Quantum-path analysis and phase matching of high-order harmonic generationand high-order frequency mixing processes in strong laser fields

We study phase-matching conditions for high-order harmonic generation as we ll as high-order sum- and difference-frequency mixing processes in strong l aser fields, using a graphical approach described in Balcou et al (1997 Phy s. Rev. A 55 3204-10). This method is based on the analysis of the differen t quantum paths that contribute, with different phase properties, to the si ngle-atom response. We propose a simple numerical method to disentangle the quantum paths contributing to the generation process. We present graphical maps of the phase matching around the laser focus, which allow one to pred ict the geometries that optimize the conversion efficiency of the process c onsidered. The method is applied to the study of sum- and difference-freque ncy mixing processes. The qualitative predictions of the graphical phase-ma tching approach are confirmed by numerical propagation calculations.