Angular momentum of the electromagnetic field: the plane wave paradox resolved

2005/04/13 by A. M. Stewart · 1 voice
Physics and Astronomy · #physics.class-ph

paper · pdf · doi:10.1088/0143-0807/26/4/008

published as European Journal of Physics Vol 26, 635-641 (2005) · 12 pages, 1 figure

arxiv created 2005/09/09 · arxiv updated 2009/12/01

Abstract

The angular momentum of a classical electromagnetic plane wave of arbitrary extent is predicted to be, on theoretical grounds, exactly zero. However, finite sections of circularly polarized plane waves are found experimentally to carry angular momentum and it is known that the contribution to the angular momentum arises from the edges of the beam. A mathematical model is described that gives a quantitative account of this effect and resolves the paradox.

Discussions

• $\newcommand{\bv}[1]{\boldsymbol{#1}}$ Plane Waves Let's first address the case of a circularly polarized plane wave. Consider $$ \bv{J}^{(1)} = \epsilon_0 \int \bv{r}\times(\bv{E}\times\bv{B})d^3\bv{ [stackexchange, 6 points]

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