Selection Rules for Multiphoton Absorption

The selection rules will be mentioned briefly here. In general, the process of multiphoton absorption is similar to that of single-photon absorption. The multiple photons are absorbed simultaneously to a real excited state in the same quantum event, where the energy of the transition corresponds to the sum of the energies of the incident photons. Thus selection rules for these transitions may be derived from the selection rules for one-photon transitions as they can be considered multiple one-photon transitions [20]. 

The selection rules governing transitions between electronic energy levels are the spin rule (AS = 0), according to which allowed transitions must involve the promotion of electrons without a change in their spin, and the Laporte rule (AL = 1 for one photon). This parity selection rule specifies whether or not a change in parity occurs during a given type of transition. It states that one-photon electric dipole transitions are only allowed between states of different parity [45], 

Relaxation of the rules can occur, especially since the selection rules apply strongly only to atoms that have pure Russell-Saunders (I-S) coupling. In heavy atoms such as lanthanides, the Russell-Saunders coupling is not entirely valid as there is the effect of the spin-orbit interactions, or so called j mixing, which will cause a breakdown of the spin selection rule. In lanthanides, the f-f transitions, which are parity-forbidden, can become weakly allowed as electric dipole transitions by admixture of configurations of opposite parity, for example d states, or charge transfer. These f-f transitions become parity-allowed in two-photon absorptions that are g g and u u. These even-parity transitions are forbidden for one photon but not for two photons, and vice versa for g u transitions [46], 

According to the selection rules, one-photon absorption occurs only if the change in angular momentum (change in L) is +1 or -1 (Al = 1, A/ = 0, 1 (0 o 0 not allowed), AL = 0, 1, AS = 0) (Al is according to the hydrogenic atom model, whereas AL is for multielectron atoms). The selection rules allow transition in one-photon absorption only to the p states from the s ground state as a result only even-to-odd parity is allowed. 

Since photons have angular momentum of +1 or -1, an electronic state absorbing two photons simultaneously may change angular momentum by +2, 0. Two L = +1 photons cause a change of +2 a photon of L = +1 and one of I = -1 cause a change of 0 (A1 = 0, 2, AJ = 0, 2, AL = 0, 2, AS = 0). Thus the selection rules for two-photon absorption allow the excited electron to be either in an s or a d state, states which are of even-to-even parity or odd-to-odd parity such as f-f transitions, which now become allowed. An electron therefore cannot go from an s state 

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Examples of studies on multiphoton absorption processes and nonlinear second-and third-harmonic generation processes will be discussed along with some possible radiative and nonradiative processes. The selection rules for multiphoton absorption will be mentioned in Section 7.3, and molecular examples will be shown along with their correlating photophysical properties in Section 7.4. The effect of some parameters relating to second-order activity along the lanthanide... 

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