Phase matching for large-scale frequency upconversion in plasma

We consider phase matching in the generation of very short-wavelength coherent radiation by nonlinear frequency upconversion in plasma and suggest some ways to improve phase matching in high-order harmonic generation. We obtain what are to our knowledge the first simple analytical expressions for a phase-matching factor in multiphoton mixing of an arbitrary order and demonstrate theoretically that high-order difference-frequency mixing in plasma could be, owing to its potential for phase-matching optimization, a more promising method of large-scale frequency upconversion than high-order harmonic generation.