Computation of internal optical forces using the Helmholtz tensor

Abstract

The computation of the internal optical force density inside a metamaterial is a controversial subject. Various stress tensors have been proposed; however, each yields a different result. Here, by adopting the Helmholtz stress tensor and effective medium theories, we calculated the force densities acting on metamaterials composed of a one-dimensional deep-subwavelength dielectric-air multilayer or a two-dimensional square lattice cylinder array. Our results agree remarkably with the benchmarking noneffective medium treatment. The key is to treat the effective parameters as operators; i.e., take different values for the wave with different $k$ vector. This work provides an approach to compute the internal optical force in metamaterials.