Fig. 1. Scheme of numerical simulation of HHG. d is the transverse dimension at full width at half maximum (FWHM), ϕ_i is the angle of incidence, ϕ_m is the angle of reflection, and ω₀, …, ω_n are generated harmonics.

Fig. 2. (a) Typical electron density distribution in units of N_cr, (b) field component E_y in units of the relativistic electric field E_rel, and (c) spatial spectrum of high harmonics in arbitrary units for 30 fs, focusing f/4, and a₀ = 30.

Fig. 3. (a) Typical spectrum of generated high harmonics in arbitrary units for the parameters of Fig. 2 and (b) typical time profile of electric field component after the interaction of the laser pulse with the target surface in units of E_rel for 30 fs, focusing f/4, and a₀ = 30.

Fig. 4. Integral spectra of high harmonics at different laser pulse intensities. The colors show the spectra for different laser pulse intensities. The amplitude is in arbitrary units.

Fig. 5. Relative amplitude of harmonics [(a) and (c)] and averaged relative amplitude [(b) and (d)] as functions of incident laser pulse intensity (in W/cm²); different harmonics are shown by different colors. Dashed lines show approximation by a power function in (a) and (b) and approximation by a linear function in (c) and (d).

Fig. 6. Comparison of the integrated spectra of HHG at different angles of incidence of the laser pulse on the target for 30 fs, focusing f/4, and a₀ = 30. Spectra at different angles of incidence are shown by color. The amplitude is in arbitrary units.

Fig. 7. (a) and (c) Amplitudes of low (a) and high (c) harmonics as functions of focusing depth D for 30 fs, focusing f/4, and a₀ = 30; the amplitudes of different harmonics are shown by different colors. (b) and (d) Averaged relative amplitudes of harmonics as functions of focusing depth, taking into account low harmonics (b) and only high harmonics (d).

Fig. 8. Comparison of integrated spectra with and without density gradient for 30 fs, focusing f/4, and a₀ = 30. Spectra are shown in color for different density gradients. The amplitude is in arbitrary units.

Fig. 9. Density distribution at the moment of interaction of the laser pulse center with the target in the case of a sharp boundary (a) and in the case of a linear growth with L = 0.5λ₀ (b) for 30 fs, focusing f/4, and a₀ = 30. The density is normalized to N_cr.

Fig. 10. (a) Amplitude of high harmonics as a function of density gradient scale for 30 fs, focusing f/4, and a₀ = 30; the amplitudes of different harmonics are shown by different colors. (b) Averaged relative amplitude of harmonics as a function of density gradient scale.