Ultrashort-pulse second-harmonic generation with longitudinally nonuniformquasi-phase-matching gratings: pulse compression and shaping

We present a theory of ultrashort-pulse second-harmonic generation (SHG) in materials with longitudinally nonuniform quasi-phase-matching (QPM) gratin gs. We derive an expression for the output second-harmonic field generated in an arbitrary QPM grating from an arbitrary fundamental field, valid for arbitrary material dispersion in the undepleted-pump approximation In the c ase when group-velocity dispersion can be neglected, a simple transfer-func tion relationship describes the SHG process. This SHG transfer function dep ends only on material properties and on the QPM grating design. We use this SHG transfer function to show that nonuniform QPM gratings can be designed to generate nearly arbitrarily shaped second-harmonic output pulses. We an alyze in detail a technologically important example of pulse shaping: the g eneration of compressed second-harmonic pulses from linearly chirped fundam ental input pulses. The efficiency of these interactions as well as the lim its imposed by higher-order material dispersion are discussed. (C) 2000 Opt ical Society of America [S0740-3224(00)00401-X].