Metamaterial lens tomography

Possibilities of the coherent scanning tomography with negative-index metamaterial lens are studied. Such lens (a slab of negative refractive index material) has the power to focus the source field into a sounded media with dielectric inhomogeneities. By the 2D scanning with a source-receiver system at a number of levels from the lens surface, this focus can be immersed far into the studied region that makes it possible to realize the proposed tomography. The solution of the corresponding inverse scattering problem, i.e., the retrieval of 3D distributions of the complex permittivity in the inhomogeneous region, is based on the solution of the 3D integral equation for the scattered field that is reduced to the one-dimensional Fredholm integral equation of the 1-st kind relative to the depth profile of lateral spectrum of inhomogeneities. After the solution of this equation for each pair of spectral components, the inverse Fourier transform leads to the desired solution. The feasibility of this tomography for low-contrast targets is demonstrated in numerical simulation.