Consistency of time averaged optical force laws for embedded chiral and achiral objects

Although it is commonly believed that all the volumetric optical force laws should lead to the same total optical force for chiral and achiral objects, this idea has been invalidated in some recent works by investigating several previous experiments involving material background. To identify the exact reason of such significant disagreement, we inspect two tractor beam and one lateral force experiments on using distinct stress tensors (STs). To solve the problems of total force, we propose two consistency conditions of time averaged forces. We demonstrate that exactly at the boundary of an object, the difference of the consistent external Minkowski ST and internal ST of Chu (and Einstein-Laub) is found in agreement with the surface force yielded by Chu (and Einstein-Laub) force only when the background is air rather than a material. We identify this as one of the main reasons (among few other identified reasons) of the disagreements observed for real experiments. Finally, based on the proposed consistency conditions, we demonstrate that: by modifying the Einstein-Laub or Chu formulation, time-averaged STs and volume forces are obtainable those can overcome the aforementioned inconsistencies of real experiments for both chiral and achiral Mie objects embedded in even complex material backgrounds.