Circuit-based Modeling and Inverse Design of Metastructures

Abstract

During the past several decades metamaterials and metastructures research has provided a valuable set of tools for designing devices with extreme control over electromagnetic wavefronts. Both metamaterials and metastructures use subwavelength features to control the electromagnetic response, but they require different design methodologies. Metamaterials are composed of subwavelength scatterers with subwavelength spacings that can be characterized using effective material properties. Design methods for metamaterial-based devices typically rely on equivalent material properties that are locally periodic (possess slowly varying subwavelength features) to perform field transformations. Metastructures, on the other hand, share many of the same features as metamaterials, but they do not require the existence of an equivalent effective medium. As such, metastructured devices require design methods that model individual scattering elements and are capable of modeling devices with local aperiodicity and fast variations in subwavelength features. This makes the development of practical and accurate design methods for metastructures a challenging task.

This dissertation presents recent developments in methods for modeling and designing metamaterial devices and metastructures using concepts from microwave network theory. The presented modeling and design approaches build on earlier work in ac{TL}, or circuit-based metamaterials, that were used to realize guided-wave negative index metamaterials, hyperbolic metamaterials, and transformation optics designs. In the first part of this work, the range of effective material properties in circuit-based metamaterials is extended to include 2D omega bianisotropic responses. In the second part, an efficient computational inverse design tool is developed that utilizes the large degrees of freedom that metastructures provide to design multi-input multi-output metastructures. The efficiency of the design procedure is enhanced through the use of a fast forward problem solver and the adjoint variable method. The fast forward problem solver avoids the use of full-wave solutions through the use of reduced-order models and circuit theory. The adjoint variable method enables efficient gradient calculations in the large design variable space that metastructures provide.

The design procedure is then verified experimentally through the realization of a printed-circuit beamformer for a multi-beam antenna system operating at 10 GHz. The multi-beam antenna system produces nine orthogonal radiation patterns that are excited from nine input ports that are impedance match and isolated. Two examples of beamformers are designed. The first design exhibits positive refraction and the second exhibits negative refraction. The measured antenna system fed by the positive refraction beamformer has a minimum return loss of 18.1 dB, a minimum input isolation of 19.2 dB and a radiation efficiency of -2.7 dB at the frequency of operation. The measured antenna system fed by the negative refraction beamformer has a minimum return loss of 11.6 dB, a minimum input isolation of 21.3 dB and a radiation efficiency of -2.8 dB at the frequency of operation.