Selection rules for two-photon excitation

The selection rules for multiphoton transitions are clearly different from the usual dipole selection rules, since each photon carries an angular momentum 1 Thus, for two-photon transitions, one rule is A J = 0 2, but further control can be exercised by selecting the polarisation of the light the A J = 0 transitions are only possible if the laser light is linearly polarised (i.e. contains both r+ and a circular polarisation), while the choice of either circular polarisation results in an increase or a decrease of J. Detailed discussion of the selection rules for two-photon transitions can be found in several papers [453, 455, 459]. For multiphoton transitions, the same principles apply, and the role of polarisation is still more significant. A general reference is [460], in which selection rules are derived from first principles, and a list of selection rules for two-photon transitions is given in table 9.1. 

Note that these rules are somewhat different from the rules for two-step 

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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... 

The selection rules for two-photon transitions are different and many dyes that have a large coefficient for one-photon absorption exhibit two-photon cross sections in the order of at most a few GM [14]. Correspondingly, a two-photon emission (excited state two photons) is observed as a weak emission, since only the total energy is conserved, not the energy of each individual photon. Thus, emission is a weak continuum of interest more of astrophysicists than of chemistry practitioners, but advancement in the field has been remarkable [15]. 

Different upper states can therefore be selected by a proper choice of the polarization. In many cases it is possible to gain information about the symmetry properties of the upper states from the known symmetry of the ground state and the polarization of the two light waves. Since the selection rules of two-photon absorption and Raman transitions are identical, one can utilize the group-theoretical techniques originally developed for Raman scattering to analyze the symmetry properties of excited states reached by the different two-photon techniques [243, 244]. 

Selection rules for single-photon and two-photon excitation (TPE) are different [42,107, 108] however, most resins that polymerize under UV (A) exposure can undergo similar reactions when two photons (2A) are absorbed simultaneously (two-photon photopolymerization), provided that the fight intensity is large enough. 

Thus it was not observed until lasers were invented. In principal, one-photon and two-photon excitation follow different selection rules. For example, the inner shell one-photon transitions in transition metal, rare earth, and actinide ions are formally forbidden by the parity selection rule. These ions have d- or/-shells and transitions within them are either even to even (d d) or odd to odd (f /). The electric dipole transition operator is equal to zero. 

The two-photon excitation spectrum of 22h taken as a neat film shows a broad peak with an onset of 1.32 eV and a maximum at 1.63 eV [391]. The larger TP excitation energy (1.32 eV 2hco = 2.65 eV) compared to OP excitation (2.34 eV) implies that the TP transition has a different selection rule than the OP transition. This is similar to behavior obtained in solution [384], A similar excitation pattern as disclosed in Figure 3.2a was obtained for such polymeric materials that is, the TP excited state possesses a higher excitation energy in comparison with the lowest OP excited state. Thus, the results obtained for diphenylpolyenes with more than two ethylene moieties, in which the Sj state is assigned to the TP excited state, are considered as an exception for chromo-phores with no donor substitution pattern [29]. 

Fig. 19. Composite two-photon excitation spectrum of the 4f ->5d transition in 0.003% in CaF, at 6K. The transition is studied by monitoring the 5d— 4f, no phonon transition occurring at 313.1 nm. As noted in text this transition is normally two-photon forbidden because of parity selection rules, however, odd crystal-fields components admix parity to make the transitions partially allowed. The pure electronic transition of the state is labeled as 0 other excitations, 1 to 12, are identified as phonon or normal mode excitations of the lattice which couple to the pure transition. Selection rules for assisted transitions follow selection rules which differ from the one-photon case. After Gayen and Hamilton (1982).

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