## Computational Modeling of Photonic Crystal Microcavity Single-Photon Emitters

#### thesis

In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.

Conventional cryptography is based on algorithms that are mathematically complex and difficult to solve, such as factoring large numbers. The advent of a quantum computer would render these schemes useless. As scientists work to develop a quantum computer, cryptographers are developing new schemes for unconditionally secure cryptography. Quantum key distribution has emerged as one of the potential replacements of classical cryptography. It relies on the fact that measurement of a quantum bit changes the state of the bit and undetected eavesdropping is impossible. Single polarized photons can be used as the quantum bits, such that a quantum system would in some ways mirror the classical communication scheme. The quantum key distribution system would include components that create, transmit and detect single polarized photons.

The focus of this work is on the development of an efficient single-photon source. This source is comprised of a single quantum dot inside of a photonic crystal microcavity. To better understand the physics behind the device, a computational model is developed. The model uses Finite-Difference Time-Domain methods to analyze the electromagnetic field distribution in photonic crystal microcavities. It uses an 8-band k · p perturbation theory to compute the energy band structure of the epitaxially grown quantum dots. We discuss a method that combines the results of these two calculations for determining the spontaneous emission lifetime of a quantum dot in bulk material or in a microcavity. The computational models developed in this thesis are used to identify and characterize microcavities for potential use in a single-photon source. The computational tools developed are also used to investigate novel photonic crystal microcavities that incorporate 1D distributed Bragg reflectors for vertical confinement. It is found that the spontaneous emission enhancement in the quasi-3D cavities can be significantly greater than in traditional suspended slab cavities.