## 2 Experiment
### QPM in LPPs
They were centered at H43, H36, and H31 (see Figure 3 from top to bottom) and corresponded to the MJF structures with the sizes of single jet of 0.25, 0.31, and 0.35 mm. The analysis of the harmonics intensity as a function of the number of plasma jets (\(n\)) can provide a proof of the decisive role of the QPM in the variations of harmonic spectrum. The coherent accumulation of harmonic yield along the whole length of divided nonlinear optical medium is demonstrated in the present studies. We used the indium target for ablation and the two-color pump (1300 nm + 650 nm) for HHG in indium plasma. The heating areas on the target (shown in the inset in Figure 1) were shielded one by one to allow the generation of harmonics in different numbers of plasma jets. The number of jets was increased one by one from single jet to 8 jets. The width of each jet was 0.3 mm and the empty area on the target surface between jets was also equal to 0.3 mm. The whole length of the 8-jet structure was \(\sim\)5 mm. The harmonic spectrum in the case of single jet showed a plateau-like shape of weak harmonics. Each addition of the next jet caused growth of the group of harmonics centered at around H34. This harmonic had the coherent length of \(\sim\)0.3 mm at the used fluence of heating pulses on the surface of In target (1.2 J cm\({}^{-2}\)) and the intensity of driving NIR pulses (\(1.4\times 10^{14}\) W cm\({}^{-2}\)). Figure 3: Raw images of harmonic spectra from the multi-jet silver LPP produced using tilted MSM with single plasma jet sizes of (top to bottom) 0.25, 0.31, and 0.35 mm pumped by two-color (1310 nm + 655 nm), 70 fs pulses. The intensities of 1310 nm and 655 nm pumps in plasma area were \(1.3\times 10^{14}\) and \(1\times 10^{13}\) W cm\({}^{-2}\), respectively. Maximally enhanced harmonics (H43, H36, and H31) are determined for each of these plasma configurations. Bottom spectrum corresponds to homogeneous extended silver plasma. Similar conditions of plasma ablation using the same energy fluence of heating pulses and data collection times are applied for these four cases. The coherence length (in mm) of some harmonics at the conditions of using the 1300-nm driving laser could be presented as \(L_{\mathrm{coh}}\approx 1\times 10^{18}/(N_{e}\times H_{\mathrm{qpm}})\)[1; 16]. Here \(H_{qpm}\) is the maximally-enhanced harmonic at QPM conditions and \(N_{e}\) is the electron density in cm\({}^{-3}\). H34 has coherence length of \(\sim\)0.3 mm at the used fluence (1.2 J cm\({}^{-2}\)) of the heating pulses on the surface of In target, and \(1.4\times 10^{14}\) W cm\({}^{-2}\) intensity of the driving NIR pulses. We used the MSM containing slits with the sizes of 0.3 mm and excited the target in such a manner that electron density satisfied the above relation for the H34 at the length of single jet of 0.3 mm. Correspondingly, at another excitation of target the electron concentration of plasma may satisfy to another harmonic order at the fixed sizes of single jet in the MJP. The yield of H34 increased as \(I_{\mathrm{H34}}\)\(-\)\(n^{2}\) up to \(n=4\). Further addition of jets led to deviation from quadratic dependence [Figure 4a] due to some inequality of plasma jets, which led to violation of the optimal phase relations between driving and H34 waves. At these conditions of the imperfect coherent accumulation of nonlinear optical response we were able to observe the 40-fold growth of H34 in the case of 8-jet plasma compared with the single-jet one. H34 was perfectly suited for comparative analysis of the role of number of separated jets on the variation of the intensity of generated harmonic. The coherence length in these experiments has a direct relation with the coherent addition of harmonic emission after propagation of H34 through each next jet. As it was shown, even at these favorable conditions for coherent summing of harmonic waves in each next jet, the additional impeding processes did not allow following the theoretically predicted quadratic rule once the number of jets exceeded four coherence zones.