Rotational Symmetry and Absolute Sign of Second-Order Susceptibility of α-Quartz

We investigate the rotational symmetry and absolute sign of the effective second order susceptibility of the right-handed z-cut α-quartz crystal in different crystal orientations through the second-harmonic-generation phase interference between standard and reference of thin α-quartz plates. The D₃ rotational symmetry of the z-cut α-quartz crystal shows 6 alternating sign sections of the second order susceptibility in the 360°rotation, which leads to two distinctive interference patterns between the reference and standard second harmonic field. From this information, the sign of the interference pattern in the second harmonic phase measurement could be readily derived.