Separating Non-linear Optical Signals of a Sample from High Harmonic Radiation in a Soft X-ray Free Electron Laser

Second harmonic generation (SHG) is a unique non-linear optical effect that can be used to investigate chemical states of molecules at surfac-es/interfaces. By the use of soft X-rays, SHG gains element selectivity through the inner-core excitation resonance. However, it is challenging to observe SHG signals separately from the second-order light generated from the undulator. Here, we report a new ellipsometry method for soft X-ray SHG to suppress the contribution of second-harmonic radiation from the light source. Through measurements of a GaAs(100) crystal, we demonstrate that pure SHG signals can be obtained for the horizontally polarized component. The present method is generally applicable regard-less of the incident photon energy and hence the absorption edge of the targeted materials. If combined with optical filters blocking the sec-ond-harmonic radiation and equipped with soft X-ray phase shifters, the method allows one to obtain further information from SHG signals such as tensor components of second-order non-linear sus-ceptibility.