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Dispersion Engineering of Microwave and High-power Devices with Exceptional Points of Degeneracy

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In a world where high-speed communications and energy-aware electronic devices are becoming ubiquitous, efficient electromagnetic (EM) radiation sources remain vital. A precision oscillation frequency, high output power, and high efficiency are all coveted properties in EM oscillators, as well as low phase noise and a small form factor to fit into ultra-small but densely packed devices. This dissertation’s main focus is on a new class of electromagnetic/RF devices, primarily oscillators, which rely on dispersion engineering utilizing the slow-light phenomenon associated with exceptional points of degeneracy (EPD).

An EPD is formed in the parameter space of the dynamical system when two, or more, physical eigenstates coalesce into a degenerate eigenstate and bifurcate when a parameter is varied. A coupled transmission line (CTL) theory is established which provides a paradigm for dispersion engineering concepts at radio frequencies based on EPDs. A special fourth-order EPD, so-called degenerate band edge (DBE) occurs in an infinitely long and lossless periodic system that, given proper operational condition, four of its eigenstates coalesce. In practice, since the DBE ideal condition of having an infinitely long and lossless periodic system is impossible, the operation of a finite-length periodic device near the DBE ideal condition can lead to unique and beneficial properties such as enhanced quality factor and giant gain enchantment. A figure of merit is developed to assess the practical occurrence of fourth-order EPDs in CTLs with tolerances and losses.

First, experimental observation of the DBE is demonstrated in microstrip CTLs at microwaves even in the presence of fabrication tolerances and dissipative losses. We further introduce the “gain and loss balance" regime in CTLs as a mean of recovering an EPD in the presence of radiation and/or dissipative losses, without necessarily resorting to Parity-Time (PT)-symmetry regimes. Second, a new class of distributed oscillators is introduced by engineering the dispersion of two-coupled periodic waveguides to exhibit a DBE. The distributed DBE oscillator is realized in periodic CTLs with a unique mode selection scheme that leads to a stable single-frequency oscillation, even in the presence of load variation. We demonstrate its performance through full-wave transient simulations. Moreover, we introduce a general theoretical framework to exhibit EPDs for applications that incorporate discrete distributed coherent sources and radiation loss elements, such as a waveguide comprising of uniform lossless segments together with discrete gain and radiating elements.

Finally, we harness the dispersion engineering concept to conceive different DBE slow-wave structures (SWSs) for highly efficient electron-beam-driven oscillators. A DBE oscillator (DBEO) is demonstrated for sub-terahertz frequency where the DBE operation synchronization regime was manifested through particle in cell (PIC) simulations. Moreover, an accurate traveling wave tube analytic (TWT) model is constructed based on the Lagrangian field theory as a mean to recover the complex-valued dispersion diagram and the information of hot eigenmodes in a full-interactive TWT. A helical-based TWT analytical model was reconstructed and the agreement between the analytical model and CST-PIC simulations results was remarkable.

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