Photon momentum transfer in inhomogeneous dielectric mixtures and induced tractor beams

Abstract

The determination of optical force as a consequence of momentum transfer is inevitably subject to the use of the proper momentum density and stress tensor. It is imperative and valuable to consider the intrinsic scheme of photon momentum transfer, particularly when a particle is embedded in a complex dielectric environment. Typically, we consider a particle submerged in an inhomogeneous background composed of different dielectric materials, excluding coherent illumination or hydrodynamic effects. A ray-tracing method is adopted to capture the direct process of momentum transfer from the complex background medium, and this approach is validated using the modified Einstein–Laub method, which uses only the interior fields of the particle in the calculation. In this way, debates regarding the calculation of the force with different stress tensors using exterior fields can be avoided. Our suggested interpretation supports only the Minkowski approach for the optical momentum transfer to the embedded scatterer while rejecting Peierls's and Abraham's approaches, though the momentum of a stably moving photon in a continuous background medium should be considered to be of the Abraham type. Our interpretation also provides a novel method of realizing a tractor beam for the exertion of negative force that offers an alternative to the use of negative-index materials, optical gain, or highly non-paraxial or multiple-light interference. Support for the Minkowski formulation has been obtained by considering photon momentum transfer for a scatterer at a liquid–gas interface. To shed light on the century-old debate regarding the momentum of light in dielectric media (the so-called Abraham–Minkowski controversy), a team of scientists from Singapore, China and the USA investigated direct momentum transfer from the two media. To do this, they performed ray-tracing calculations combined with modified Einstein–Laub equations that consider only the fields inside the particle, thereby side-stepping problems arising from the use of different stress tensors for fields outside the particle. Their analysis also suggests an alternative way to realize tractor beams (that is, beams that pull rather than push a particle) other than using negative-index materials, optical gain, highly non-paraxial beams or multiple-light interference.