Measuring linear electric quadrupole susceptibility of non-centrosymmetric crystals with reflectivity difference

I report experimental methods for measuring real and imaginary parts of the linear electric quadrupole susceptibility tensor of nonlinear optical crystals that lack inversion centers. The third-ranked tensor is related to the corresponding second-order nonlinear susceptibility tensor. For opaque materials such as GaAs, the methods involve normal-incidence reflectivity difference detection schemes. For transparent materials, quadrupole susceptibility tensor elements may be measured with similarly construed transmission difference detection schemes.