A local model for the optical energy and momentum transfer in dielectric media and the microscopic origin of Abraham's force density

We report on the continuity equations for linear momentum and energy associated to a recently introduced electromagnetic formulation based on classical dipolar sources [Eur. Phys. J. Plus 138, 1034 (2023)]. When connected to the mass-polariton quasi-particle dynamics, these equations provide a consistent microscopic description of the local optical energy and momentum transfer inside dielectric media, called microscopic mass-polariton formulation. This procedure also unveils the true microscopic origin of the long-known Abraham optical force density as an interplay between induced dipoles and mechanical stresses generated within the material.