Abstract
The history and current state of the field of soft X-ray nonlinear optics is discussed. The development of soft X-ray nonlinear optics has been largely based upon the earlier work done with visible and infrared spectroscopy. While nonlinear optics in those frequency regimes are relatively mature today, soft X-ray nonlinear optics is a young field. This delayed development was due to the lack of intense ultrafast X-ray light sources, but with the recent rise of X-ray free electron lasers and other intense X-ray sources, there has been an explosion in the field. The specific soft X-ray nonlinear optics techniques that have been employed so far are discussed in detail and the underlying physical principles are discussed. These include non-sequential multiple-photon absorption, stimulated emission to drive lasing, and various forms of stimulated Raman scattering. These techniques have enabled new measurements that were previously infeasible, providing access to dipole forbidden states, driving anisotropic X-ray emission, and allowing for the understanding of excited state surfaces in an unprecedented way. Additionally, four wave mixing has been demonstrated and a dedicated four wave beamline built for the study of complex phenomena such as diffusional dynamics. By performing four wave mixing in the soft X-ray region, one accesses particularly large momentum transfer and thus spatially small volumes. Second harmonic generation has also been demonstrated in the soft X-ray region, allowing for the study of symmetry breaking and surfaces in materials ranging from batteries to graphite. This technique has recently been extended to a variation of sum frequency generation, where the soft X-ray beam is mixed with a visible laser pulse and has been shown to be a sensitive probe of charge localization. Finally, the available computational methods which can be used to model and understand these phenomena are discussed.
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Acknowledgements
We thank Hisazumi Akai for his comment on theoretical calculation of nonlinear spectral analysis. We appreciate Tomoaki Senoo, **ngYu Su, Toshihide Sumi and Iwao Matsuda for editing and revising the chapter. This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC-0023397.
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Schwartz, C.P., Drisdell, W.S. (2023). Nonlinear Soft X-Ray Spectroscopy. In: Matsuda, I., Arafune, R. (eds) Nonlinear X-Ray Spectroscopy for Materials Science. Springer Series in Optical Sciences, vol 246. Springer, Singapore. https://doi.org/10.1007/978-981-99-6714-8_4
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