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. Keywords: dielectric interface; Minkowski photon momentum transfer; modified Einstein-Laub method; optical pulling force; optical tractor beams
INTRODUCTIONFollowing the pioneering work of Marston 1 in acoustics, optical 'tractor beams' have attracted considerable interest by virtue of their unusual mechanism for micromanipulation. [2][3][4][5][6][7][8][9][10][11][12][13] Generally speaking, a tractor beam is a customized light beam that exerts a negative scattering force (NSF) on a scatterer and pulls it opposite to the propagation direction of the light, in contrast to conventional pushing forces. 14 Optical pulling forces provide a novel approach to gradientless optical manipulation techniques distinct from optical tweezers, 15-17 optical conveyors 13,18,19 and nanooptomechanical systems. 20,21 Recently, various types of tractor beams have been experimentally demonstrated using a Gaussian beam with an optical mirror (involving the interference of incident and reflected light beams in certain limited regions) 8 and using dodecane droplets sitting on a dielectric interface. 22 However, in the presence of a high-powered laser, hydrodynamic effects (uneven heat dissipation, particle absorption, temperature gradients, liquid convection, surface energy wells, etc.) may also contribute. Moreover, the stability criteria for tractor beams, which are very important for practical application, have not yet been investigated.Although the mechanical effect has been demonstrated 22 to be an overall consequence of all possible contributing factors, the mechanism of the optical momentum transfer from a mixe...