10 - A dynamical, classical oscillator model for linear and nonlinear optics

Abstract

We employ a classical, nonlinear Lorentz–Duffing oscillator model to predict second and third harmonic conversion efficiencies from a variety of structures. We use the approach to examine energy and momentum refraction characteristics of a pulse as interfaces are crossed and study a phase-locking mechanism that inhibits absorption of the generated harmonics even in a regime of high absorption. We then combine the nonlinear oscillator model with a classical hydrodynamic model of a free electron gas to study harmonic generation from a variety of structures, including smooth metal layers and a metal grating. As expected, the plasmonic grating yields the largest narrow-band conversion efficiencies. The method includes both linear and nonlinear material dispersions that in turn sensitively depend on linear oscillator parameters. Concurrently, and unlike other techniques, the integration scheme is numerically stable. By design, one thus avoids the introduction of explicit, third order nonlinear coefficients and also takes into account linear and nonlinear material dispersions simultaneously, elements that are often necessary to fully understand many of the subtleties of the interaction of light with matter.