Conformal Transformation Electromagnetics Based on Schwarz-Christoffel Mapping for the Synthesis of Doubly Connected Metalenses

An innovative transformation electromagnetics (TE) paradigm, which leverages on the Schwarz-Christoffel (SC) theorem, is proposed to design effective and realistic field manipulation devices (FMDs). Thanks to the conformal property, such a TE design method allows one to considerably mitigate the anisotropy of the synthesized metalenses (i.e., devices with artificially engineered materials covering an antenna to modify its radiation features) with respect to those yielded by the competitive state-of-the-art TE techniques. Moreover, devices with doubly connected contours, thus including masts with arbitrary sections and lenses with holes/forbidden regions in which the material properties cannot be controlled, can be handled. A set of numerical experiments is presented to assess the features of the proposed method in terms of field-manipulation capabilities and complexity of the lens material in a comparative fashion.