Applications of Mathematical Optics and the Electrodynamics of Nonlinear Media to the Design of Novel Radio Frequency Devices

Abstract

Metamaterials, or engineered materials with properties not found in nature, are at the fore-front of an exciting and rapidly developing inter-disciplinary field of material science that encompasses many sub-fields of physics and engineering. The ability to spatially tailor the wide variety of material properties afforded by metamaterials provides scientists and engineers the capability to create meta-devices with unprecedented and novel capabilities. Paradoxically, added flexibility and an expanded catalog of design degrees of freedom can increase the difficulty in converging to a point design. The added degrees of freedom can risk overwhelming a prospective innovator without advanced methods of analysis to complement their raw inspiration. This dissertation leverages Radio Frequency (RF) metamaterials and the methods of mathematical physics to design and analyze quasi-optical RF devices with novel properties. Two case studies are presented whereby methods and device architectures adapted from optics form the inspiration of new RF devices. The first case study concerns the development of a device that launches non-diffracting Bessel beams. The methods of mathematical optics are applied to synthesize a gradient index lens that forms a Bessel beam from an antenna located at the surface of the lens. The spherical symmetry of the lens lends itself well to the implementation of multiple electrically steered beam systems via placement of a multitude of antennas across the surface of the lens. The performance of the Bessel launcher is analyzed via ray tracing and full wave simulations and found to show decent agreement with a Bessel beam synthesized via standard methods. The second case study concerns the development of a phase conjugator implemented via nonlinear RF metamaterials. The strong magnetic third order nonlinear susceptibility provided by varactor split ring resonator (SRR) media provides a medium with nonlinear properties that dwarf the capabilities of natural materials, which usually display exceedingly linear properties at field levels accessible in typical laboratory settings. The strong nonlinearity is coupled with strong loss, which presents a complicated design optimization problem that spans both material and device level designs. Material level trade studies and optimization is presented to frame the material level problem in terms of device level degrees of freedom. An advanced analysis technique is presented to extract all linear and nonlinear susceptibilities of interest from harmonic balance cosimulation of the full wave structure with a commercially available circuit simulator. A one-dimensional effective medium model for coupled mode propagation in nonlinear metamaterials is utilized to perform a parametric study of the phase conjugation efficiency in a quasi-optical device composed of a distributed SRR medium illuminated with counter-propagating pumps. A parametric study of the saturated gain of the resulting device is studied via harmonic balance cosimulation and found to be limited by fifth order processes in the SRR medium.