IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 10, 2011 1499 Metasurfing: Addressing Waves on Impenetrable Metasurfaces S. Maci, Fellow, IEEE, G. Minatti, M. Casaletti, and Marko Bosiljevac (Invited Paper) Abstract—Metasurfaces constitute a class of thin metamaterials, which are used from microwave to optical frequencies to create new antennas and microwave devices. Here, we propose the use of variable-impedance metasurfaces for transforming surface or guided waves into different wavefield configurations with desir- able properties. We will shortly refer to this metasurface-driven wavefield transformation as “metasurfing.” Metasurfing can be obtained by an appropriate synthesis of inhomogeneous metasur- face reactance that allows a local modification of the dispersion equation and, at constant operating frequency, of the local wave vector. The general effects of metasurface modulation are similar to those obtained in solid (volumetric) inhomogeneous meta- material as predicted by the transformation optics—namely, readdressing the propagation path of an incident wave. However, significant technological simplicity is gained. Several examples are shown as a proof of concept. Index Terms—High impedance surface, leaky waves, metamate- rials, metasurfaces, surface waves. I. INTRODUCTION M ETAMATERIALS have found several applications in designing antennas and microwave components. These artificial materials can be formed by periodic arrangements of many small inclusions in a dielectric host environment for achieving macroscopic electromagnetic or optical properties that cannot be found in nature. After about 10 years from the first pioneering works on metamaterials, the new concept of “transformation optics” (TO) has been recently introduced [1], which establishes criteria to obtain control on optical ray-paths within inhomogeneous anisotropic metamaterials. This control is achieved on the basis of macroscopic equivalent constituent tensors of the anisotropic material. This methodology has been, for instance, applied to design “TO cloaks,” or shells of anisotropic metamaterials capable of rendering any object within their interior cavities invisible to detection from outside (see [2] and references therein). The technological difficulties Manuscript received October 16, 2011; revised December 23, 2011; accepted December 30, 2011. Date of publication January 10, 2012; date of current ver- sion January 30, 2012. S. Maci, G. Minatti, and M. Casaletti are with the Department of Informa- tion Engineering, University of Siena, 50124 Siena, Italy (e-mail: macis@dii. unisi.it; minatti@dii.unisi.it; casaletti@dii.unisi.it). M. Bosiljevac is with the Faculty of Electrical Engineering and Computing, University of Zagreb, 10000 Zagreb, Croatia (e-mail: marko.bosiljevac@fer. hr). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LAWP.2012.2183631 in controlling the variation of the homogenized constitutive tensor of volumetric metamaterials, together with anisotropy and extreme parameters, complicates the engineering imple- mentation of TO in practical devices. Our main starting point is the observation that similar and even more general effects to addressing waves in volumetric media may be obtained by changing the properties of a metasurface that supports surface or guided waves. A metasurfaces is a thin metamaterial layer characterized by unusual reflection properties of plane waves and/or dispersion properties of surface/guided waves. Meta- surfaces may be distinguished as penetrable and impenetrable. A penetrable metasurface (sometimes called metafilm) is constituted by a planar distribution of small periodic elements in a very thin host medium. Its effective properties can be studied for instance by applied generalized sheet transition conditions (GSTCs) [3], which allow a characterization in terms of an unambiguous anisotropic sheet impedance. Impenetrable metasurfaces, those treated in this letter, are obtained by a dense periodic texture of small elements printed on a grounded slab without or with shorting vias. These have been used for realizing electromagnetic band-gaps (EBG) or equivalent magnetic walls [4], [5]. Impenetrable metasurfaces can be also simply constituted by a dense distribution of pins [6] on a ground plane. When the printed elements are not grounded, impenetrable metasurfaces can be characterized in terms of anisotropic surface impedance through the use of the pole-zero matching method [7]. Due to the impenetrability, absence of losses in the dielectric and in the metal implies that the surface impedance loses its resistive part and becomes a surface reactance. This happens for periodicities small in terms of a wavelength. Large periodicity may imply indeed transfer of energy in higher-order modes that can be effectively interpreted as loss [7]. This case is excluded by our treatment. The basic assumption in a metasurface is the periodicity of the elements. In this letter, we indeed remove this assumption dealing with aperiodic elements. The aperiodicity is obtained by gradually changing the geometry of the elements in contiguous cells. This allows for changing the phase velocity and/or the propagation path of the guided wave sustained by the metasur- face. We will synthetically refer to this metasurface-driven wave transformation as “metasurfing.” II. METASURFING Metasurfing (MTS’ng) is introduced here as the transforma- tion of electromagnetic surface/guided waves into a different 1536-1225/$31.00 © 2012 IEEE