Extended sampling method for inverse electromagnetic scattering problems using a single incident wave

We consider the inverse electromagnetic problem to reconstruct an obstacle from the far-field data due to a single incident wave. It is shown that if two obstacles generate identical far-field patterns then they must intersect. Then we construct a novel far-field equation and prove the properties of its solutions, based on which we define an indicator function and propose an extended sampling method (ESM) for the location and support of the obstacle. The ESM is extremely simple to implement and has the ability to process limited aperture data. Numerical examples demonstrate the effectiveness of the method with little prior information and noisy data.