Phase matching directions in optical mixing in biaxial crystals having quadratic susceptibility

Expressions are derived for all the possible directions of collinear and noncollinear phase matching in optical mixing in biaxial crystals having quadratic susceptibilities. The familiar Hobden classification is generalized to frequency summation and subtraction processes. The types of phase-matched interaction of optical waves in the principal planes permitted by dispersion and anisotropy are indicated for each class.