Generalized Spin–Curl Force Beyond the Stress Tensor

The optical force exerted on a dipole particle can be divided into gradient force, scattering force, and spin-curl force, all of which can be derived from Maxwell's stress tensor with the dipole approximation. Here, we identify an additional spin-curl force for arbitrary objects beyond the dipole approximation, which is named the generalized spin-curl force in this paper. The generalized spin-curl force originates from the Minkowski force density and depends on the imaginary parts of the permittivity, permeability, and chirality of the object. However, it remains imperceptible in conventional optical force calculations due to its exact cancellation by a compensatory surface force during MST surface integration. The study of the generalized spin-curl force provides critical insights into elucidating the mechanisms underlying optical momentum transfer and internal force distribution within complex media. Furthermore, the generalized spin-curl force offers a novel mechanism for enhancing optical sensors, enabling highly sensitive detection of absorptive or chiral perturbations in systems such as microcavities and metasurfaces. Its ability to manipulate internal force distributions also provides new pathways for advancing optical force probes and chirality-selective sensing at the nanoscale.