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

TL;DR

This paper introduces a conformal transformation electromagnetics method based on Schwarz-Christoffel mapping for designing metalenses with reduced anisotropy and complex doubly connected geometries, enhancing field manipulation capabilities.

Contribution

It presents a novel TE design approach using Schwarz-Christoffel mapping that effectively handles doubly connected contours and reduces anisotropy in metalenses.

Findings

Mitigates anisotropy in metalenses compared to existing TE methods

Enables design of devices with complex doubly connected geometries

Demonstrates improved field manipulation through numerical experiments

Abstract

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.