# Interference-Induced Phenomena in High-Order Harmonic Generation from Bulk Solids
## 3 Results
### Even and Odd Harmonics
However, the overall HH gain increases when the pulses considerably overlap--it has a maximum at zero delay, that is, when the peak value of the net electric field is maximal. For the individual harmonics, we can see that in accordance with the previous results, the presence of the THz radiation increases the height of the even-order harmonic peaks. (Note that in order to decrease numerical errors, Figure 7 shows the intergral of the spectrum around the given HH frequencies.) On the other hand, surprisingly, odd-order harmonics become weaker when the infrared and the THz pulses overlap considerably. For the strength of the seventh harmonic, as it is shown  
Figure 5: The suppression of even-order harmonics. Panel (**a**) [**(b)**] corresponds to \(U^{(a)}\)[\(U^{(b)}\)]. In both panels, the contributions of given values of \(k\) is shown together with that of \(-k\) and their combined effect, for parameters \(F_{0}=4.0\,\)GV/m (\(2.13\times 10^{12}\) W/cm\({}^{2}\) peak intensity), \(\lambda_{L}=3\) μm and \(\tau=300\,\)fs. by Figure 7, the dependence on the delay exhibits strong modulations with the half-cycle period of the THz field. For the case of the eighth harmonic, this is less obvious, and fast modulations are more apparent. Although the qualitative features of Figure 7 can be explained, and they are in agreement with Figure 6, it is clear that in order to completely explore the case of THz-assisted HHG with different delays, a more detailed investigation is needed--however, this is beyond the scope of the current paper. Figure 6: The appearance of even-order harmonics. Panel (**a**) infrared excitation, panel (**b**) THz assisted infrared excitation. The time dependences of the vector potentials of the exciting fields are shown by the insets, where the units for the horizontal and vertical axes are fs and GV-fs/m, respectively. Panel (**c**) shows the current density \(J\), which is the source of the HH radiation. Figure 7: The contribution of different frequency ranges to the HHG radiation as a function of the delay between the infrared and the THz pulses for the same amplitudes as in Figure 6. Negative delays mean that the THz pulse arrives first. For the \(n\)th individual harmonic, the integral of the spectrum for an interval of the length of \(0.6\omega_{L}\) that is centered around \(n\omega_{L}\) is shown. For ”all harmonics”, the integration runs from \(1.5\omega_{L}\) to \(30\omega_{L}\). It is also worth plotting the populations in the four bands that we took into account. The result is shown by Figure 8, where it can be seen why, in the intensity range we considered, four bands were enough for the appropriate description: the population of the third conduction band is practically negligible. As a closer look (and the Fourier transform as well) reveals, harmonic frequencies modulate the time evolution of the populations. Finally, it is worth mentioning that for multi-cycle infrared excitations (without the THz field), the populations in the conduction bands were practically zero when the pulse was over. On the other hand, with the additional THz field, these final populations increased orders of magnitude (definitely above the level of the numerical errors), but they still had the order of magnitude of \(10^{-6}\)-\(10^{-8}\).