Photon momentum transfer in inhomogeneous dielectric mixtures and induced tractor beams

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 composedofdifferent 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 ofthe Abraham type. Our interpretation also provides a novel methodof realizing a tractor beam for the exertionof negative force that offers an alternative to the use of negative-index materials, optical gain, or highly non-paraxial or multiple-light interference.