Unraveling the angular symmetry of optical force in a solid dielectric

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 the exact force are still going on due to lack of experimental evidence. Here, we report the first experimental investigation of angular symmetry of optical force inside a solid dielectric, aiming to distinguish the two formulations. The experiments surprisingly show that the optical force exerted by a Gaussian beam has components with the angular mode number of both 2 and 0, which cannot be explained solely by the Lorentz or the Einstein-Laub formulation. Instead, we found a modified Helmholtz theory by combining the Lorentz force with additional electrostrictive force could explain our experimental results. Our results represent a fundamental leap forward in determining the correct force formulation, and will update the working principles of many applications involving electromagnetic forces.