Electromagnetic surface and line sources under coordinate transformations

Although the analysis of electromagnetic sources in the context of coordinate transformations and the implications for transformation optics have been discussed in the literature, a correct formulation that includes surface and line currents has not been reported. Here we derive how surface and line currents behave under coordinate transformations and validate the analysis through numerical validation of a specific example. This analysis enables transformation optics to be applied to problems that include singular source distributions, which is often the case for practical radiating systems and antennas, to make a given current distribution produce the same fields as a different current distribution by surrounding it with a material with specific electromagnetic properties.