A Nonlinear Least Squares Framework for Periodic Grating Identification with a HOPS Implementation

This thesis focuses upon the scattering of time-harmonic plane waves by a periodic interface. In particular, we consider an inverse problem which involves reconstruction of the interface when provided with measured scattered field quantities along an artificially imposed "transparent" boundary layer close to the interface. Appealing to a High-Order Perturbation of Surfaces methodology coupled with a Nonlinear Least Squares framework, we numerically simulate the scattered field at the "transparent" boundary using the former and ultimately reconstruct the interface using the latter. We furnish numerical results which compare favorably to alternative methodologies employed to solve related inverse problems, and demonstrate the efficiency and accuracy of our numerical schemes.