Harmonic emission from cluster nanoplasmas subject to short intense infrared laser pulses is studied. In a previous publication [M. Kundu et al., Phys. Rev. A 76, 033201 (2007)] we reported particle-in-cell simulation results showing resonant enhancements of low-order harmonics when the Mie plasma frequency of the ionizing and expanding cluster resonates with the respective harmonic frequency. Simultaneously we found that high-order harmonics were barely present in the spectrum, even at high intensities. The current paper is focused on the analytical modeling of the process. We show that dynamical stochasticity owing to nonlinear resonance inhibits the emission of high order harmonics.
Deep Dive into Harmonic emission from cluster nanoplasmas subject to intense short laser pulses.
Harmonic emission from cluster nanoplasmas subject to short intense infrared laser pulses is studied. In a previous publication [M. Kundu et al., Phys. Rev. A 76, 033201 (2007)] we reported particle-in-cell simulation results showing resonant enhancements of low-order harmonics when the Mie plasma frequency of the ionizing and expanding cluster resonates with the respective harmonic frequency. Simultaneously we found that high-order harmonics were barely present in the spectrum, even at high intensities. The current paper is focused on the analytical modeling of the process. We show that dynamical stochasticity owing to nonlinear resonance inhibits the emission of high order harmonics.
The study of rare gas and metal clusters interacting with intense infrared, optical, and ultraviolet laser pulses has emerged as a new promising research area in strong field physics (see [1,2] for reviews). The generation of fast electrons and ions, the production of high charge states, the generation of x-rays and nuclear fusion (in the case of deuterium-enriched clusters) was observed using cluster targets in strong laser fields of intensities up to 10 20 W/cm 2 . Hot and dense nonuniform, nonequilibrium and nonstationary plasmas produced under such conditions and confined on a femto-or picosecond time scale to nanometer sizes-so-called nanoplasmas-are new physical objects with unusual properties.
One of the most important features of nanoplasmas is the very efficient energy transfer from light to charged particles, which is much higher (per particle) than for an atomic gas of the same average density [3]. Although the particular mechanisms responsible for the laser energy deposition in clusters still remain debated [4,5,6,7,8,9,10,11,12], the pivotal role of collective plasma dynamics (in particular the excitation of surface plasmons) and of nonlinear resonance (a definition is given below in Sec. III) in the energy transfer from laser light to the electrons in the nanoplasma and the subsequent outer ionization was proved in experiments, simulations, and simple analytical models [6,8,9,10,13,14].
While the energy absorption from intense laser pulses by nanoplasmas has been widely studied both in experiments and theory, much less attention has been paid to harmonic emission from such systems. Naturally the question arises whether laser-driven clusters, being highly nonlinear systems, may be a source of high-order harmonics as efficient as atoms in the gas phase (or even more efficient?). There are at least two essentially different physical mechanisms which could be responsible for emission of harmonics from such a system.
First, the mechanism based on recombination of the virtually ionized electron with its parent ion [15], wellstudied in gaseous atomic targets, may also work in clusters where it can be modified by the fact that the atoms are closer to each other, so that the electron’s motion between ionization and recombination can be distorted by the field of the other ions. Moreover, the electron may recombine with an ion different from its parent. This leads to modifications in the single-electron dynamics and in the phase matching conditions while the physical origin of harmonic generation (HG) remains the same as in a gas jet. Modifications of the atomic recombination mechanism in clusters have been considered in [16,17]. However, in high intensity fields where each atom is loosing one or several electrons already during the leading edge of the laser pulse the recombination mechanism can hardly be efficient. Second, as dense electron plasmas is produced inside a cluster, its coherent motion may be an efficient source of radiation. In a collisionless plasma, as it is generated by intense laser fields inside small clusters, individual electron-electron and electron-ion collisions cannot destroy the coherency of the collective electron motion. This coherent, collective electron motion may cause HG if it is nonlinear. Recently, several experiments on high harmonic emission from plasma surfaces illuminated by short laser pulses of intensity 10 17 W/cm 2 and higher were reported (see, e.g., [18,19]). The physical picture which is behind such plasma harmonics appears to be more complicated and diverse than the recombination mechanism in atomic HG.
In macroplasmas the magnetic component of the Lorentz force is a typical source of nonlinearity. In this case the nonlinearity parameter is v/c where v is the typical velocity related to collective oscillations of the electron plasma and c is the speed of light. As a consequence, generation of harmonics from dense macroplsmas may require relativistic intensities [18]. As compared to macroplasmas, clusters introduce an extra source of nonlinearity due to their small spacial size, namely X/R 0 , where R 0 is the cluster radius and X is the amplitude with which the electron cloud oscillates under the action of the laser field [20]. Therefore, one could expect strongly nonlinear electron motion even in the nonrelativistic regime. It should be noted, however, that although individual collisions may not be important, there are other effects which can spoil the coherency required for efficient radiation. Most of these undesirable effects can be attributed to dynamical instabilities induced by the interaction of particles with the mean self-consistent field (in the presence of the laser field). Therefore, the examination of plasma harmonics usually requires not only the analysis of the collective motion but that of individual electron trajectories as well.
Up to now only a few experiments on HG from clusters are known. In Refs. [21,22,23] HG from raregas clusters
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