Instantaneous optical forces in metamaterials

One important open aspect of the physics of metamaterials is the form of the optical force density. In this work, we investigate the optical force density in metamaterials based on instantaneous conservation laws of energy and momentum. We simulate light pulses in metamaterials in which the atoms are initially at rest and start to move as a result of the optical force density. We solve Newton's equation of motion to find out how the velocity of the medium under the influence of the optical force density is varying as a function of the position and time. We also study the assumptions used in the conventional derivation of electrostrictive forces, often discussed in optics literature. The theory of electrostriction, see e.g. Electrodynamics of Continuous Media by Landau and Lifshitz (1984), is based on changes in the volume of a dielectric under the influence of an external electromagnetic field. It is assumed that there is a thermodynamical balance between the dielectric and the external forces caused by the field. This assumption is no more valid at optical frequencies. Therefore, the possible role of electrostriction at optical frequencies is not obvious. Our work aims at revisiting the derivation to be consistent with the covariant theory of light in dispersive media.