Photon mass drag and the momentum of light in a medium

Abstract

Conventional theories of electromagnetic waves in a medium assume that the energy propagating with the light pulse in the medium is entirely carried by the field. Thus, the possibility that the optical force field of the light pulse would drive forward an atomic mass density wave (MDW) and the related kinetic and elastic energies is neglected. In this work, we present foundations of a covariant theory of light propagation in a medium by considering a light wave simultaneously with the dynamics of the medium atoms driven by optoelastic forces between the induced dipoles and the electromagnetic field. We prove that the transfer of mass as MDW associated with the light pulse, the photon mass drag effect, gives an essential contribution to the total momentum of the light pulse, which becomes equal to the Minkowski momentum. Thus, our theory also resolves the centenary Abraham-Minkowski controversy of the momentum of light in a nondispersive medium. We derive the photon mass drag effect using two independent but complementary covariant models. In the mass-polariton (MP) quasiparticle approach, we consider the light pulse as a coupled state between the photon and matter, isolated from the rest of the medium. The momentum and the transferred mass of MP follow unambiguously from the Lorentz invariance and the fundamental conservation laws of nature. To enable the calculation of the mass and momentum distribution of a light pulse, we have also generalized the electrodynamics of continuous media to account for the optoelastic dynamics of the medium. In this optoelastic continuum dynamics (OCD) approach, we obtain a numerically accurate solution of the Newtonian continuum dynamics of the medium when the light pulse is propagating in it. We finally discuss a possibility of an optical waveguide setup for experimental measurement of the transferred mass of the light pulse.