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 an atom or a molecule from one state (usually the ground state), via a virtual energy level, to a higher energy, most commonly an excited electronic state. Absorption of two photons with the same frequency is called degenerate two-photon absorption, while absorption of two photons with different frequencies is called non-degenerate two-photon absorption. The energy difference between the involved lower and upper states is equal or smaller than the sum of the photon energies of the two photons absorbed.

Since TPA depends on the simultaneous absorption of two photons, the probability of two-photon absorption is proportional to the photon dose (D), which is proportional to the square of the light intensity D ∝ I² thus it is a nonlinear optical process. 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 absorption 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 two-photon absorption when two-photon-excited fluorescence was detected in a europium-doped crystal. Soon afterwards, the effect was observed in cesium vapor and then in cadmium sulfide, a semiconductor.

Two-photon absorption is a nonlinear optical process dependent on the third-order nonlinear susceptibility. The relationship between the number of photons - or, equivalently, order of the electronic transitions - involved in a two-photon absorption process (two, in the case of TPA) and the order of the corresponding nonlinear susceptibility (three, in the case of TPA) may be understood using the optical theorem. This theorem relates the imaginary part of an all-optical process of a given perturbation order ${\displaystyle m}$ with a process involving charge carriers with half the perturbation order, i.e. ${\displaystyle m/2}$. To apply this theorem it is important to consider that the order in perturbation theory to calculate the probability amplitude of an all-optical ${\displaystyle \chi ^{(n)}}$process is ${\displaystyle m=n+1}$. Since in the case of two-photon absorption there are electronic transitions of the second order involved (${\displaystyle m/2=2}$), it results from the optical theorem that the order of the nonlinear susceptibility is ${\displaystyle n=m-1=3}$, i.e. it is a ${\displaystyle \chi ^{(3)}}$process.

There are two (quite orthogonal) models that can be used to understand TPA, namely classical optics and quantum mechanics. In the classical picture, third-order optical process are described by the equation ${\displaystyle {\tilde {P}}_{i}(\omega =\omega _{j}+\omega _{k}+\omega _{\ell })={\tilde {\chi }}_{ijk\ell }^{(3)}(\omega _{j},\omega _{k},\omega _{\ell }){\tilde {E}}_{j}(\omega _{j}){\tilde {E}}_{k}(\omega _{k}){\tilde {E}}_{\ell }(\omega _{\ell })}$, where ${\displaystyle {\tilde {P}}_{i}}$ is the i-th component of the polarization field, ${\displaystyle {\tilde {E}}_{j}}$, etc. are the j-th, etc. components of the three electric fields involved in a third-order process, and ${\displaystyle {\tilde {\chi }}_{ijk\ell }^{(3)}}$ is the fourth-rank susceptibility tensor. The tilde over each of these values denotes that they are, in general, complex. TPA can happen when the imaginary part of the relevant ${\displaystyle {\tilde {\chi }}_{ijk\ell }^{(3)}(\omega )+1}$ component is positive. When this value is negative, the opposite process, two-photon emission, can occur. This follows from the same physics that describes single-photon loss and gain in a medium using the first-order equation ${\displaystyle {\tilde {P}}_{i}(\omega )={\tilde {\chi }}_{ij}^{(1)}(\omega ){\tilde {E}}_{j}(\omega )}$. Note that this convention of absorption for ${\displaystyle {\mathcal {Im}}[{\tilde {\chi }}_{ijk\ell }^{(3)}+1]>0}$ and emission for ${\displaystyle {\mathcal {Im}}[{\tilde {\chi }}_{ijk\ell }^{(3)}+1]<0}$ is the one commonly followed in physics; in engineering, the opposite convention is often used.

In the quantum mechanical model, we think of light as photons. In non-resonant two-photon absorption, neither photon is at resonance with the system energy gap, and two photons combine to bridge the energy gap larger than the energies of each photon individually. If there were an intermediate electronic state in the gap, this could happen via two separate one-photon transitions in a process described as "resonant TPA", "sequential TPA", or "1+1 absorption" where the absorption alone is a first order process and the generated fluorescence will rise as the square of the incoming intensity. In non-resonant two-photon absorption the transition occurs without the presence of the intermediate state. This can be viewed as being due to a "virtual state" created by the interaction of the photons with the molecule.

The "nonlinear" in the description of this process means that the strength of the interaction increases faster than linearly with the electric field of the light. In fact, under ideal conditions the rate of two-photon absorption is proportional to the square of the field intensity. This dependence can be derived quantum mechanically, but is intuitively obvious when one considers that it requires two photons to coincide in time and space. This requirement for high light intensity means that lasers are required to study two-photon absorption phenomena. Further, in order to understand the two-photon absorption spectrum, monochromatic light is also desired in order to measure the two-photon absorption cross section at different wavelengths. Hence, tunable pulsed lasers (such as frequency-doubled Nd:YAG-pumped optical parametric oscillators and optical parametric amplifiers) are the choice of excitation.

In a semiconductor, TPA is impossible if two photons cannot bridge the band gap. So, many materials can be used for the Kerr effect that do not show any one- or two-photon absorption and thus have a high damage threshold.