Light-induced dynamics in the Lorentz oscillator model with magnetic forces

Abstract

The classical Lorentz oscillator model of bound electron motion ordinarily excludes magnetic forces at nonrelativistic intensities for the simple reason that their magnitude is small. However, perturbative and numerical results show that when the $\mathrm{vP\vec}\ifmmode\times\else\texttimes\fi{}\mathrm{BP\vec}$ term is retained, dynamically enhanced terms give rise to large amplitude, magnetically induced charge displacements at zero frequency and at twice the driving frequency in the Cartesian laboratory frame. Numerical simulations of electron motion are in accord with the predictions of perturbative theory for steady-state motion in the classical picture. Direct integration shows that magnetic response which is comparable to electric dipole response can arise in transparent dielectrics at optical frequencies. Parametric instability in the equations of motion is implicated as the source of rapid energy transfer from electric to magnetic motions by reduction of the equations to a complex Mathieu equation.