A time harmonic electromagnetic (EM) source inside a 2D metallic cavity is considered. Scatterers of known geometry and dielectric constants are present inside the cavity. These scatterers alter the fields in the cavity. The coordinates of the source are unknown, while those of the scatterers are given. The magnitude of the resulting electric field is measured at certain locations in the cavity. The goal is to locate the source from these magnitude-only measurements. As there is only one source, its localization is formulated as a sparse source reconstruction problem. The 2D metallic cavity is discretized using a Finite Difference scheme. Determination of the source location is posed as a constrained minimization problem with the cost being the norm of the error between the measured and the simulated sumulated (obtained using the discretized Maxwell's equation). An additional L1 regularization is added to the cost to impose sparsity. Linear constraints based on the principle of Electromagnetic Time Reversal (EMTR) are derived and enforced. Numerical results are presented for random choices of measurement locations. Numerical experiments suggest that the source can be localised with measurements taken at 5% of the total points on the search grid.

This paper presents a method for localization of a time-harmonic source in a cavity with magnitude-only measurements using the principles of electromagnetic time reversal. A time-harmonic point source that radiates an electromagnetic field at a specific frequency is considered. The source is assumed to be at an unknown position within the cavity. Scatterers of known geometry and dielectric constants present in the cavity alter the source field. The magnitude of the electric field is measured at certain locations within the cavity. Using these magnitude measurements, the position of the source is determined. Linear constraints based on electromagnetic time reversal are derived. These constraints depend only on the magnitude of electric fields. A convex optimization problem minimising the L1 norm subject to the derived linear constraints is formulated. The Matching pursuit algorithm is used to solve the optimization problem. The solution to this optimization problem reveals the source location. The proposed method is validated by numerical experiments in both 2D and 3D cavities. Numerical results suggest that it is possible to localize a time-harmonic point source with three magnitude-only measurements (despite having many scatterers).