Unraveling the topological charge of optical force in a solid dielectric

The force exerted by electromagnetic fields is of fundamental importance in physics, but its formulation inside media is still controversial and unclear. The textbook-accepted formulation of electromagnetic force was proposed by Lorentz in the 19th century, but its validity has been challenged due to incompatibility with the special relativity and momentum conservation. The Einstein-Laub formulation, which can reconcile those conflicts, was suggested as an alternative to the Lorentz formulation. However, intense debates on these two formulations are still going on due to lack of experimental evidences. Here, we report the first experimental investigation of topological charge of optical force inside a solid dielectric, aiming to distinguish the two formulations. The experimental results show that the optical force exerted by a Gaussian beam has components with the topological charge of both 2 and 0, which cannot be supported solely by the Lorentz or the Einstein-Laub formulation. Instead, we found a modified Helmholtz theory could explain our experimental results. The unraveled topological charge of optical force will not only contribute to the ultimate determination of the correct force formulation in classical electrodynamics, but also have broad and far-reaching impact on many science and engineering branches involving electromagnetic forces.