Semianalytical methods in the design of transparent metasheets with applications to microwave radomes

Abstract

In recent years, metamaterials have been attracting immense attention in electrical and optical engineering. These are artificial materials which are engineered to shape the electromagnetic responses and properties. Metamaterials are realized by the adjustment of many electrically small inclusions in a dielectric substrate. Changing size, position and shape of those particles affects the electromagnetic response. Two-dimensional metamaterials are called metasheets, and their application to microwave radomes is the subject of this study. While there exist closed expressions for the scattering parameters of some geometrical structures, for others such expressions cannot be found and only full-wave simulations can be used. Despite its geometrical simplicity, the circular ring inclusion belongs to the latter group. A dimensional parametric analysis with full-wave simulations is performed in this thesis to understand the electromagnetic response of an infinite planar periodic array of circular rings. An important aim of this thesis is to find a way of controlling microwave transmission through metasheets realized as periodic planar arrays of circular inclusions. As the transmission is dominated by the geometrical parameters of the circular inclusions, it is useful to find an analytical expression for the transmission coefficient as a function of those geometrical parameters. This expression cannot be derived from first principles. Thus, an empirical expression with free parameters is proposed to describe the transmission behavior of the metasheet by using the results of full-wave simulations at discrete values of the geometrical parameters of the ring inclusions. The free parameters are determined by fitting so that the simulated values for the transmission coefficient are recovered in the best way. As an application of this semianalytical method, a metasheet (metalens) compensating the phase distortions of a hemispheric radome for a fixed frequency in the Ka-band is designed. The phase distortions are calculated by ray tracing and the resulting fields are incident on the metasheet. The electric fields transmitted through the finite electrically large metasheet are calculated by Physical Optics (PO) upon homogenization of the metasheet. To check the accuracy of the approach, the method is firstly applied to a circular finite electrically large metasheet with circular rings as inclusions. In order to decrease the complexity of the calculation, the equivalent surface currents are calculated by using the tranmission coeffcient of the homogenized metasheet, and cylindrical coordinates are chosen to reduce the two-dimensional integral to a line integral over the rim of the metasheet. In the PO calculation for the hemispheric radome, the PO integration surface is subdivided into small facets, followed by an expansion in Taylor series of the phase part of the free-space Green function, which permits analytical integration. The approach provides a good estimation of the electromagnetic response of the metalens, which is confirmed by measurements.