Generalized study on angular dependence of induced second-order nonlinear optical polarizations and phase matching in biaxial crystals

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Abstract
The induced second‐order nonlinear coefficients in the noncentrosymmetrical biaxial crystals are formulated in a general way as functions of the their crystal symmetry and directions of propagation of optical waves in the crystal. The direction of light propagation is determined from the phase matching among three optical waves. The optimum operating condition is also derived analytically by investigating the effective nonlinearity under the phase‐matched direction. This treatment is applied to the case of the second harmonic generation of Nd : YAG laser (1.064 μm), using α‐iodic acid, lithium formate, sodium formate, and lithium‐sodium formate crystals. Experimental results were compared quite favorably with the theoretical analysis given in this paper.