Phase-matched frequency conversion in ionizing atomic gases

We solve the one-dimensional wave equation for high-order mixing of the type omega(h)=q omega(0) -l omega(c)(q much greater than l > = 1) using a Keldysh-type model to describe the high-field atomic nonlinear susceptibility. When omega(c) is selected to give static phase matching, we show that the conversion efficiency of the mixed field can be increased by about an order of magnitude compared to non-phase-matched high-order harmonic generation but that fundamental limitations are introduced by axial electron-density gradients.