Nonlinear Duffing oscillator model for third harmonic generation

Abstract

We employ a classical, nonlinear Lorentz–Duffing oscillator model to predict third harmonic conversion efficiencies in the ultrafast regime, from a variety of metal nanostructures, including smooth, isolated metal layers, a metal–dielectric photonic band gap structure, and a metal grating. As expected, the plasmonic grating yields the largest narrow-band conversion efficiencies. However, interference phenomena at play within the multilayer stack yield comparable, broadband conversion. 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.