Analytic derivation of electrostrictive tensors and their application to optical force density calculations

Using multiple scattering theory, we derived for the first time analytical formulas for electrostrictive tensors for two-dimensional metamaterial systems. The electrostrictive tensor terms are found to depend explicitly on the symmetry of the underlying lattice of the metamaterial, and they also depend explicitly on the direction of a local effective wave vector. These analytical results enable us to calculate light induced body forces inside a composite system (metamaterial) using the Helmholtz stress tensor within the effective medium formalism in the sense that the fields used in the stress tensor are those obtained by solving the macroscopic Maxwell equation with the microstructure of the metamaterial replaced by an effective medium. Our results point to some fundamental questions of using an effective medium theory to determine optical force density. In particular, the fact that Helmholtz tensor carries electrostrictive terms that are explicitly symmetry dependent means that the standard effective medium parameters cannot give sufficient information to determine body force density, even though they can give the correct total force. A more challenging issue is that the electrostrictive terms are related to a local effective wave vector, and it is not always obtainable in systems with boundary reflections within the context of a standard effective medium approach.