Dependence of Harmonic Spectrum Shape on Laser Beam Intensity in Interaction With Atoms

We present a method to calculate the harmonic spectrum of the radiation emitted at the interactions between intense laser beams and atoms. Our relations describe accurately, in good agreement with the experiment, important features of the harmonic spectrum and the evolution of its shape with the increase of the laser beam intensity. More specifically, for low intensities, of the order of 10¹³ W/cm², the spectrum has the well-known plateau shape, after which follows a sharp decrease at the cutoff edge. When the beam intensity is increased, toward 10¹⁵ W/cm², the slope of the plateau increases, corresponding to a decrease by one or two orders of magnitude of the harmonic intensities. When the beam intensity is increased more, toward 10¹⁷ W/cm², there is a maximum at the left edge of the spectrum, which is followed by a strong decrease of many orders of magnitude, and the spectrum concentrates in a very limited domain, under a certain frequency, far lower than the theoretical cutoff frequency. These theoretical results are in good agreement with numerous experimental data from the literature, for many atoms and ions, and for a large spectrum of intensities of laser beams. This result has important implications in the emerging field of generation of high intensity hard X-rays.