A model is presented for the resonant third harmonic generation of short pulse lasers in cluster plasma in the presence of density ripple. Because of ripple in cluster density and plasma electron density outside the cluster, the phase-matching condition for the third harmonic process is satisfied, leading to resonant enhancement of harmonic generation. We explore the impact of laser intensity, cluster size, and collisional frequency of electrons on the efficiency of third harmonic generation. Moreover, since the group velocity of the third harmonic wave is greater than that of the fundamental wave, it causes the slippage of the generated harmonic pulse out of the fundamental laser pulse and its amplitude increases with time.

A theoretical model of soft X-ray emission from laser irradiated clusters is developed. An intense short pulse laser of Gaussian radial and temporal profiles impinged on a clustered gas jet, heats the cluster electrons, leading to Bremsstrahlung emission of X-rays. As the clusters expand under hydrodynamic pressure, plasma frequency of the cluster electrons ωpe decreases. When plasma frequency of a cluster approaches plasma resonance ${\rm \omega}_{\,pe} = \sqrt{3} {\rm \omega}$ (where ω is the laser frequency), the electrons are resonantly heated by the laser and a rapid rise in X-ray emission occurs. After a while, when cluster expansion detunes the plasma resonance, X-ray emission falls off.