Two-photon absorption

Two-photon absorption (TPA) 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 electronic state. The energy difference between the involved lower and upper states of the molecule is equal to the sum of the photon energies of the two photons. Two-photon absorption is a third-order process several orders of magnitude weaker than linear absorption at low light intensities. It differs from linear absorption in that the atomic transition rate due to TPA depends on the square of the light intensity, thus it is a nonlinear optical process, and can dominate over linear absorption at high intensities.

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 the TPA when two-photon-excited fluorescence was detected in a europium-doped crystal

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. For example, in a centrosymmetric molecule, one- and two-photon allowed transitions are mutually exclusive. In quantum mechanical terms, this difference results from the need to conserve angular momentum. Since photons have spin of ±1, one-photon absorption requires excitation to involve an electron changing its molecular orbital to one with an angular momentum different by ±1. Two-photon absorption requires a change of +2, 0, or −2.

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