Simple method for determining the crystalline axes of nonlinear uniaxial crystal with second-harmonic generation

For uniaxial crystal the optic axis (Z axis) can be determined easily by means of observing its growth pattern or by linear optical methods such as conuscopy. However, determination of the other crystalline axes is not so trivial, normally requiring x-ray diffraction measurements. We propose a simple method for determining the other two axes of the nonlinear uniaxial crystal, using second-harmonic generation. For several uniaxial crystals (with 3m, 62m, 42m, and 32 point groups) the intensity change of the second-harmonic output is calculated as the crystal is rotated azimuthally with respect to the Z axis. The principle is demonstrated in an experiment with LiNbO(3) crystal to determine the X axis with 0.2 degrees accuracy.