Group-velocity-matched three-wave mixing in birefringent crystals

It is shown that the combination of pulse-front slant, kappa -vector tilt, and crystal birefringence often permits exact matching of both phase and group velocities for three-wave mixing in birefringent crystals. This exact match makes possible more-efficient mixing of short light pulses, and it permits efficient mixing of chirped or broadband light. I analyze this process and present examples.