Recently, the complexity behind manipulations of reflected fields by metasurfaces has been addressed, showing that, even in the simplest scenarios, nonlocal response and excitation of auxiliary evanescent fields are required for perfect field control. In this work, we introduce purely local reflective metasurfaces for arbitrary manipulations of the power distribution of reflected waves without excitation of any auxiliary evanescent field. The method is based on the analysis of the power flow distribution and the adaptation of the reflector shape to the desired distribution of incident and reflected fields. As a result, we find that these power-conformal metamirrors can be easily implemented with conventional passive unit cells. The results can be used for the design of reflecting surfaces with multiple functionalities and for waves of different physical nature. In this work, we present the cases of anomalous reflection and beam splitting for both acoustic and electromagnetic waves.

INTRODUCTION

Metasurfaces, the two-dimensional (2D) versions of metamaterials, have opened new possibilities to control scattering of waves, with many applications in thin-sheet polarizers, beam splitters, beam steerers, lenses, and more (1–3). The interest in thin structures capable of controlling and transforming impinging waves increased after the formulation of the generalized reflection and refraction law (GSL) (4), which states that, by using small phase-shifting elements, it is possible to control the directions of reflected and transmitted waves. Among all possible scenarios where metasurfaces can be applied, this work is focused on the analysis of reflective metasurfaces, so-called metamirrors.

In this context, the simplest nontrivial functionality is probably the anomalous reflection, which is the phenomenon of plane-wave reflection in directions different from the specular one. Anomalous reflection can be obtained by using conventional diffraction gratings (blazed gratings), where the energy scattered into each propagating Floquet harmonic is carefully engineered (5–7). The efficiency of these systems, defined as the percentage of the incident power that is sent into the desired direction, can be high only if there is not more than one or two unwanted propagating Floquet modes or in the retroreflection case. Recent studies of the physics of conventional gratings resulted in new possibilities of controlling reflected waves (8, 9). In these systems, by designing the period of the grating, the scattering properties of the constituent inclusions, and the mutual coupling between them, one can engineer the amount of power reflected into different directions. This novel concept, the metagratings, has shown promising results for both anomalous reflection and beam splitting (both systems allow propagation of only three Floquet harmonics). It is important to mention that the unit cells of the inclusions are not necessarily small in comparison with the wavelength and, for these examples, only one element per period gives enough degrees of freedom for controlling the energy distributed into the three harmonics allowed in the system. As the number of propagating harmonics increases, more inclusions have to be considered, and the analytical solutions become too involved, as they must account for interactions of many different inclusions in the unit cell. For this reason, it is difficult to extend this method to more general and complex distributions of fields, where the amplitude, phase, and direction of numerous reflected waves should be fully controlled, or to nonperiodic systems, such as lenses.

Metasurfaces, which allow subwavelength-scale control of fields, have been proposed as an alternative to gratings, potentially offering full control over the reflection directions, when the number of potentially propagating Floquet modes can be arbitrarily large. In the design of metasurfaces, local response of the constitutive elements is commonly assumed. This assumption has two important implications. First, for a given application, the metasurface can be homogenized and the required properties of the constituent elements can be easily found. Second, the constituent meta-atoms can be individually designed. Despite the simplicity of the anomalous reflection problem, which has been extensively studied for electromagnetic (4, 10, 11) and acoustic (12–15) waves, it was only recently that the physics of this wave transformation by metasurfaces was properly understood (16–23). In particular, it was shown that phase-gradient metasurfaces designed on the basis of the generalized reflection law (4) can have high efficiencies only if the deflection angle does not exceed 40° to 45° (18, 21).

To understand the difficulties related to control of reflections from metasurfaces, one can consider power flow in the vicinity of anomalous reflectors. Here, multiple propagating waves with different transverse wave numbers coexist in one medium, and the interference between them results in inhomogeneous power flow profiles, where the power flow vector crosses the metasurface plane. In other words, there will be regions where the power carried by the desired distribution of the incident and reflected waves “enters” the metasurface and other regions where the power “emerges” from the surface. It means that the metasurface requires periodically distributed gain/loss response (17) or strongly nonlocal behavior (9, 16, 18, 20).

It was shown theoretically that the nonlocal properties, required for high-efficiency reflections into arbitrary directions, can be, in principle, realized by carefully engineering the surface reactance profile (20). The first known experimental realizations of perfect anomalous reflectors were based on numerical optimizations (18, 21), because the intrinsically nonlocal behavior of any meta-atom combined with the goal to engineer the nonlocal properties of many interacting meta-atoms complicates the implementation of all nonlocal solutions. The next step toward full engineering of wave reflection is the simultaneous control of two reflected waves. As it was demonstrated in (24), flat beam splitting metasurfaces also require strong nonlocal responses and, consequently, the use of numerical optimizations. Finding possibilities for controlling multiple reflected waves without parasitic reflections using local metasurfaces can open new avenues for the design of highly efficient devices such as holograms or lenses. To recover the local response of the metasurface, Epstein and Eleftheriades proposed the use of auxiliary evanescent fields behind the metasurface as a power-guiding mechanism (19). In this scenario, the required nonlocal interactions between meta-atoms are realized using carefully engineered evanescent fields behind the surface. This solution requires full control of the bianisotropic response of the meta-atoms that can complicate the implementation, especially at high frequencies. In addition, the complexity of the evanescent fields that ensure the nonlocal coupling of meta-atoms will increase for more sophisticated applications.

Here, we study the possibility of creating metamirrors that are capable of reflecting waves into arbitrary directions without parasitic scattering and without the need for any evanescent fields close to the metasurface. In this scenario, the fields in front of the metamirror are perfect combinations of the desired propagating plane waves in the far zone and in the vicinity of the metasurface. Absence of evanescent fields in front of the metamirror implies that the response is local and that it is possible to design metamirrors using analytical formulas, without any further numerical optimization of complex nonlocal structures. We approach the problem by analyzing the distributions of propagating power flow in the desired set of plane waves, not restricting the study to waves of a specific physical nature. Previously, analysis of the power flow distribution has been used for studying surface-relief gratings (6), where the metallic (or dielectric) shape of the grating can be designed to control the energy scattered into a specific diffraction mode. However, these solutions do not ensure exact fulfillment of the boundary conditions on the surface. The method proposed here allows us to design theoretically perfect anomalous reflectors with rather general functionalities. Illustrations are provided for anomalous reflectors and beam splitters. The derivations are made for acoustic and electromagnetic (see the Supplementary Materials) scenarios.