Time-dependent theory of optical electro- and magnetostriction

Abstract

Electrostriction, the deformation of dielectric materials under the influence of an electric field, is of continuous interest in optics. The classic experiment by Hakim and Higham [Proc. Phys. Soc. 80, 190 (1962)] for a stationary field supports a different formula of the electrostrictive force density than the recent experiment by Astrath et al. [Light Sci. Appl. 11, 103 (2022)] for an optical field. In this work, we study the origin of this difference by developing a time-dependent covariant theory of optical force densities in photonic materials. When a light pulse propagates in a bulk dielectric, the field-induced force density consists of two parts: (i) The optical wave momentum force density ${\mathbf{f}}_{\mathrm{owm}}$ carries the wave momentum of light and drives forward a mass density wave of the covariant coupled field-material state of light. (ii) The optostrictive force density ${\mathbf{f}}_{\mathrm{ost}}$ arises from the atomic density dependence of the electric and magnetic field energy densities. It represents an optical Lorentz-force-law-based generalization of the electro- and magnetostrictive force densities well known for static electromagnetic fields and derived from the principle of virtual work. Since the work done by ${\mathbf{f}}_{\mathrm{ost}}$ is not equal to the change of the field energy density during the contraction of the material, we have to describe this difference with optostriction-related dissipation terms to fulfill the energy conservation. The detailed physical model of the dissipation is left for further work. The optostrictive force density can be understood in terms of field-induced pair interactions inside the material. Because of the related action and reaction effects, this force density cannot contribute to the net momentum transfer of the optical field. The theory is used to simulate the propagation of a Gaussian light pulse through a dielectric material. We calculate the electric and magnetic fields of the Gaussian light pulse from Maxwell's equations and simultaneously solve Newton's equation of motion of atoms to find how the velocity and displacement fields of atoms develop as a function of time under the influence of the field-induced force density.