Metasurfaces (MTSs) constitute a class of thin metamaterials used for controlling plane waves and surface waves (SWs). At microwave frequencies, they are constituted by a metallic texture with elements of sub-wavelength size printed on thin grounded dielectric substrates. These structures support the propagation of SWs. By averaging the tangential fields, the MTSs can be characterized through homogenized isotropic or anisotropic boundary conditions, which can be described through a homogeneous equivalent impedance. This impedance can be spatially modulated by locally changing the size/orientation of the texture elements. This allows for a deformation of the SW wavefront which addresses the local wavevector along not-rectilinear paths. The effect of the MTS modulation can be analysed in the framework of transformation optics. This article reviews theory and implementation of this MTS transformation and shows some examples at microwave frequencies.
This paper presents an effective approach for the derivation of the 2D frequency-wavenumber dispersion surface of anisotropic metasurfaces (MTSs) consisting of elliptical patches printed over a grounded slab. These MTSs are important in the design of leaky-wave antennas and Transformation Optics surface-wave based devices. The formulation resorts to an analytical expression of the currents excited on the element of the periodic texture to define a reduced spectral MoM procedure with only three basis functions. An exact compact formula, which links the MoM matrix to the homogenized equivalent anisotropic impedance of the MTS, is derived. The formulation presented here has been found accurate and useful for designing MTS antennas and Transformation Optics devices.MENCAGLI et al.:SURFACE WAVE DISPERSION FOR MTS 2 decreased and/or the magnitude of the transverse wavenumber is increased [17], [18]. As a result, the proposed approach provides an excellent accuracy in the description of the MTS dispersion characteristics all over the irreducible Brillouin region. At the same time, it provides intuitive physical insight and practical design-oriented equivalent circuits. The equivalent circuit derivation is performed here with a new formulation which, under "homogenization" conditions, allows one to extract the dominant quasi-static capacitances and inductances of the MTS.The paper is articulated as follows. Section II presents the analytical expression of the basis functions for elliptical patches. Section III describes an effective spectral domain procedure for the derivation of the 2D dispersion surface of the MTS and formulates the extraction of the dominant capacitances and inductances at low frequency (section IIIC). Section IV presents numerical results. Finally, conclusions are drawn in Section V. TM TE TM TE J J j k a f k J f k J g k J f k J g k
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