Linear Superposition Effect at Sources and in Waves

Abstract: The superposition law (SL) sums the components of electromagnetic (EM) waves at each spatial point when these waves meet in space. In contrast, the energy conservation law requires energy to be summed in the quadratic form of the EM fields. The mathematical discrepancy of the two laws can lead to different physical results. Specifically, when two co-phase radiation dipoles are placed in close proximity, their radiation waves undergo a co-phase interference throughout space, therefore causing a net increase in wave's power globally. In the exploration of this, we find that the SL applies not only to waves, but also to the radiation dipoles. By defining the superposed dipole conceptually, we describe the effective radiation power that is twice the power-sum of the two waves, providing a comprehensive understanding of the SL, which is supported by the results of the previous theoretical and experimental studies.