On the origin and properties of dipolar recoil force and torque

Abstract

The recoil optical force and torque acting on an electromagnetic dipole are typically derived by computing the imbalance in radiated linear and angular electromagnetic momentum coming from the source, using Maxwell stress tensor integration. This quantifies the recoil's outcome without revealing its physical origin or the underlying forces that produce it. The recoil force and torque exist even in the absence of external illumination, such that an isolated dipole emitter can experience them. In contrast to the other terms, the recoil terms are odd under time reversal. To clarify their nature and properties, we re-derive the recoil force from first principles using the total Lorentz force on a system of charges that form a simultaneous electric and magnetic dipole. The results agree with the standard momentum-based derivation and reveal their ultimate origin from retardation effects -- arising from the finite speed of light -- in the mutual interactions between charges. This result provides fundamental insight into the recoil mechanism, offering a clearer conceptual foundation for future theoretical and experimental studies of light-induced forces.