The coupling of light to ensembles of strongly interacting Rydberg atoms via electromagnetically induced transparency (EIT) has emerged as a particularly promising approach towards quantum nonlinear optics, allowing freely propagating photons to acquire long-ranged effective interactions of unprecedented strength. This thesis explores different photon interaction mechanisms enabled by this general approach, and examines how these can be utilized for various different practical applications. Considering dissipative photon interactions, we first examine the effect of blockade-induced photon scattering on the spatial coherence of collective Rydberg excitations stored in an atomic medium, and how this influences the efficiency of photon storage and retrieval. Based on this developed understanding, we examine the performance of single-photon switching capabilities enabled by dissipative scattering and establish optimized switching protocols over a range of parameters. We then generalize this to consider the many-body decoherence of multiple stored excitations. Here we identify a correlated coherence protection mechanism in which photon scattering from one excitation can preserve the spatial coherence of all others in the medium, and consider the utility of this effect for implementing robust single-photon subtraction. We then outline a new approach towards coherent quantum nonlinear optics via Rydberg-EIT, in which the emergent photon interaction features intrinsically suppressed photon losses. The underlying idea exploits Rydberg blockade to modify rather than break EIT conditions for multiple photons in close proximity, the effect of which alters the underlying dispersion relation of light propagation in a coherent fashion. We devise a specific implementation of this general mechanism fostering a reflective optical nonlinearity and discuss how this can enable efficient single-photon routing with a multitude of unique practical applications.

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Silicon photonics has been widely recognized as a key technology that enables guiding, modulating, detecting, and computing of light in silicon chips. Photonic chips can be fabricated in a similar fashion as microelectronic chips, leveraging the mature CMOS fabrication and metrology infrastructure. Extending this technology, this dissertation focuses on two different areas : silicon microresonator-based mid-infrared light sources, and efficient strain engineering of the bandgap of two-dimensional materials. First, we review the basic theory of waveguides and ring resonators, laying the groundwork for the rest of the dissertation. Second, nonlinear optics is introduced with an emphasis on third order nonlinear phenomena including four wave mixing, the basis for Kerr frequency comb generation. Third, starting with the basic theory of lasers, we present the basic principles of quantum well lasers, leading to the discussion of quantum and interband cascade lasers. Fourth, we demonstrate a simple approach to generate mid-infrared frequency comb using a passive high-Q microresonator as well as an over one million quality factor silicon microresonator at 4.5 ?m. The novel suspended inverse taper with sub-3dB coupling loss is reported. Fifth, we demonstrate a compact narrow-linewidth widely-tunable mid-infrared laser using a high-Q external on-chip cavity. Lastly, we demonstrate highly efficient modulation of transition metal dichalcogenide monolayers (TMD) monolayers as well as TMD monolayer integrated on a silicon nitride waveguide. Additionally, we present a heterogeneous integration platform based on a thin polymer, which allows bonding as well as in principle, evanescent coupling between the two substrates.

An optical frequency comb is a structure of equidistant, coherent spectral components which can be thought of as a large array of individual phase-locked laser sources. Their utilization in precision spectroscopy garnering part of the 2005 Nobel prize, optical frequency combs constitute a relatively novel technology with a large number of potential and actual applications. The research interest grew further with the 2007 discovery of comb structures in microresonators enclosing a nonlinear Kerr medium pumped by an external continuous wave laser, offering both substantially wider combs and the prospect of chip-scale integration. In this thesis work, the modeling of frequency comb spectra generated through optical Kerr cavities is considered using both an Ikeda map and the mean-field Lugiato-Lefever equation to describe the intracavity field evolution. Derivations of these mathematical models are first reviewed alongside relevant physics. They are then treated analytically to constrain model parameters to regions of interest in the context of Kerr-comb dynamics. Finally, numerical parameter sweeps are conducted in both models with respect to the pump power and frequency detuning, where the Ikeda map is additionally examined in the high-energy regime not faithfully described by the Lugiato-Lefever equation. The produced phase diagrams reveal a complex landscape of dynamics including Turing patterns, temporal cavity solitons, breathers and chaos. Ikeda map parameters in the high-energy regime capable of supporting previously reported super energetic cavity solitons are also investigated. Lastly, the numerical simulation package developed for parameter sweeps is presented.

<p>This study examined the self-trapping of light emitted by a miniature green laser in a photopolymerizable medium and the interactions between two parallel-propagating self-trapped beams. The work included the design and fabrication of an Intra-Cavity Frequency-Doubling (IC-FD) Nd: YVO₄/MgO: PPLN miniature green laser with a stable and tunable output intensity. Emission from this laser enabled a systematic examination of self-trapping phenomena at incident intensities spanning 8 orders of magnitude (3.2× W·cm^-2to 6368 W·cm^-2). When launched into a photopolymerizable medium, light emitted by the miniature green laser self-trapped by initiating polymerization and corresponding changes in refractive index along its propagation path. The evolution and dynamics of the self-trapped beam corresponded to the behaviour of self-trapped beams of coherent light. Interactions between a pair of parallel-propagating self-trapped beams were also characterised at a range of intensities. This study shows that the miniature green laser is an efficient, coherent source with a large range of output intensities for the excitation of self-trapped beams. This opens opportunities for its incorporation into small-scale optical systems designed to operate based on the generation and interactions of self-trapped beams.</p> / Master of Applied Science (MASc)