Anomalies in high-order harmonic generation at relativistic intensities

High-order harmonic generation from a solid target surface has been investigated using femtosecond laser pulses focused to intensities greater than ${10}^{18}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2.$ The experiments show that the harmonics are very intense, with a conversion efficiency that is one or two orders of magnitude larger than that of harmonics generated in gases. Beside the observation of presently the shortest wavelength harmonics from femtosecond-laser solid target interaction, i.e., down to 22 nm, an anomaly has been observed in the harmonic spectrum. In contrast to the expected well-known continuous “roll off” of the high-harmonic orders, the harmonic intensity decreases with the increase of harmonic order, but in between shows minima which are significantly less intense than the neighboring harmonics. Furthermore, the order of the harmonic minima depend on target material. Additional calculations using numerical kinetic particle simulations and a simpler oscillating mirror model show that the physical origin of these modulations is an intricate interplay of resonance absorption and ponderomotive force which leads to a complex electron density profile evolution. Furthermore, this is emphasized by a spectral line analysis of the harmonics. In agreement with the theory, broad lines have been observed and, in particular for the harmonics in the minima, a complex interference structure is present.