Superkicks and momentum density tests via micromanipulation

TL;DR

This paper investigates the correct expressions for electromagnetic momentum and angular momentum densities, highlighting differences between canonical and symmetric forms, and proposes micromanipulation experiments to test these predictions.

Contribution

It introduces test scenarios and numerical estimates to distinguish between different theoretical expressions for electromagnetic momentum densities.

Findings

Different expressions predict significantly different forces and angular momenta on small objects.

Structured light interactions can reveal the correct momentum density expression.

Numerical estimates suggest feasible experimental tests.

Abstract

There is an unsettled problem in choosing the correct expressions for the local momentum density and angular momentum density of electromagnetic fields (or indeed, of any non-scalar field). If one only examines plane waves, the problem is moot, as the known possible expressions all give the same result. The momentum and angular momentum density expressions are generally obtained from the energy-momentum tensor, in turn obtained from a Lagrangian. The electrodynamic expressions obtained by the canonical procedure are not the same as the symmetric Belinfante reworking. For the interaction of matter with structured light, for example, twisted photons, this is important; there are drastically different predictions for forces and angular momenta induced on small test objects. We show situations where the two predictions can be checked, with numerical estimates of the size of the effects.