A high-order perturbation approach to profile reconstruction: I. Perfectlyconducting gratings

A new method for the reconstruction of two-dimensional periodic structures from scattered far-field data is presented. The approach is based on the re cently developed 'methods of variation of boundaries' (MVB) for the solutio n of forward-scattering problems. Here, the inverse problem is formulated a s that of minimization of an appropriate nonlinear least-squares cost funct ional J. The analytic continuation ideas inherent to MVB are then advanced to enable a global line search at each step of a proposed conjugate gradien ts algorithm. Through a number of numerical examples it is demonstrated tha t such globalization may be necessary to overcome the non-convexity of J wh ich, in rum, is shown to persist even when the global minimizer is known to be unique.