Coherent Control of Spatial Resolution Enhancement with Scalar and Vector Beams

Abstract

This thesis investigates the coherent manipulation of light–matter interactions using scalar and vector beams to achieve controlled enhancement of spatial resolution in atomic and quantum-dot systems. By exploring both linear and nonlinear optical regimes, the work demonstrates how structured light can be harnessed to engineer susceptibility, beam dynamics, and super-resolution imaging. A semiclassical framework is adopted to describe light–matter interaction, beginning with Maxwell’s equations and wave propagation in linear and nonlinear media under the paraxial approximation. The atom–field interaction Hamiltonian is developed within the electric-dipole approximation, and the density-matrix formalism is introduced to analyze quantum coherence effects. Fundamental concepts including exciton–phonon interactions in quantum dots, multi-level atomic systems, vector beam generation, and the resolution limit of stimulated emission depletion (STED) microscopy are also discussed.