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 v × B 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.

Quantum theory of coherent transverse optical magnetism

“…This phenomenon manifests itself in Eqs. (31) and (42) through the doubled-frequency detuning parameter ⌬ 2 , but its impact only becomes apparent in numerical simulations [16]. The result of this dynamic enhancement is that magnetic dipole response can be nearly as intense as the electric response at intensities far below the relativistic threshold [21] due to transfer of energy between the motions associated with the E and B components of the light field.…”

“…(33) at nonrelativistic intensities. This may be demonstrated by direct numerical integration of the equations of motion [15] and is the subject of a forthcoming publication [16]. Ultrafast growth (on a timescale ⌬t Ͻ 100 fs [1,3]) of magnetic response takes place via energy transfer from electric field-induced linear motion along x, to the azimuthal motion initiated by the magnetic field along Ј, and is due to the phenomenon of parametric resonance [17].…”

Optically-induced charge separation and terahertz emission in unbiased dielectrics

“…Perturbative solutions of these equations, correct to first order in the weak optical magnetic field, 6 are…”

“…5 It appears at sub-relativistic intensities due to parametric enhancement. Classical analysis, 2 numerical simulations and perturbation theory, 6 as well as quantum theory 7 of this phenomenon -transverse optical magnetism -have now been published. These treatments describe charge oscillations that are driven jointly by the electric and magnetic field components of a linearly-polarized light field.…”

Decoherent Excitation of Transverse Free Currents in Dielectric Liquids via Inter-Molecular Interactions

“…These experiments, in which a dielectric liquid (such as water or carbon tetrachloride) is excited by a short-duration ( ≈ 100 − 150 fs), highintensity ( ≈ 1 × 10 8 − 4 × 10 8 W/cm 2 ) electromagnetic pulse, have shown that the scattered, freeemitted light in the propagation direction orthogonal to that of the incident light, has a significant intensity in the polarization direction orthogonal to the incident polarization. These results, suggestive of magnetic dipole radiation patterns, have led to the theory that intense optical fields induce magnetism in individual molecules, that lead to the generation of significant transverse free currents, which in turn generate the observed radiation patterns [9][10][11][12]. This "transverse optical magnetism" theory has encountered a number of criticisms, primarily centered around the need for a large relative magnetic permeability μ r ≈ c for agreement with experiments [9,10,[13][14][15][16].…”