Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings

We present a theory of ultrashort-pulse difference-frequency generation (DFG) with quasi-phase-matching (QPM) gratings in the undepleted-pump, unamplified-signal approximation. In the special case of a cw (or quasi-cw) pump, the spectrum of the generated idler is related to the spectrum of the signal through a transfer- function relation that is valid for arbitrary dispersion in the medium. The engineerability of this QPM-DFG transfer function establishes the basis for arbitrary pulse shaping. Experimentally we demonstrate QPM- DFG devices operating in a frequency-degenerate type II configuration and producing pulse-shaped output at 1550 nm from 220-fs pulses at 1550 nm.