On the Superposition and Elastic Recoil of Electromagnetic Waves

Abstract

Superposition demands that a linear combination of solutions to an electromagnetic problem also be a solution. This paper analyzes some very simple problems: the constructive and destructive interferences of short impulse voltage and current waves along an ideal free-space transmission line. When voltage waves constructively interfere, the superposition has twice the electrical energy of the individual waveforms because current goes to zero, converting magnetic to electrical energy. When voltage waves destructively interfere, the superposition has no electrical energy because it transforms to magnetic energy. Although the impedance of the individual waves is that of free space, a superposition of waves may exhibit arbitrary impedance. Further, interferences of identical waveforms allow no energy transfer between opposite ends of a transmission line. The waves appear to recoil elastically one from another. Although alternate interpretations are possible, these appear less likely. Similar phenomenology arises in waves of arbitrary shape and those propagating in free space as well. We may also interpret this behavior as each wave reflecting from the impedance variations the superposition imparts on free space. This work has practical implications to quantum mechanics, field diversity antenna systems, and near-field electromagnetic ranging.