Photon-pair generation in photonic crystal waveguides
In this thesis, I overcome the challenges and fill the gaps in knowledge for the design and analysis of photonic crystal slab waveguides (PCSWs) as spontaneous parametric down-conversion (SPDC) sources of photon-pairs, as well as to investigate their potential for engineering the properties of the photon-pair quantum state. I have developed the required formalism for analyzing both the quantum process of SPDC and its classical counterpart of second-harmonic generation (SHG). In studying SHG, I verified my formalism through comparing its results with direct nonlinear simulations. In these formulations, special attention was given to treating lossy modes, as they prove to be an inherent part of the SPDC designs in PCSWs. Moreover, I have found a practical set of PCSW designs, phase-matched for three-wave-mixing processes, while demonstrating that PCSWs can offer a strong control over the phase-matching configuration. This includes reaching phase-matching between modes of different propagation directions, reaching simultaneous phase-matching between multiple processes, and controlling the group velocity of the modes at the point of phase-matching. These capabilities proved to be the key to discovering the unique strength of PCSWs for the SPDC application. Through the use of various phase-matching configurations, I showed how compact SPDC sources can be designed using PCSWs that are capable of creating entanglement and tuning its extent in different degrees of freedom, with specific examples for path and spectral degrees of entanglement, all in a fully integrated way and directly at the generation step. This work also includes my experimental results on characterizing lithium niobate nanostructured ridge waveguides, demonstrating phase-matched SHG. Finally, I propose the concept of atom-mediated SPDC, for interfacing a single-emitter source with a photon-pair source, relying on the bandgap evanescent modes of a periodic waveguide.