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

We present numerical simulations of high-order harmonic generation in helium using a temporally synthesized and spatially nonhomogeneous strong laser field. The combination of temporal and spatial laser field synthesis results in a dramatic cutoff extension far beyond the usual semiclassical limit. Our predictions are based on the convergence of three complementary approaches: resolution of the three dimensional time dependent Schrödinger equation, time-frequency analysis of the resulting dipole moment, and classical trajectory extraction. A laser field synthesized both spatially and temporally has been proven capable of generating coherent extreme ultraviolet photons beyond the carbon K edge, an energy region of high interest as it can be used to initiate inner-shell dynamics and study time-resolved intramolecular attosecond spectroscopy.