S. A. R. Horsley, M. Artoni, and G. C. La Rocca
A general theory of optical forces on moving bodies is here developed in terms of generalized 4×4 transfer and scattering matrices. Results are presented for a planar dielectric of arbitrary refractive index placed in an otherwise empty space and moving parallel and perpendicular to the slab-vacuum interface. In both regimes of motion the resulting force comprises lateral and normal velocity-dependent components, which may depend in a subtle way on the Doppler effect and s-p-polarization mixing. For lateral displacements in particular, polarization mixing, which is here interpreted as an effective magnetoelectric effect due to the reduced symmetry induced by the motion of the slab, gives rise to a velocity-dependent force contribution that is sensitive to the phase difference between the two polarization amplitudes. This term gives rise to a rather peculiar optical response on the moving body, and specific cases are illustrated for incident radiation of arbitrarily directed linear polarization. The additional force due to polarization mixing may cancel to first order in V/c with the first order Doppler contribution yielding an overall vanishing of the velocity-dependent component of the force on the body. The above findings bear some relevance to modern developments of nano-optomechanics and to the problem of the frictional component of the Casimir force.