A stable imaging functional for anisotropic periodic media in electromagnetic inverse scattering

The paper is concerned with the inverse scattering problem for Maxwell's equations in three dimensional anisotropic periodic media. We study a new imaging functional for fast and stable reconstruction of the shape of anisotropic periodic scatterers from boundary measurements of the scattered field for a number of incident fields. This imaging functional is simple to implement and very robust against noise in the data. Its implementation is non-iterative, computationally cheap, and does not involve solving any ill-posed problems. The resolution and stability analysis of the imaging functional is investigated. Our numerical study shows that this imaging functional is more stable than that of the factorization method and more efficient than that of the orthogonality sampling method in reconstructing periodic scatterers.