Imaging of periodic dielectrics (Q2379364)

The paper deals with the problem of imaging of periodic penetrable structures from measurements of scattered electromagnetic waves. As a model problem, the detection of a periodic interface between two dielectrics in two dimensions is considered. Such a material configuration, called a diffraction grating, is a simple model for a photonic crystal --- a dielectric structure with periodically varying material parameters taking only two values. The presented factorization method is a sampling technique which requires near-field measurements of reflected waves scattered from the periodic dielectric structure for several incident fields. An auxiliary tool is the analysis of the Dirichlet-to-Neumann operators on the periodic interface. Numerical examples illustrating the imaging technique are provided.