Three-photon absorption, selection rules

This rule is analogous for any number of photons thus, in a three-photon absorption process the allowed states are the p and f states, which allows even-to-odd or odd-to-even parity. This means that transitions can be divided between states of either the same or different parity corresponding to absorption of either even or odd numbers of photons. Hence the selection rules are the same for one and three photons and for two and four photons, respectively [49]. 

The second factor in (2.66) describes quite generally the transition probability for all possible two-photon transitions such as Raman scattering or two-photon absorption and emission. Figure 2.30 illustrates schematically three different two-photon processes. The important point is that the same selection rules are valid for all these two-photon processes. Equation (2.66) reveals that both matrix elements D,- and Dkf must be nonzero to give a nonvanishing transition probability A,/. This means that two-photon transitions can only be observed between two states i) and I/) that are both connected to intermediate levels fe) by allowed single-photon optical transitions. Because the selection rule for single-photon transitions demands that the levels i) and A ) or A ) and /) have opposite parity, the two levels i) and I/) connected by a two-photon transition must have the same parity. In atomic two-photon spectroscopy s s or s d transitions are allowed, and in diatomic homonuclear molecules Eg Eg transitions are allowed. 

The second factor in (7.53) describes quite generally the transition probability for all possible two-photon transitions such as the Raman scattering or the two-photon absorption and emission. Figure 7.26 illustrates schematically three two-photon processes. The important point is that the same selection rules are valid for all these two-photon processes. Equation (7.53)... 

The vibrational selection rule for the harmonic oscillator, Au = 1, applies to polyatomic molecules just as it did to diatomic molecules. Vibrational energy can, therefore, change in units of hcoi/ln. Transitions in which one of the three normal modes of energy changes by Au = - -1 (for example Ui = 0 1, U2 = U3 = 0 or 1 = 1) 2 = 3, i>3 = 2 3) result from absorption of a photon having one of three fundamental frequencies of the molecule. In the actual case, anharmonicities also allow transitions with Au, = 2, 3,... so that, for example, weak absorption also occurs at 2coi, 3(Ui, etc. and at coi + coj, 2vibrational transitions often play major roles in planetary spectroscopy. 

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