Oblique superposition of two elliptically polarized lightwaves using geometric algebra: is energy–momentum conserved?

Abstract

In this paper, we use Clifford (geometric) algebra Cl(3,0) to verify if electromagnetic energy-momentum density is still conserved for oblique superposition of two elliptically polarized plane waves with the same frequency. We show that energy-momentum conservation is valid at any time only for the superposition of two counter-propagating elliptically polarized plane waves. We show that the time-average energy-momentum of the superposition of two circularly polarized waves with opposite handedness is conserved regardless of the propagation directions of the waves. And, we show that the resulting momentum density of the superposed waves generally has a vector component perpendicular to the momentum densities of the individual waves.