Nonlinearity in the Lorentz Oscillator Model

The magnetic force is retained in the Lorentz Oscillator Model and a perturbation solution is derived beyond the dipole approximation. Perturbation series for the electric dipole, magnetic dipole, and electric quadrupole moments in addition to their macroscopic, spatially-averaged counterparts are also obtained. These expressions are shown to describe many optical phenomena: the normal, linear Zeeman, Faraday, and magneto-optic Kerr effects, the linear Stark, Pockels, and Kerr effects (when the restoring force is anharmonic), the momentum and angular momentum of a photon in matter (contributing to the Abraham-Minkowski debate), the photon drag and inverse Faraday effects, and sum-frequency and second-harmonic generation in centrosymmetric media. The qualitative and quantitative accuracy is assessed by comparison to both experiment and more fundamental theory (e.g. quantum mechanics). New insights into the relationship between the Stark and Pockels/Kerr effects also emerge.