Harmonic generation in clusters

A model is presented for the nonlinear response of a small cluster, with a size much smaller than the wavelength, at the third harmonic of the laser frequency. The model involves collective modes of a cold electron core confined within a positively charged ion background. The response of the electron core to the laser field is similar to that of a weakly nonlinear oscillator driven by an external force. In particular, there is a resonant enhancement of the third harmonic when the frequency of the applied field is close to one third of the core eigenfrequency. It is shown that density nonuniformity or nonspherical shape of the ion background is necessary for harmonic generation. Particle-in-cell simulations have been performed to model the time evolution of the third harmonic response as the ion density profile changes due to cluster expansion. The simulation results are consistent with the predictions of the cold electron core model. In addition, the code quantifies the role of stochastic electron heating, an alternative harmonic generation mechanism