Two-photon Absorption - Background

Background

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 and subsequently observed in a cesium vapor.

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 for 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.

The third order can be rationalized by considering that a second order process creates a polarization with the doubled frequency. In the third order, by difference frequency generation the original frequency can be generated again. Depending on the phase between the generated polarization and the original electric field this leads to the Kerr effect or to the two-photon absorption. In second harmonic generation this difference in frequency generation is a separated process in a cascade, so that the energy of the fundamental frequency can also be absorbed. In harmonic generation, multiple photons interact simultaneously with a molecule with no absorption events. Because n-photon harmonic generation is essentially a scattering process, the emitted wavelength is exactly 1/n times the incoming fundamental wavelength. This may be better called three photon absorption. In the next paragraph resonant two photon absorption via separate one-photon transitions is mentioned, where the absorption alone is a first order process and any fluorescence from the final state of the second transition will be of second order; this means it will rise as the square of the incoming intensity. The virtual state argument is quite orthogonal to the anharmonic oscillator argument. It states for example that in a semiconductor, absorption at high energies 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 absorption and thus have a high damage threshold.

Two-photon absorption can be measured by several techniques. Two of them are two-photon excited fluorescence (TPEF) and nonlinear transmission (NLT). Pulsed lasers are most often used because TPA is a third-order nonlinear optical process, and therefore is most efficient at very high intensities. Phenomenologically, this can be thought of as the third term in a conventional anharmonic oscillator model for depicting vibrational behavior of molecules. Another view is to think of light as photons. In nonresonant TPA two photons combine to bridge an energy gap larger than the energies of each photon individually. If there were an intermediate 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". In nonresonant TPA 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 TPA 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 TPA phenomena. Further, in order to understand the TPA spectrum, monochromatic light is also desired in order to measure the TPA cross section at different wavelengths. Hence, tunable pulsed lasers (such as frequency-doubled Nd:YAG-pumped OPOs and OPAs) are the choice of excitation.