Time dependent force outside a complex magneto-dielectric particle: Abraham-Minkowski controversy

Abraham and Minkowski momenta in material medium have been a long standing dilemma for the last hundred years. It is well-known that the difference between the outside forces of a dielectric particle calculated from Abraham and Minkowski formula is generally difficult to observe due to the cancellation of their time dependent part in the averaging process. However, the missing information can be closely observed from the transient parts of the corresponding formulation of the force densities. Here, in this work, we have theoretically demonstrated the discrepancy between Abraham and Minkowski forces in time domain which clearly indicates their different nature for both absorbing and gain media. In addition, the study broadly supports the fact that the distinction between the two rival force densities is more obvious in a gain medium than in an absorbing one. The results can be applied in case of theoretical and practical optical manipulation of both the force and torque.