Analytical algorithms for direct and inverse problems pertaining to the electromagnetic excitation of a layered medium by N dipoles

The direct problem of exciting a multilayered spherical medium by a distribution of arbitrarily located (internal and external) electric dipoles is considered. A formulation based on excitation operators is adopted. The solution of the direct problem is obtained by means of an overall superposition method that combines elements of the T‐matrix approach, the Sommerfeld's method, and Green's functions' techniques. Approximations are extracted for the obtained far‐field patterns in the long‐wavelength (low‐frequency) regime. A set of source‐localization inverse problems is considered. Analytical algorithms are devised in which nonlinear systems are obtained from specifically selected low‐frequency far‐field measurements. These systems are subsequently solved explicitly including all special cases. The developed algorithms are noninvasive and can determine accurately the characteristics of internal sources.