Effective nonlinear coefficient for sum-frequency generation with collinear phase matching calculated taking account of the birefringence in biaxial crystals

The effective nonlinear coefficient for sum-frequency generation with collinear phase matching is calculated taking account of the birefringence (anisotropy or drift) in biaxial crystals. It is shown that the components of the unit vectors along the directions of oscillations of the electric vector of the ‘fast’ and ‘slow’ wave can be found without resorting to direct solution of equations derived directly from the wave equations. These components are expressed in terms of the birefringence angles which, in turn, are calculated in terms of the components of the ray vectors and the refractive indices of the waves. A method for calculating the effective nonlinear coefficient is given. All the calculations are made for collinear phase matching.