A century has now passed since the origins of the Abraham-Minkowski controversy pertaining to the correct form of optical momentum in media. Experiment and theory have been applied at both the classical and quantum levels in attempt to resolve the debate. The result of these efforts is the identification of Abraham’s kinetic momentum as being responsible for the overall center of mass translations of a medium and Minkowski’s canonical or wave momentum as being responsible for translations within or with respect to a medium. In spite of the recent theoretical developments, much confusion still exists regarding the appropriate theory required to predict experimental outcomes and to develop new applications. In this paper, the resolution of the longstanding Abraham-Minkowski controversy is reviewed. The resolution is presented using classical electromagnetic theory and logical interpretation of experiments disseminated over the previous century. Emphasis is placed on applied physics applications: modeling optical manipulation of cells and particles. Although the basic interpretation of optical momentum has been resolved, there is still some uncertainly regarding the complete form of the momentum continuity equation describing electromagnetics. Thus, while a complete picture of electrodynamics has still yet to be fully interpreted, this correspondence should help clarify the state-of-the-art view.

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Various trapping configurations have been realized so far, either based on the scattering force or the gradient force. In this Letter, we propose a new trapping regime based on the equilibrium between a scattering force and optical binding forces only. The trap is realized from the interaction between a single plane wave and a series of fixed small particles, and is efficient at trapping multiple free particles. The effects are demonstrated analytically upon computing the exact scattering from a collection of cylindrical particles and calculating the Lorentz force on each free particle via the Maxwell stress tensor.

The Maxwell stress tensor and the distributed Lorentz force are applied to calculate forces on lossless media and are shown to be in excellent agreement. From the Maxwell stress tensor, we derive analytical formulae for the forces on both a half-space and a slab under plane wave incidence. It is shown that a normally incident plane wave pushes the slab in the wave propagation direction, while it pulls the half-space toward the incoming wave. Zero tangential force is derived at a boundary between two lossless media, regardless of incident angle. The distributed Lorentz force is applied to the slab in a direct way, while the half-space is dealt with by introducing a finite conductivity. In this regard, we show that the ohmic losses have to be properly accounted for, otherwise differing results are obtained. This contribution, together with a generalization of the formulation to magnetic materials, establishes the method on solid theoretical grounds. Agreement between the two methods is also demonstrated for the case of a 2-D circular dielectric particle.

The momentum transfer to absorbing particles is derived from the Lorentz force density without prior assumption of the momentum of light in media. We develop a view of momentum conservation rooted in the stress tensor formalism that is based on the separation of momentum contributions to bound and free currents and charges consistent with the Lorentz force density. This is in contrast with the usual separation of material and field contributions. The theory is applied to predict a decrease in optical momentum transfer to Mie particles due to absorption, which contrasts the common intuition based on the scattering and absorption by Rayleigh particles.