Two-photon absorption

In atomic physics, two-photon absorption (TPA or 2PA), also called two-photon excitation or non-linear absorption, is the simultaneous absorption of two photons of identical or different frequencies in order to excite a molecule from one state (usually the ground state) to a higher energy, most commonly an excited electronic state. Absorption of two photons with different frequencies is called non-degenerate two-photon absorption. Since TPA depends on the simultaneous absorption of two photons, the probability of TPA is proportional to the square of the light intensity; thus it is a nonlinear optical process. The energy difference between the involved lower and upper states of the molecule is equal or smaller than the sum of the photon energies of the two photons absorbed. Two-photon absorption is a third-order process, with absorption cross section typically several orders of magnitude smaller than one-photon absorption cross section. Two-photon excitation of a fluorophore (a fluorescent molecule) leads to two-photon-excited fluorescence where the excited state produced by TPA decays by spontaneous emission of a photon to a lower energy state. The phenomenon was originally predicted by Maria Goeppert-Mayer in 1931 in her doctoral dissertation. Thirty years later, the invention of the laser permitted the first experimental verification of TPA when two-photon-excited fluorescence was detected in a europium-doped crystal. Soon afterwards, the effect was observed in cesium vapor and then in CdS, a semiconductor. TPA is a nonlinear optical process. In particular, the imaginary part of the third-order nonlinear susceptibility is related to the extent of TPA in a given molecule. The selection rules for TPA are therefore different from one-photon absorption (OPA), which is dependent on the first-order susceptibility. The relationship between the selection rules for one- and two-photon absorption is analogous to those of Raman and IR spectroscopies.