## 2 Experiment
### QPM in LPPs
As for non-phase matched harmonics, for example H18 of 1320 nm + 660 nm pump, this consideration (i.e., quadratic growth of harmonic efficiency with the growth of the number of jets) is not applicable, since phase mismatch between harmonic and fundamental waves does not allow the growth of harmonic yield. We also analyzed the QPM-enhanced spectrum from indium MJP using 1360 nm + 680 nm two-color pump at the conditions when the calcite quarter-wave plate was inserted before the BBO crystal. In that case the polarization of the driving 1360 nm pulses was changed from linear to circular  
Figure 4: **(a)** Dependence of H34 intensity on the number (\(n\)) of jets of the indium MJP. The multi-jet indium LPP was produced using the tilted MSM with the single plasma jet sizes of 0.23 mm and pumped by two-color near infrared (NIR) + visible (1320 nm + 660 nm), 70 fs pulses. The peak intensity of 1320 nm pump was \(1.4\times 10^{14}\) W cm\({}^{-2}\). The dashed line shows the slope \(l=2\) of the experimental dependence up to \(n=4\). **(b)** Harmonic distribution obtained from indium MJP in the case of propagation of driving pulses (1360 nm + 680 nm) through the plasma [bottom spectrum, similarly to the case shown in the upper panel of Figure 2b] and calcium quarter-wavelength plate and plasma (upper panel, see text). **(c)** Influence of heating pulse energy on the maximally enhanced harmonic in the case of silver (filled spheres) and aluminum (empty circles) MJPs. The pump radiation after propagating in the BBO crystal consisted of a circularly polarized 1360 nm pump and a linearly polarized 680 nm pump. The variation of polarization conditions caused the generation of high-order harmonics only from the 680 nm pump. The generated spectrum of harmonics is seen in the upper panel of Figure 4b showing the strong odd harmonics of 680 nm radiation. In the case of absence of calcite, the spectral pattern (bottom graph) contained a whole set of two groups of enhanced harmonics, as has already been shown in the above-described results [Figure 2b]. The aim of this study is to show the QPM at different combinations of the driving fields. The results presented in Fig. 4b are related to QPM studies at variable polarization conditions of the driving waves, when the linearly polarized second harmonic field (680 nm) and two linearly polarized fields (1360 nm and 680 nm) were applied for HHG. The harmonics occur at the conditions of the interaction of linearly polarized radiation and plasma. Circularly-polarized 1360 nm radiation splits into two orthogonally polarized waves during the propagation through BBO. One of these waves partially converts to the second harmonic. After propagation through the BBO crystal, these two orthogonally-polarized 1360 nm waves combine to create the circularly polarized 1360 nm radiation, which does not participate in HHG. Then only the second harmonic radiation serves as the driving field for HHG at the conditions of QPM. The optimization of QPM for shorter wavelengths at lesser excitation of the target during formation of multi-jet plasmas can be observed in different materials. We analyzed the dependence of the highest enhanced harmonic order on the energy of the heating pulse producing MJPs on the surfaces of silver and aluminum [Figure 4c]. This dependence underlines the influence of over-dense plasmas and electrons on the formation of QPM conditions in different plasmas. We observed the tuning of the maximum of spectral envelope towards the higher-order harmonics at smaller fluence of heating radiation. A decrease of electron concentration at weaker excitation of the target led to optimization of the QPM for higher orders of harmonics to keep the product \(H_{\mathrm{qpm}}\times N_{\mathrm{e}}\) unchanged at the fixed spatial characteristics of the plasma jets. Figure 4c, showing the log-log dependence of \(H_{\mathrm{qpm}}\) on the energy of heating pulses for two different targets (Ag and Al), confirms the relation \(H_{\mathrm{qpm}}\times N_{\mathrm{e}}\sim\) constant.