Virtual intermediate states

The fact that the single photon transitions require so little power prompts us to consider two photon transitions. Consider the Na 16d — 16g transition via the virtual intermediate 16f state which is detuned from the real intermediate 16f state as shown by the inset of Fig. 16.3. If the detuning between the real and virtual intermediate states is A and the matrix elements between the real states arefxx and fi2, the expression analogous to Eq. (16.5) for a two photon transition is... 

This holds for the realm of linear optics. There is, however, new theoretical [4,5] and some experimental [4,6] work that seems to indicate that for 2-photon excitation, the existence of a CD effect can be due to pure electronic-dipole allowed transitions. Damping of fhe virtual intermediate state seems to be a requirement [5]. This phenomenon waits for broader investigation. 

Figure 5. Schematic representation of bridge-mediated superexchange of the "electron" (top, left to right) and hole (bottom, right to left) type, illustrated for the case of intermolecular electron transfer between two metal/ligand (M/L) complexes, where D = M/ B = L/ L, and A = M,. The virtual intermediate states for the hole and eleetron processes involve, respectively, charge localization based on the filled ( valence") and empty ("conduction ) bands of the bridge.

Given that the molecule is initially in its ground state, there are initially q photons of the pump mode (k, X) and q photons of the harmonic mode (k, X ). There are three possible sequences of photon annihilation and creation (a, b, and c) that can provide a route from the initial to the final state, each involving different virtual intermediate states. To avoid confusion, the intermediate state labels r[Pg.619]

Figure 6.2 Allowed two-photon pathways via the NO A2E+ virtual state for the two-photon Oie2e and Oif2f rotational branches. Solid lines indicate a strongly allowed pathway and dashed lines indicate a weakly allowed pathway. The fi, 1 2 character of the virtual intermediate state is specified in parentheses in the one-photon branch labels. The A—X P( l)2e nominally satellite transition is strong because the A—X transition is case(b)-case(a) and the C—A -Pi/(2) satellite transition is weak because the C—A transition is case(b)-case(b).

The third step after desorption and cooling is the multiphoton ionization. As demonstrated later, in most cases the ionization takes place by a resonance enhancement of an intermediate excited state but in several cases the ionization can occur via a virtual intermediate state. 

The two-photon absorption (TPA) phenomenon was proposed by Gbeppert-Mayer in 1931 [118] and experimentally first observed by Kaiser and Garrett [119]. TPA is one of the important third-order NLO features. When a molecule is exposed to an intense optical field such as from a pulse laser, it can absorb two photons simultaneously by involving a virtual intermediate state. Figure 49.9 schematically represent this process. If the two photons are of the same frequency, the process is called degenerate TPA if they are of different frequency, the process is a nondegenerate TPA [120]. 

However it also follows that if there were only dipole forces all the even terms in Zp would be zero for the dipole-allowed transitions. Each term in the Bom series progresses from the initial state to the final by a series of transitions between virtual intermediate states. There are as many transitions as there are orders in the Born term. Each transition changes the parity of the state. Thus an odd number of transitions are required for a dipole-allowed state and therefore only the odd order Born terms contribute. In reality though we only have dipole dominance, not a pure selection rule. Also, first order Born terms are usually not negligible even when forbidden. In any case in the example shown in fig. 5.3, when the sign of Zp is reversed, the cross section 1S-2P remains the same but this is not true of the forbidden transition 1S-2S. 

In (10.3) i) and (f denote the initial and final states of the radiative process whiled,. . are the so-called virtual intermediate states that are not physical states that take part in the process.This is indicated by the Dirac delta function that reflects the energy-conservation law, and it covers the energies of the initial and final states between which the physical transition occurs. 

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