High-harmonic generation in GaAs beyond the perturbative regime

The field-intensity dependence of high-harmonic generation in bulk gallium arsenide is studied. We experimentally find the oscillatory behavior at high fields where a perturbative scaling law no longer holds. By constructing a theoretical framework based on the Luttinger-Kohn model, we succeed in reproducing the observed oscillatory behavior. The qualitative agreement between the experiment and theory indicates that field-induced dynamic band modification is crucial in the nonperturbative regime. We show that the oscillatory behavior is naturally understood by dynamic localization that is based on the the Floquet subband picture.

Figure 1

(a) Experimental setup for HHG in reflection geometry using bulk GaAs and MIR laser source. Ti:sapphire regenerative and multipass amplifiers (450 Hz, 5 mJ, 70 fs) were used to pump the optical parametric amplifier (OPA) [60]. WGPs, a pair of wire-grid polarizers; L1 ($f=300$ mm) and L2 ($f=50$ mm), ${\mathrm{CaF}}_2$ lenses; M1 ($R=100$ mm), Al-coated concave mirror. (b) Structure of the (110) surface of GaAs and direction of the laser polarization. (c) Field-intensity dependencies of the fifth, seventh, and ninth harmonic spectra. (d) HHG spectrum at the peak field of 10 MV/cm.

Figure 2

(a) Field-intensity dependencies of the fifth (red), seventh (green), and ninth (blue) HHG intensities. Two data sets (squares and triangles) were measured in a single sweep starting from 2 to 12 MV/cm and then from 12 to 2 MV/cm, respectively. Small HHG signals (circles) were measured with a longer acquisition time. (b) Calculated results of the Luttinger-Kohn model. In the weak-field regime, the harmonic intensities almost obey an $E^{2n}$ perturbative scaling law for both the measured and calculated results (dashed black lines).

Figure 3

(a) Schematic diagram of the band structure of GaAs in the absence of an external field for $\mathit{k}=(0,0,k_z)$. The four bands, each of which is twofold degenerate, correspond to conduction (C), light-hole (LH), heavy-hole (HH), and split-off (SO) bands. We express the band gap and split-off band energy as $E_g$ and ${\mathrm{\Delta }}_{\mathrm{SO}}$. (b) Schematic diagram of the dispersion relations of the simplified model (the Kane model) under an external field. The blue and red lines indicate dispersion relations for $A_z>0$ and $A_z<0$. Numerical results of field-intensity dependence of fifth (red dots), seventh (green dots), and ninth (blue dots) harmonics in GaAs based on the Kane model with (c) and without (d) the band modification term $\epsilon (k_z,t)$. These results indicate the effect of the field-induced dynamic band modification on the oscillatory behavior.