Engineering structured light across linear, nonlinear, and quantum regimes

Abstract

The spatial structure of the electromagnetic field has emerged as a fundamental degree of freedom in modern optics, enabling advanced applications in imaging, micromanipulation, and information processing.This thesis investigates the generation, manipulation, and application of complex spatial modes across the linear, nonlinear, and quantum optical regimes. Central to this exploration is the use of digital holography via spatial light modulators (SLMs) to provide dynamic, high-fidelity control over the phase and amplitude of optical fields. In the linear optical regime, we establish the theoretical and experimental framework for synthesizing structured light arrays in free space. Building upon this foundation, we address the fundamental challenge of deterministic light propagation through highly disordered, scattering media. By retrieving the complex-valued transmission matrix using a reference-less feedback system, we achieve precise control over highly scattered light. This capability is extended into three-dimensional space, enabling the point-by-point construction of volumetric architectures and diffraction-limited interference patterns directly within speckle fields. Transitioning into nonlinear optics, we explore the multiplicative spatial interactions inherent in second-harmonic generation. By intentionally introducing astigmatic aberrations into a Bessel-Gauss pump beam, we discover the emergence of a novel class of structured light fields, termed "Gamma-dots." The characterization of these nonlinearly generated beams reveals unique propagation dynamics, distinct symmetry at the focal plane, and robust self-healing properties. These results demonstrate how nonlinear processes can transform geometric spatial aberrations into a highly structured, resilient optical field. Finally, we extend these spatial control techniques to the quantum limit. We integrate wavefront shaping with spontaneous parametric down-conversion (SPDC) to engineer the non-local spatial correlations of entangled photon pairs. Leveraging the high-dimensional Hilbert space of these spatial modes, we propose a hybrid quantum microscopy system that independently combines wide-field spatial acquisition with the precise temporal resolution of single-photon event recorders. This platform paves the way for single-photon tracing, sub-shot-noise imaging, and the study of entanglement transfer between different systems. Ultimately, this progressive mastery of spatial modes—from overcoming complex linear scattering to harnessing nonlinear transformations and quantum entanglement—provides a unified framework for robust modal engineering. The methodologies developed herein offer new avenues for deep-tissue microscopy, stable particle manipulation, and the next generation of quantum optical technologies.