Linear Superposition Effect at Sources and in Waves

TL;DR

This paper investigates the superposition law in electromagnetic waves and dipoles, revealing that superposition can lead to an effective radiation power twice the sum of individual powers, challenging traditional energy conservation perspectives.

Contribution

It introduces the concept of superposed dipoles, demonstrating that superposition effects extend beyond waves to dipoles, and clarifies the physical implications of superposition law versus energy conservation.

Findings

Superposition law applies to both waves and dipoles.

Effective radiation power can be twice the sum of individual powers.

Supports previous theoretical and experimental results.

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.