Calculation of the effective second-order non-linear coefficients along the phase matching directions in acentric orthorhombic biaxial crystals

The effective second-order non-linear coefficients for the four acentric orthorhombic biaxial point groups are formulated in a general way from the definition given by Boyd and Kleinman as a function of the crystal symmetry and direction of propagation of light in the crystal. The effective non-linear coefficients are calculated numerically in the case of the second harmonic generation at 1064 nm from a Nd:YAG laser, under the phase matched condition for eight orthorhombic nonlinear crystals: ammonium oxalate, iodic acid, lithium formate, potassium titanyl phosphate, calcium tartrate tetrahydrate, lithium gallium oxide, barium sodium niobate and potassium niobate.