Optimal phase matching for second harmonic generation in monoclinic non-linear optical crystals determined by extreme surfaces method

The optimal phase matching is determined for the second harmonic generation (SHG) in biaxial non-linear optical crystals of monoclinic symmetry - BiBO, LCB (point group 2), GdCOB, YCOB (point group
$m$
). For the case of vector phase matching, the directions of wave vectors of input and output beams corresponding to the highest possible SHG efficiency are determined by the extreme surfaces method. It is shown, that the use of vector phase matching allows to increase the SHG efficiency on a value about a few percent for the considered crystals.