## 1 Introduction  
The interaction of ultrashort laser pulses with gases, plasmas, surfaces, and solids allows the conversion of longer-wavelength laser sources towards the extreme ultraviolet (XUV) region. This approach took special attention due to relative easiness in generating coherent short-wavelength radiation. Increasing the length of laser-matter interaction to attain stronger nonlinear optical response from extended media is one of the methods that has been applied to enhance the coherent XUV yield during high-order harmonic generation (HHG). This method, though attractive in the case of ablation of extended targets, has a significant drawback related to the phase mismatch between the interacting waves of the driving pulse and the generated harmonic when the length of medium exceeds the coherence length of the generated harmonic order. To diminish the effect of phase mismatch in laser-produced plasmas (LPP) on the HHG efficiency, the concept of quasi-phase matching (QPM) using the modulated shape of the LPP, was employed to minimize the difference between the phases of two waves. This modulation is based on the division of extended plasma into a set of equidistantly-separated plasma jets either by inserting multi-slit mask (MSM) in front of ablating surface [1], or by using perforated targets [2]. Initially, QPM concept for HHG was introduced in the gaseous media and was studied both theoretically and experimentally using different methods of gaseous medium modulation [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. Previously, phase mismatch compensation was obtained by using counter-propagating driving beams,off-axis phase matching, phase-matching in low-frequency fields, control of the pressure in modulated waveguides, the addition of a buffer gas with anomalous dispersion, self-focusing by the Kerr nonlinearity, and the application of gaseous multi-jet structures. The conditions of QPM in multi-jet plasmas are similar to those reported in the case of gaseous multi-jet structures [6; 9; 10]. The principles of QPM developed in those studies, as well as the theoretical approaches proposed in the case of QPM in plasmas [15; 16; 17], allow describing the main peculiarities of this approach and comparing the theoretical predictions and experimental observations of QPM. In the study of QPM conditions, it is usually assumed that the target is in some fixed state with some given degree and level of ionization. The model that is used in the numerical calculations takes into account the amplitudes and phases of the harmonics generated by single atoms placed in any point of the medium. The values of the amplitudes and phases are calculated by solving the quantum-mechanical problem of a single atom interacting with laser field. However, while using the single atom response under different laser parameters, it is also important to take into account the change in the profile of the driving pulse while propagating in the medium [18]. Currently, the use of two-color pumps (TCP) in gases and plasmas is a reliable approach to enhance the HHG conversion efficiency. Strong harmonic generation in the case of TCP is possible due to the formation of a quasi-linear field, and a selection of a short quantum path component, which has a denser electron wave packet and higher ionization rate compared to the single-color pump (SCP) [19]. The orthogonally-polarized second field also participates in the modification of the trajectory of accelerated electrons from being two-dimensional to three-dimensional, which may lead to the removal of the medium symmetry. With suitable control of the relative phase between the fundamental and the second harmonic radiation, the latter field enhances the short path contribution resulting in a clean spectrum of harmonics.