Goppert-Mayer

All the previous discussion in this chapter has been concerned with absorption or emission of a single photon. However, it is possible for an atom or molecule to absorb two or more photons simultaneously from a light beam to produce an excited state whose energy is the sum of the energies of the photons absorbed. This can happen even when there is no intemrediate stationary state of the system at the energy of one of the photons. The possibility was first demonstrated theoretically by Maria Goppert-Mayer in 1931 [29], but experimental observations had to await the development of the laser. Multiphoton spectroscopy is now a iisefiil technique [30, 31]. 

In the 1930s, Maria Goppert-Mayer [12], theoretically predicted the process of an atom being raised to an excited state of energy equal to the sum of two simultaneously... 

Goppert-Mayer, M. 1931. Uber Elementarakte mit zwei Quantensprungen. Annalen der Physik 9 273-294. 

Two-photon excitation fluorescence is currently the most widely nsed nonlinear contrast mechanism for microscopic investigations. The first experimental demonstration of two-photon excitation fluorescence was provided in 1961 (Kaiser and Garrett 1961), even though the first theoretical description of two-photon excitation flnorescence stems back to 1931 (Goppert-Mayer 1931). Three-photon absorption was demonstrated a few years later by Singh and Bradley (1964). Two-photon absorption is a third-order nonlinear effect, whereas three-photon absorption is a fifth-order nonlinear effect. The transition rate for two-photon absorption, R, depends on the square of the intensity, /, as follows (see Boyd 1992) ... 

Xu C, Webb WW (1997) Nonlinear and two-pboton-induced fluorescence In Lakow-icz J (ed) Topics in fluorescence spectroscopy, vol 5. Plenum Press, New York, p 471 So PTC, Dong CY, Masters BR, Berland KM (2000) Annu Rev Biomed Eng 2 399 GOppert-Mayer M (1931) Ann Phys (Leipzig) 9 273 Peticolas WL (1967) Annu Rev Phys Cbem 18 233 McClain WM (1974) Acc Cbem Res 7 129... 

GM Light E-fields Goppert-Mayer GM units of TPA cross-section... 

Maria Goppert-Mayer (1906-1972). Johannes Hans Daniel Jensen (1907-1973). 23John Dalton (1766-1844). 

M. Goppert-Mayer, Uber Elementarakte mit zwei Quantenspriingen, Ann. Phys. 9 273-294 (1931). 

The possibility of simultaneous absorption of two quanta was concluded on purely theoretical basis by Goppert-Mayer in 1931 [64]. First experimental observations of this process in organic systems were reported in early 196O s by Peticolas et al. [96, 97]. Basically, there are two methods of calculation of two-photon absorptivities. The first technique is based on response theory [90]. The two-photon absorption cross section can be determined by the single residue of the cubic... 

Since its theoretical prediction by GOppert-Mayer in 1931 [1], the nonlinear optical (NLO) process of two-photon absorption (TPA) has received considerable attention, owing to numerous relevant applications in several fields [2], such as optical limiting [3-5], three-dimensional microfabrication [7-15], up-converted lasering [16-18], photodynamic therapy [19-22], data storage [23-28], and biomedical imaging [29-33]. 

GOppert-Mayer M (1931) Ann Phys 9 273 Reinhardt BA (1999) Photon Sci News 4 21... 

The Goppert-Mayer-Fermi theory of orbital contraction 139... 

This idea was followed up by Goppert-Mayer [195] in 1941, who solved the radial equation for a number of elements in the d and / sequence. Unfortunately, she used the Thomas-Fermi model, which gives a fairly poor description of the radial potential and, as is now appreciated, does not account properly for the shell structure of the atom. Thus, although she found a certain number of interesting properties of 4/ elements (lanthanides), she was unable to account for the filling of the d subshells, and her paper did not therefore have the impact it might otherwise have achieved.1... 

Fig. 5.8. Comparison between the effective radial potential for / electrons in H and the double-well radial potential in a heavy element by Goppert-Mayer-Fermi theory (not to scale).

The subject of multiphoton excitation spectroscopy began in 1931 when Goppert-Mayer [450] wrote a theoretical paper in which she calculated the transition rate for an atom in the presence of two photons rather than just one. At the time, the process seemed rather exotic, and it was reassuring that the calculated rate was so low as to guarantee that it could not readily be observed in the laboratory with conventional sources. This conclusion was reassuring because it implies that a simple perturbative theory (one photon per transition is the weak-field limit) is adequate for most purposes. 

M. Goppert-Mayer and J.H.D. Jensen (1955) Elementary Theory of Nuclear Shell Structure John Wiley, New York... 

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