Force Detection of Electromagnetic Beam Chirality at the Nanoscale

Abstract: Many nanophotonic applications require precise control and characterization of electromagnetic field properties at the nanoscale. The chiral properties of the field are among its key characteristics, yet measurement of optical chirality at dimensions beyond the diffraction limit has proven difficult. Here we theoretically show that the chiral properties of light can be characterized down to the nanometer scale by means of force detection. To measure the chiral properties of a beam of given handedness at the nanoscale, we determine the photo-induced force exerted on a sharp tip, which is illuminated first by the beam of interest and second by an auxiliary beam of opposite handedness, in a sequential manner. We show that the difference between the force measurements is directly proportional to the chiral properties of the beam of interest. In particular, the gradient force difference $\Delta\langle F_{grad, z}\rangle$ is found to have exclusive correspondence to the time-averaged helicity density of the incident light, whereas the differential scattering force provides information about the spin angular momentum density of light. We further characterize and quantify the helicity-dependent $\Delta\langle F_{grad, z}\rangle$ using a Mie scattering formalism complemented with full wave simulations, underlining that the magnitude of the difference force is within an experimentally detectable range.