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The process of high harmonic generation (HHG) has a wide area of different applications, in particular, in nanoscale imaging, study the nanoscale energy transport in complex molecules and solids, probe the charge and spin dynamics with the femtosecond time resolution, etc. Here we discuss a possible application of HHG effect related with the study of nuclear transition dynamics. We analyse the efficiency of excitation of the isomeric nuclear state 229mTh by the fifth harmonic of Ti: Sa laser generated in thorium by two-color femtosecond pulse consisting of the fundamental and thensecond harmonic of Ti: Sa laser (ω+2ω). It is shown that the rate of isomeric state excitation can be enhanced significantly with respect to other nucleus excitation processes in laser plasma or by an external coherent source at the resonance wavelength. This enhancement is due to the discussing process of “nonlinear laser nuclear excitation”.

We compare the results of experimental and theoretical studies of the quasi-phase matching (QPM) of high-order harmonic generation (HHG) during propagation of two-color femtosecond pulses through the indium multi-jet plasmas. The role of number of coherent zones and size of plasma jets on the HHG efficiency at QPM conditions is analysed. We demonstrate the enhancement of the HHG efficiency due to QPM during laser-plasma interaction.