Shifted-frequency internal equivalence

The shifted frequency internal equivalence (SFIE) theorem involving inhomogeneous regions is introduced and proven. For a lossless inhomogeneous region using a vector Green´s theorem and potential formulation, it is shown that the frequency-domain electromagnetic field at frequency ω inside the region can be obtained using a set of equivalent volume and surface currents radiating in free space and at the different frequency ω₀. The equivalent currents thus obtained are functions of the two frequencies, electric- and magnetic-volume-type sources of the original problem, material parameters, and the original field phasors at ω, and they only exist inside the region and on its boundary. A direct application of this equivalence is that it can be used to construct an internal equivalence at a shifted frequency for electromagnetic scattering problems if data are needed in a band of frequency. ω₀ can be kept constant while the incident field frequency changes and, as a result, full computation of fields at each different frequency for volume-type equivalent sources can be avoided