Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

The study of resonances in electromagnetics plays a critical role in the design of optical systems. This dissertation investigates the interaction between resonance and gain in optical structures to establish a universal principle for achieving ultra-low-threshold lasing. Through the analysis of geometric symmetries, material properties, and coupling mechanisms, this research develops prototype structures applicable to a wide range of optical and electromagnetic systems. A range of models is considered, starting from a simple onedimensional string-resonator system (based on the model of H. Lamb), then advancing to two- and three-dimensional waveguide models, and culminating with a realistic high-contrast model in open space. A key finding of this work is that Fano resonance, arising from the interaction of bound states and radiation continua, can be exploited to minimize the power input required to reach the lasing threshold. By balancing radiation losses with an appropriate gain mechanism, Fano resonance allows the lasing threshold to be achieved at very low gain, thus enabling more energy-efficient optical components. This work derives a universal law governing the relation between the Fano interaction strength and gain threshold, which is valid in all of the models analyzed. The proposed framework for gain threshold minimization contributes to the development of ultra-low-power optical technologies, providing optimism for applications in telecommunications, quantum computing, and sensing.

Date

7-14-2025

Committee Chair

Stephen Shipman

DOI

10.31390/gradschool_dissertations.6859

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