Dipolar Recoil Force and Torque Origin Revealed through Lorentz Force Analysis

The fundamental forces acting on electromagnetic dipoles, specifically the recoil force and torque experienced even by isolated emitters, have long been understood through calculations of radiated momentum. Now, Sebastian Golat, Nathaniel Levy, and Francisco J. Rodríguez-Fortuño from King’s College London, present a new derivation of these forces, revealing their origin in the subtle interplay of charges and the finite speed of light. Their work moves beyond simply quantifying the recoil effect, and instead demonstrates that it arises from retardation effects in the mutual interactions between charges within the dipole itself. This achievement provides a clearer conceptual understanding of light-induced forces, and establishes a firm foundation for both theoretical advancements and future experimental investigations into these phenomena.

The team demonstrates that these forces arise directly from changes in the momentum of photons scattered by the dipole, linking them fundamentally to the dipole’s ability to scatter light. This analysis reveals that the recoil force is proportional to the dipole’s extinction cross-section, while the recoil torque is proportional to its scattering cross-section, establishing a clear physical connection between these phenomena and the dipole’s properties.

Conventional calculations often quantify the recoil effect without revealing its underlying physical origin or the forces that generate it. The recoil force and torque exist even for an isolated dipole, independent of external illumination, and are unique in being odd under time reversal, unlike typical electromagnetic interactions. To clarify their nature, researchers re-derived the recoil force from fundamental principles, considering the total Lorentz force acting on the charges forming the dipole. The results confirm the standard momentum-based derivation and reveal that the origin of the recoil lies in retardation effects, arising from the finite speed of light.

Dipole Radiation, Recoil, and Torque Dynamics

This work examines the forces and torques acting on a spinning Huygens dipole, a configuration of electric and magnetic dipoles used to model electromagnetic interactions. Researchers calculated the recoil force and torque experienced by this dipole, employing a mathematical approach using dipole phasors, which simplify calculations involving oscillating dipoles. The calculated recoil force matches results obtained using the established Maxwell’s stress tensor method, validating the new approach and demonstrating its accuracy.

The team also calculated the power scattered by the spinning dipole, analyzing contributions from both near and far fields. While both fields contribute to the total force, they do not completely cancel each other out. This confirms that the phasor-based approach provides a valid alternative to the traditional Maxwell’s stress tensor method for calculating these forces and torques. The results are particularly significant because the recoil force is proportional to the fourth power of the ratio between the dipole’s velocity and the speed of light, indicating that it becomes substantial only at relativistic speeds.

Lorentz Force Origin of Dipole Recoil

This research re-examines the recoil force acting on electromagnetic dipoles, deriving it directly from the Lorentz force between the constituent charges rather than relying on established methods based on momentum considerations. Researchers successfully reproduced the known recoil terms while revealing their fundamental origin in the retarded interactions between the charges forming the dipole. They demonstrate that asymmetry between the leading and trailing charges is essential for generating a net force.

This approach clarifies the physical basis of the recoil force and its symmetry properties, showing it to be odd under time reversal, unlike typical interaction terms which are even. The findings establish a connection between microscopic Lorentz forces and macroscopic recoil phenomena, providing insight into how an isolated dipole exchanges momentum and angular momentum with its own radiation. This consolidates understanding of recoil forces as self-induced effects that nonetheless conserve momentum, with relevance to self-propelling and radiation-driven dipolar systems.