Quantum optics of structures with extreme dielectric confinement

In this thesis, I study dielectric structures with great sub-wavelength confinement, termed extreme dielectric confinement (EDC), and deal with their design and quantum optical properties through finite element and finite-difference time-domain calculations. I begin with a short background on these novel structures in a first introductory section, where I also discuss the content and purpose of this work. In part I, I start by introducing the quasinormal mode (QNM) formulation, which is fundamental for both parts I and II. I then describe and motivate the intuitive design simplification approach I have used to derive simpler designs from original complicated topology-optimized designs. In the following chapter, I use QNMs for calculations using first-order perturbation theory, showing that an EDC structure is extremely sensitive to local perturbations to its bowtie. In the final chapter, I introduce three numerical methods for calculating the point dipole response, and I calculate the spontaneous emission factor of EDC structures by comparing the singlemode response to the total response, showing that the beta factor is close to unity for a broad spectral region and in a relatively broad spatial region around the bowtie. In part II, I introduce the challenge of deterministic quantum dot (QD) fabrication, and suggest creating a lithographically defined quantum dot in the region of the bowtie hotspot. The motivation in doing this is to address deterministic fabrication, and to take advantage of the high radiative enhancement to improve the performance of etched quantum dots, that have historically suffered from high non-radiative rates. By modifying the central bowtie feature, we can achieve localized, finite-lifetime electronic states in the region of the optical hotspot, enabling simultaneous optical and electronic confinement. I introduce a method for calculating the coupling strength between the exciton in the mesoscopic dot and the optical field, resulting in an intuitive overlap integral with simple selection rules for allowed radiative transitions. In the last chapter, I describe one possible design process and the characterization of the resulting device in terms of radiative rate and radiative quantum efficiency. In Part III, I explore dynamics of QDs placed in a bowtie cavity, using a selfconsistent Maxwell-Bloch - FDTD (MB-FDTD) solver. I first generally discuss the validity of the semiclassical approach, introduce the concepts of non-Markovianity and the rotating-wave approximation, and describe the self-consistent MB-FDTD solver while outlining some numerical challenges. I then show transient Purcell factor dynamics for a single QD coupled to a low-Q bowtie cavity – transient enhancement and suppression for a single short exciting pulse, and oscillatory dynamics under periodic pulse excitation. Additionally, I compare these results with Markovian Master equation results and show that the MB-FDTD solver captures counterintuitive features that are not present in the Markovian solution.