Two-photon absorption

Schematic representation of a two-photon absorption from state 0 to state 2 via the virtual intermediate level 1

When two-photon absorption is called the simultaneous absorption of two photons by a molecule or atom , which thereby turns into an energetically excited state. The energy of one of these photons alone is not enough to bridge the energy difference between the basic state (state 0 in the adjacent figure) and the excited state (state 2 in the adjacent figure).

description

There is no permitted energy level between state 0 and state 2, so the photons must be absorbed almost simultaneously, i.e. H. within a time interval of the order of magnitude 0.1 femtoseconds = 10 ⁻¹⁶ s, which results from the energy-time uncertainty relation. A virtual intermediate level is used to describe this process, the lifespan of which corresponds approximately to the duration of the absorption process. In the figure on the right, absorption takes place from state 0 to 2 via virtual intermediate level 1. Such a figure is also called a Jablonski diagram . The secondary processes from the excited state 2, such as B. fluorescence (shown with a dashed arrow pointing downwards), take place regardless of the type of excitation.

In order for two-photon absorption to take place, the sum of the energies of the absorbed photons must correspond to the energy difference between the molecular states: ${\ displaystyle \ Delta E}$

{\ displaystyle \, \ Delta E = E_ {1} + E_ {2} = h \ nu _ {1} + h \ nu _ {2}}

Here are the oscillation frequencies of the two photons and is Planck's quantum of action . If necessary, further selection rules (e.g. for angular momentum) must be fulfilled. ${\ displaystyle \ nu _ {i}}$ ${\ displaystyle h}$

The process of two-photon absorption was first described theoretically in 1931 by Maria Goeppert-Mayer in her dissertation. Since such a process is very unlikely, and a very high temporal and spatial photon density is required for such an event, the two-photon absorption could only be proven experimentally by Wolfgang Kaiser and CGB Garrett shortly after the invention of the laser (1961) . An impression of the probability of such an event is given in: In bright sunshine, a molecule of a good one- or two-photon absorber absorbs about one photon per second via a one-photon event. Two-photon absorption only takes place every 10 million years under the same conditions. The probability of a two-photon absorption is described by the two-photon cross-section . It is given in the Goeppert-Mayer (GM) unit . ${\ displaystyle \ sigma _ {2P}}$

{\ displaystyle \, 1 \, \ mathrm {GM} = 10 ^ {- 50} \ mathrm {cm} ^ {4} s {\ text {/ photon / molecule}}}

Applications

Applications of two-photon absorption (e.g. multiphoton microscopy ) are primarily based on its quadratic dependence on the intensity of the light (in contrast to the linear dependence in one-photon absorption) as well as the possibility of longer-wave (and thus lower-energy ) To use light. Two-photon absorbers are also used in 3D lithography, in 3D optical data storage and in markers and probes in biology. Thanks to the non-linearity, it can be achieved here that significant absorption occurs only at a desired depth in the material. Another important application is in the Doppler-free saturation spectroscopy of atomic systems. The design of so-called two-photon dyes (substances with high two-photon absorption) is an active research area. Tens of thousands of GM materials (instead of the usual <10 GM) have already been produced.

Furthermore, so-called 3D printers with two-photon polymerization technology have been developed. These are characterized by a very high resolution of less than 1 micrometer.

Individual evidence

^ Maria Goeppert-Mayer: About elementary acts with two quantum leaps . In: Annals of Physics . 9, 1931, pp. 273-294.
↑ Kaiser, W. and Garrett, CGB: Two-photon excitation in CaF ₂ : Eu ²⁺ . In: Physical Review Letters Vol. 7 (6) . August, p. 229. doi : 10.1103 / PhysRevLett.7.229 .
↑ Denk, W. and Svoboda, K .: Photon upmanship: why multiphoton imaging is more than a gimmick . Neuron, Vol. 18, pp. 351-357
↑ ^a ^b M. Pawlicki et al. : Two-photon absorption and the design of two-photon dyes . In: Angewandte Chemie . 121, No. 18, 2009, pp. 3292-3316. doi : 10.1002 / anie.200805257 .
↑ 2-photon polymerization. Institute for Bioprocess and Analytical Measurement Technology . Retrieved November 21, 2017.
↑ Karin Zühlke: 3D printer for microfabrication. Micro objective lenses on CMOS chips. elektroniknet.de. March 24, 2017. Retrieved November 21, 2017.

literature

Meschede, Dieter: Optics, light and laser. Wiesbaden: 2., revised. and exp. Ed. Teubner, 2005. ISBN 3519132486
Demtröder, Wolfgang: Laser Spectroscopy 2. Berlin / Heidelberg: 6., revised. and updates Edition Springer, 2013. ISBN 978-3-642-21446-2

Web links

Web-based calculator for the rate of 2-photon absorption

[1] Maria Goeppert-Mayer: About elementary acts with two quantum leaps . In: Annals of Physics . 9, 1931, pp. 273-294.

[2] Kaiser, W. and Garrett, CGB: Two-photon excitation in CaF ₂ : Eu ²⁺ . In: Physical Review Letters Vol. 7 (6) . August, p. 229. doi : 10.1103 / PhysRevLett.7.229 .

[3] Denk, W. and Svoboda, K .: Photon upmanship: why multiphoton imaging is more than a gimmick . Neuron, Vol. 18, pp. 351-357

[Pawlicki2009-4] M. Pawlicki et al. : Two-photon absorption and the design of two-photon dyes . In: Angewandte Chemie . 121, No. 18, 2009, pp. 3292-3316. doi : 10.1002 / anie.200805257 .

[iba-5] 2-photon polymerization. Institute for Bioprocess and Analytical Measurement Technology . Retrieved November 21, 2017.

[6] Karin Zühlke: 3D printer for microfabrication. Micro objective lenses on CMOS chips. elektroniknet.de. March 24, 2017. Retrieved November 21, 2017.