Surface symmetry resolution of nonlinear optical techniques

A general rule is derived, relating the order of a nonlinear optical process to the highest possible symmetry which can be resolved in a rotational analysis. We show that with an Nth order optical technique, rotational anisotropy can be observed only up to (N+L)-fold rotational symmetry, where L is the multipole order of the nonlinear process. We discuss the connection with rotational (non)linear optical surface studies as carried out on cubic materials, as well as implications for noncrystalline point-group symmetries.