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The high-order harmonic generation (HHG), if phase matched, opens a uniqueway to produce coherent ultrafast extreme-UV (XUV) or soft x-ray light sources.Here we describe a robust and tunable method for scaling and narrowing thebandwidth of high-order harmonics in different transversal modes based onfemtosecond dynamic grating in a gas jet. This technique has potential ofself-phase controlled XUV generation by adjusting the intersect angle and theintensity ratio of interfering fundamental beams. The limitations of using highintensity laser fundamental pulses in gas, such as non-negligible the magneticfield which prevents recombination with parent and self-focusing of laser andplasma creation in the generated harmonics beam path which prevents phasematching, can be solved by using dynamic grating generated by the fundamentalpulse and/or its harmonic with small intersect angle. The grating patternintroduces a phase modulation in the dipole emission imprint such pattern inthe gas medium. As the spatial and temporal behaviors of the grating areclosely connected in harmonic generation, by shaping of the spatial profile ofthe interfering beams it is possible to create a more complex tunable beatingpattern as harmonic sources to transfer desired optical information to XUVpulses. In this case, the phase mismatch can be completely compensate by tuningthe gas pressure, adjusting the intersect angle as well as intensity ratio ofthe interfering beams to produce a bright XUV with desired transversal mode.

Efficient, self-phase matched, narrow-band, engineered shape, tunable high-order harmonic generation based on femtosecond dynamic grating