Quantum signatures in the classical limit of electromagnetic waves

It is common both in the classical and quantum optics to describe the optical field as a superposition of plane waves. However, it is well known that optically active materials emit photons vastly dominantly in the electric dipole approximation. The photons emitted in the electric dipole transitions are not plane waves, but spherical photon states corresponding to eigenstates J = 1 of the total angular momentum and M = ±1 of the z component of the total angular momentum. In addition, electric dipole photons are separated from the magnetic photons by the state index η = e for electric photons in distinction to η = m for magnetic photons. In this work, we study the far-field of light that is generated when a two-dimensional matrix of atoms emits electric dipole photons and compare this far-field at large distance from the emitting matrix with a plane wave. The goal of our work is to find out if the light emitted from the electric dipole transitions carry the memory of being electric dipole photons when they are far from the emitting atoms. In particular, it is well known that a plane wave includes all angular momentum components corresponding to quantum numbers J = 1, 2, 3, ..., while the far field of the emitting matrix can include only the angular momentum component J = 1. Although the two-dimensional atomic matrix used as a light source in our simulations is certainly nontrivial to fabricate, it is nevertheless fully physical and we expect that with some modifications, the conclusions from the present simulations can be generalized to atomic light sources that are more easy to realize experimentally.