Indiana University-Purdue University Indianapolis (IUPUI) / The tight-binding model that has been used for many years in condensed matter physics, due to its analytic and numerical tractability, has recently been used to describe light propagating through an array of evanescently coupled waveguides. This dissertation presents analytic and numerical simulation results of light propagating in a waveguide array. The first result presented is that photonic transport can be achieved in an array where the propagation constant is linearly increasing across the array. For an input at the center waveguide, the breathing modes of the system are observed, while for a phase displaced, asymmetric input, phase-controlled photonic transport is predicted. For an array with a waveguide-dependent, parity-symmetric coupling constant, the wave packet dynamics are predicted to be tunable. In addition to modifying the propagation constant, the coupling between waveguides can also be modified, and the quantum correlations are sensitive to the form of the tunneling function. In addition to modifying the waveguide array parameters in a structured manner, they can be randomized as to mimic the insertion of impurities during the fabrication process. When the refractive indices are randomized and real, the amount of light that localizes to the initial waveguide is found to be dependent on the initial waveguide when the waveguide coupling is non-uniform. In addition, when the variance of the refractive indices is small, light localizes in the initial waveguide as well as the parity-symmetric waveguide. In addition to real valued disorder, complex valued disorder can be introduced into the array through the imaginary component of the refractive index. It is shown that the two-particle correlation function is qualitatively similar to the case when the waveguide coupling is real and random, as both cases preserve the symmetry of the eigenvalues. Lastly, different input fields have been used to investigate the quantum statistical aspects of Anderson localization. It is found that the fluctuations in the output intensity are enhanced and the entropy of the system is reduced when disorder is present in the waveguides.

Indiana University-Purdue University Indianapolis (IUPUI) / Adaptive optics-optical coherence tomography (AO-OCT) is a non-invasive method of imaging the human retina in vivo. It can be used to visualize microscopic structures, making it incredibly useful for the early detection and diagnosis of retinal disease. The research group at Indiana University has a novel multi-camera AO-OCT system capable of 1 MHz acquisition rates. Until this point, a method has not existed to process data from such a novel system quickly and accurately enough on a CPU, a GPU, or one that can scale to multiple GPUs automatically in an efficient manner. This is a barrier to using a MHz AO-OCT system in a clinical environment. A novel approach to processing AO-OCT data from the unique multi-camera optics system is tested on multiple graphics processing units (GPUs) in parallel with one, two, and four camera combinations. The design and results demonstrate a scalable, reusable, extensible method of computing AO-OCT output. This approach can either achieve real time results with an AO-OCT system capable of 1 MHz acquisition rates or be scaled to a higher accuracy mode with a fast Fourier transform of 16,384 complex values.