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We present numerical simulations of high-order harmonic generation in heliumusing a temporally synthesised and spatially non-homogeneous strong laserfield. The combination of temporal and spatial laser field synthesis results ina dramatic cut-off extension far beyond the usual semiclassical limit. Ourpredictions are based on the convergence of three complementary approaches:resolution of the three dimensional Time Dependent Schr\"odinger Equation,time-frequency analysis of the resulting dipole moment and classicaltrajectories extraction. Employing a combination of temporally and spatiallysynthesised laser field provides coherent XUV photons beyond the carbon K-edgewhich is of high interest for initiating inner-shell dynamics and studytime-resolved intra-molecular attosecond spectroscopy.

Beyond Carbon K-edge harmonic emission using spatial and temporal synthesized laser field