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In this review, we present nonlinear optical methods, based on the second and third order nonlinear polarization, especially in the context of material characterization tasks outside the area of life sciences-for which these techniques are mostly designed. An overview of application studies reported to date is given, together with a discussion on the advantages and limits of the individual methods. Furthermore, new ways of experimentally combining different optical concepts are introduced, and their potential for characterisation and inspection tasks is evaluated in the context of various case studies, including the investigation of semiconductor surfaces, metals and related corrosion products, as well as of organic materials.

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