Theoretical and Historical Background

The two-photon absorption (2PA) process was predicted by M. Goppert-Mayer in 1931 during her PhD thesis [19]. Based on the quantum theory of radiation, M. Goppert-Mayer introduced the concept of virtual or intermediate states and provided the theoretical expression the 2PA probability. However, due to the very low value of this feature, the first experimental observation of this phenomenon could be only obtained for the first time at the advent of power lasers in 1960s, by the two-photon excited (2PE) up-eonverted fluoreseenee of a CaF2 Eu(II) crystal using 694.3 nm ruby laser exeitation, as described in detail below [20]. 

As a general point of view, the 2PA process corresponds to the simultaneous interaction of two photons with matter, leading to the absorption transition from a lower level to a higher excited one, through a virtual level. It is worth noting that multi-higher order ( 2) absorption processes can be also observed (multiphoton absorption, MPA, e.g. 3PA, 4PA, etc.) 2PA and 3PA processes are displayed in Pig. 5.1, as examples. 

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