A Super-Resolving Near-Field Electromagnetic Holographic Method

In this work, we study the problem of characterizing electromagnetic radiation from given near-field electromagnetic measurements on an arbitrarily shaped surface. Due to the evanescent waves present in the near-field data the inversion procedure requires special treatment in order to recover a stable physical solution. Our proposed approach to this challenging inverse problem is to seek a sparse decomposition of the fields into elementary electric and/or magnetic dipole on an equivalent source surface. As we show in this paper the incorporation of a sparsity constraint during the inversion process yields impressive stability and accuracy. Additionally the method exhibits a remarkable ability to image and identify point like dipole sources even when spaced closer than a fraction of the wavelength from each other. The proposed inversion procedure is very simple to implement, is easily adaptable to arbitrary surfaces, and is relatively fast even with dense grids. These features make the proposed method suitable for a complete on-the-spot electromagnetic radiation analysis; a capability in which many applications rely on. Proof of concept for this work is established through simple numerical experiments, and from physical measurements taken for a slotted radiating cylinder.