A method for measuring nonlinear Electromagnetic (EM) radiation emitted by a material, comprising rotating a beam of EM radiation to form a rotating beam; irradiating a surface of a material with the rotating beam at an oblique angle with respect to the surface, wherein the rotating irradiates a plurality of scattering planes in the material; and detecting nonlinear radiation emitted by the material in response to the rotating beam, such that the nonlinear radiation generated by each of the scattering planes is detected by the detector. This method opens the possibility of applying nonlinear optics as a probe of lattice and electronic symmetries on small bulk single crystals in ultra low temperature, high magnetic field or high pressure environments, which can greatly complement diffraction based techniques.
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