a negative index of refraction is by no means a sufficient criterion to achieve negative refraction and/or perfect imaging.

We derive the dispersion relation of Bloch modes in a fishnet metamaterial in the optical frequency domain. The dependence of the longitudinal wave vector component on the transverse one and the frequency, which governs diffraction and dispersive spreading of localized light excitations, respectively, are analyzed. We show that this type of metamaterial exhibits an involved anisotropic behavior with diffraction changing the sign in passing even a zero diffraction point. For completeness we derive furthermore a formal angle-dependent effective refractive index which exhibits discontinuities. Thus we conclude that an effective refractive index tends to get meaningless and that only the dispersion relation predicts reliably light propagation in metamaterials. The results are double checked with those obtained from a retrieval algorithm based on angular resolved reflection/transmission data of a finite slab. Excellent agreement is observed.

We introduce a technique to retrieve effective metamaterial parameters for arbitrary angles of incidence. It employs the complex reflection and/or transmission coefficients of a finite slab. Explicit expressions for both polarizations are derived and the constraints to be met for obtaining unique solutions are discussed. The method is applied to the fishnet structure. It turns out that all retrieved parameters strongly depend on the lateral wave vector component due to the complexity of the metamaterial structure. Thus, these parameters are mere wave parameters rather than global material parameters. The physical effects behind this behavior are very likely anisotropy and spatial dispersion.