On quantifying the spin angular momentum density of light

Abstract

In addition to energy, light carries linear and angular momentum. These are key quantities in rapidly developing optics research and in technologies focusing on light induced forces and torques on materials. Spin angular momentum (SAM) density is of particular interest, since unlike orbital angular momentum, it is uncoupled from linear momentum. The SAM density of light was first estimated in 1909 by Poynting, using a mechanical analogy. Exact expressions, based on results from quantum mechanics and field theory were subsequently developed, and are in common use today. In this paper, we show that the SAM density of light can be obtained directly from the Coulomb force and Maxwell's equations, without reliance on quantum mechanics or field theories; it could have been calculated by Maxwell and his contemporaries. Besides its historical significance, the simple derivation of our result makes it readily accessible to non-experts in the field.