We consider the nonlinear collective electron dynamics inside a large cluster irradiated by a strong linearly polarized short (≲0.1  ps) laser pulse. The equation of the centre-of-mass motion of the electron cloud driven by the strong laser field is derived using the approximation of an incompressible medium. The analysis of this equation demonstrates the presence of odd harmonics of the fundamental frequency in the cluster dipole moment, and in both the internal and the scattered electric field. Both neutral and ionized clusters are considered. For clusters with radii R ≃ 100 Å irradiated by a femtosecond titanium–sapphire laser with a peak intensity of I ≃ 1016 W cm−2, the internal electric field strength near the tripled fundamental frequency is shown to be of the same order as the field of the fundamental. The reason is that both for metallic and for laser-ionized van der Waals clusters the Mie surface-plasmon energy ℏωM is around 5 eV, which is close to three times the energy of a titanium–sapphire laser-field quantum. On the other hand, the condition for first-order resonance with the Mie frequency is not met during the presence of the main laser pulse, but only temporarily, either at the first onset of inner ionization on the leading edge of the pulse (for van der Waals clusters) or during the subsequent Coulomb explosion. In both cases, the ion density is reduced. The presence of a strong third harmonic leads, in particular, to the enhanced production of multiply charged ions in clusters irradiated by a strong laser field, as compared with isolated atoms. This point is discussed in the light of recent experimental results on the production of multiply charged ions in laser–cluster experiments. Third-harmonic generation by a cluster in a strong laser field, as a function of both the cluster and the laser-field parameters, is also considered.

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The nonlinear collective electron dynamics of a cluster irradiated by a strong near-infrared linearly polarized short laser pulse are studied by classical molecular-dynamics simulations for a small model cluster with ∼103 particles. The model naturally yields all the features of a cluster exposed to a strong laser pulse, such as inner and outer ionization, expansion of the ion core, etc. When the frequency of the incident radiation is near three-photon resonance with the Mie frequency in the laser-ionized cluster, both the electron acceleration and the local electric field acting on the ions inside the cluster exhibit a third harmonic of the fundamental frequency. The time evolution during the laser pulse of the third harmonic of the total electron acceleration as well as of the electric field inside the cluster is discussed for different parameters of the laser–cluster interaction. The effect of ion motion is investigated. The presence of a strong non-resonant second harmonic in the local electric field at ion positions off the cluster centre is reported.

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