Sampling Representation and Synthesis of Radiated Electromagnetic Fields

This dissertation investigates the sampling representation and synthesis of radiated electromagnetic fields through the lens of inverse scattering theory. The research is bifurcated into two primary thrusts: the optimization of near-field measurement strategies and the systematic design of passive dielectric structures for field shaping. The first part addresses the inefficiencies of conventional planar antenna characterization. By analyzing the operator-theoretic properties of radiation—specifically the compactness of the radiation operator and the step-like decay of its singular spectrum—this work demonstrates that the standard Nyquist-type half-wavelength sampling prescription is often redundant. A warping transformation is proposed to exploit the local spatial bandwidth of the field, enabling the implementation of non-uniform sampling grids. When integrated with sensor selection criteria and prior information, this approach significantly reduces the requisite number of samples while maintaining high fidelity in near-field to far-field transformations. The second part focuses on an inverse design problem: the synthesis of dielectric superstrates to achieve prescribed far-field radiation patterns. This is achieved by coupling a Method of Moments (MoM) forward solver with iterative inversion schemes, including the Born Iterative Method (BIM) and Tikhonov regularization. The resulting algorithm successfully reconstructs spatially varying permittivity profiles that satisfy specific beam masks, even when accounting for the inherent ill-posedness of the scattering operator.