Tuning quadratic nonlinear photonic crystal fibers for zero   group-velocity mismatch
  We consider an index-guiding silica photonic crystal fiber with a triangular air-hole structure and a poled quadratic nonlinearity. By tuning the pitch and the relative hole size, second-harmonic generation with zero group-velocity mismatch is found for any fundamental wavelength above 780 nm. The phase-velocity mismatch has a lower limit with coherence lengths in the micron range. The dimensionless nonlinear parameter is inversely proportional to the pitch and proportional to the relative hole size. Selected cases show bandwidths suitable for 20 fs pulse-conversion with conversion efficiencies as high as 25%/mW. 
Morten Bache, Hanne Nielsen, Jesper L{\ae}gsgaard, and Ole Bang