Controlling Complex Light Propagation and Statistics

In this dissertation, a methodology for experimentally creating and controlling random light in free space and in diffusive media is presented. In free space, we develop and demonstrate the ability to arbitrarily customize the intensity statistics and spatial-correlations of spatially-incoherent light. First, we present a general method for customizing the intensity statistics of speckle patterns on a target plane. Specifically, we show that by judiciously modulating the phase-front of a monochromatic laser beam, we can experimentally generate speckle patterns with arbitrarily-tailored intensity probability-density functions. Then, we experimentally demonstrate and theoretically develop a general method for creating fully-developed speckles with strong ‘non-local’ intensity correlations. The tailored correlations are considered non-local because the functional form of the spatial intensity correlations can be arbitrarily manipulated without altering the field correlations. Afterward, we develop an experimental method for customizing the intensity probability density function of speckle patterns while simultaneously introducing non-local spatial correlations among the speckle grains. The various families of tailored speckle patterns -created by our general method- can exhibit radically different topologies, statistics, and variable degrees of spatial order. Irrespective of their distinct statistical properties, however, all of these speckles are created by appropriately encoding high-order correlations into the phase front of a monochromatic laser beam with a spatial light modulator. In addition to our experimental demonstration, we explore both the theoretical and practical limitations on the extent to which the intensity PDF and the spatial intensity correlations can be manipulated concurrently in a speckle pattern. Finally, we perform a proof of principle super-resolution imaging demonstration; where we design and create bespoke speckle patterns for parallelized nonlinear pattern-illumination microscopy based on fluorescence photoswitching. In our demonstration, we obtain a spatial resolution three times higher than the diffraction limit of the illumination optics in our setup. Furthermore, we show that tailored speckles vastly outperform standard speckles, and therefore, customized speckles are a potent tool in parallelized super-resolution microscopy. In diffusive media, we demonstrate the ability to coherently control wave transport through -and throughout- multiple scattering systems. We develop a unique experimental platform based on the synthesis of nanofabricated on-chip structures and interferometric wavefront-shaping. With our setup, we investigate the fluctuations and correlations of transmission eigenchannel depth profiles in optical diffusive media. Specifically, we find that the depth profiles of high-transmission eigenchannels exhibit low realization-to-realization fluctuations. Furthermore, our experimental and numerical studies reveal the existence of inter-channel correlations, which are significant for low-transmission eigenchannels. Next, using our experimental platform’s unparalleled access to the optical field inside on-chip diffusive structures; we introduce and experimentally investigate the deposition matrix, Z: which maps any input wavefront to its internal field distribution over a specific region. Concurrently, we develop a theoretical formalism to predict the ultimate limitations on energy deposition at any depth inside a diffusive medium. Finally, we introduce the remission matrix, R, which maps the wavefronts input over a finite region of a diffusive medium’s surface to the resulting diffusive waves re-emitted from a displaced region on the same surface. Furthermore, we experimentally demonstrated that remission eigenchannels can enhance the remitted signal strength without sacrificing the penetration-depth of the collected light