![conformal mapping philosophy fish and curved space conformal mapping philosophy fish and curved space](https://d22la3wb64sie2.cloudfront.net/generated-thumbnails/47773/3qyq8t_240.png)
The general effects of MTS modulation may be therefore treated in the framework of transformation optics (TO). In fact, the impedance modulation, obtained by locally changing the sizes of the patches, imposes a local modification of the dispersion equation and hence, at constant operating frequency, of the local wavevector. In particular, here it is shown how a proper impedance modulation allows one to address SWs along desired curvilinear paths. In and in many recent papers ( and references therein), emphasis is given to the effect of reflection/transmission and only in minor part to SW propagation and local impedance modulation, which is instead the main focus of this article. The patches are positioned at the centre of the unit cells, whose size is assumed uniform. MTS at microwave frequencies consisting of small patches with variable sizes printed on a grounded slab ( a) isotropic MTS formed by square or circular patches with variable dimensions ( b) anisotropic MTS formed by circular patches with slots or cuts inside. When the element shape contains additional features, like slots, grooves or cuts, the effect is anisotropic and the anisotropy can be easily controlled for elements with two orthogonal symmetry axes ( figure 1 b).įigure 1. When the shape of the elements is regular enough ( figure 1 a), the impedance tensor becomes a scalar and therefore the average effect of the boundary conditions is isotropic with respect to the direction of propagation of the SW. This boundary condition supports the propagation of surface waves (SWs). This leads to the definition of a surface impedance tensor, which links the average tangential electric field to the average tangential magnetic field (electric currents). By averaging the tangential fields, an MTS can be described macroscopically through impedance boundary conditions. In the following, however, we will focus on patch-type MTSs. Alternatively, an impenetrable MTS can be realized by etching small holes on the upper wall of a thin parallel plate waveguide. Impenetrable MTSs, which are those treated in this paper, are realized at microwave frequencies through a dense periodic texture of small elements printed on a grounded slab with or without shorting vias to the ground plane. Its effective properties can be studied for instance by applying Generalized Sheet Transition Conditions (GSTCs), which allow one to characterize an MTS in terms of unambiguous anisotropic sheet impedance. A penetrable MTS (also called metascreen or metafilm) consists of a planar distribution of small periodic scatterers in a very thin host medium or of small holes in a conducting screen. MTSs may be distinguished as penetrable and impenetrable. Metasurfaces (MTSs) are thin metamaterials constituted by an arrangement of printed elements whose dimensions are smaller than the operational wavelength ( figure 1).