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When certain materials are bombarded with very intense light they are able to able to absorb two low energy photons and enter an excited state Two Photon Absorption(TPA). The electron quickly jumps back down from the higher energy level and releases energy as light in fluorescence (TPE). The sample is excited by light of one wavelength while fluorescing at a different wavelength. Typically a range of exciting wavelengths are tested and the fluorescence is measured at a specific wavelength that is characteristic for that material. The end result is a graph that shows the overall intensity of fluorescence compared to the exciting wavelength indicating that two photon absorption has occurred. From this the two photon cross section can be determined.
TPA with the reference sample method In the reference sample method a known sample is and a test sample are excited with the same beam. This means you don't have to characterize the beam completely, instead you compare the reference to the unknown.
TPA with well characterized beam
This is a typical optical table setup for a two photon spectroscopic study. The particular arranged of the light path is dependent on the lab but the basic components would be the same. In this case the exact properties of the exciting beam are known.