Understanding the momentum of light when propagating through optical media is not only fundamental for studies as varied as classical electrodynamics and polaritonics in condensed matter physics, but also for important applications such as optical-force manipulations and photovoltaics. From a microscopic perspective, an optical medium is in fact a complex system that can split the light momentum into the electromagnetic field, as well as the material electrons and the ionic lattice. Here, we disentangle the partition of momentum associated with light propagation in optical media, and develop a quantum theory to explicitly calculate its distribution. The material momentum here revealed, which is distributed among electrons and ionic lattice, leads to the prediction of unexpected phenomena. In particular, the electron momentum manifests through an intrinsic DC current, and strikingly, we find that under certain conditions this current can be along the photonic wave vector, implying an optical pulling effect on the electrons. Likewise, an optical pulling effect on the lattice can also be observed, such as in graphene during plasmon propagation. We also predict the emergence of boundary electric dipoles associated with light transmission through finite media, offering a microscopic explanation of optical pressure on material boundaries.
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