Spatially-Discrete Traveling-Wave Modulated Electromagnetic Structures

Abstract

Over the past two decades, metamaterials and metasurfaces have been widely used to provide engineers with material properties that go beyond those found in nature. Metamaterials are engineered structures that can be described by equivalent electromagnetic parameters (like permittivity and permeability). With recent developments in the fabrication of nonlinear materials and devices (GaAs varactor diodes, graphene, BST, etc.), metamaterials with space-time modulated electromagnetic properties are being explored. In contrast to linear, time-invariant (LTI) systems, these structures can support nonreciprocal (one-way) propagation, frequency-conversion, and amplification through parametric modulation. Traveling-wave modulation is of particular interest due to its simplicity. Often, traveling-wave modulation is realized by applying staggered time-modulation signals to a discrete array of unit cells. This modulation is referred to as spatially discrete, traveling-wave modulation (SDTWM), and the constituent time-modulated unit cells are referred to as stixels: space-time pixels. The capability to accurately model spatially-discrete traveling-wave modulated structures is critical to their design. However, analyzing these structures is challenging due to the complex space-time dependence of the stixels. The research presented in this thesis dramatically reduces the complexity of analyzing SDTWM structures by leveraging their inherent space-time periodicity.

A central research contribution of the presented research is the derivation of an electromagnetic boundary condition that has proved fundamental to the understanding and analysis of SDTWM structures: the interpath relation. The interpath relation reveals that the field within a single time-modulated stixel (rather than an entire spatial period) is sufficient to determine the field solution throughout space. Prior to this work, analyzing SDTWM structures would require at least an entire spatial period of time-varying unit-cells to be modeled simultaneously. However, a spatial period can contain a large number of stixels, which can become computationally costly. Thus, when the interpath relation is incorporated as a boundary condition into a numerical solver, electromagnetic simulations that would typically require a high-performance cluster can be performed using a personal laptop. Further, there are some cases of SDTWM where a spatial period cannot be clearly defined. In these cases, the interpath relation becomes necessary in order to characterize the structure. Based on the interpath relation, novel techniques capable of analyzing SDTWM metasurfaces, antennas, and guided wave structures are presented. These techniques are used to characterize and design devices capable of frequency-conversion, non-reciprocal propagation, and amplification. Simulation and measurement results will be shown for representative modulated structures whose capabilities transcend those of LTI systems; leading to new opportunities in applications such as full-duplex communication, reconfigurable electromagnetic devices, and low-noise amplification.