Simulating Cascaded Harmonics Generation up to the Sixth Order in β-BBO

We simulate the generation of multiple harmonics up to the sixth order extending into vacuum ultraviolet. The harmonics are generated by χ(n):χ(m) cascades, containing second- or third-order perturbative nonlinear processes. We identify three additional phase-matching conditions beyond standard phase matching, namely when only the first step or only the second step of the cascades are phase-matched and when the non-phase-matched second or third harmonic produces quasi-phase matching for higher-order harmonics, causing an essential enhancement of the harmonic signals.