Multiphoton excitation analytical results

From the results in the last section it is clear that for particular applied radiative frequencies or frequency multiples, close to resonance with particular molecular states, each molecular tensor will be dominated by certain terms in the summation of states as a result of their diminished denominators—a principle that also applies to all other multiphoton interactions. This invites the possibility of excluding, in the sum over molecular states, certain states that much less significantly contribute. Then it is expedient to replace the infinite sum over all molecular states by a sum over a finite set—this is the technique employed by computational molecular modelers, their results often producing excellent theoretical data. In the pursuit of analytical results for near-resonance behavior, it is often defensible to further limit the sum over states and consider just the ground and one electronically excited state. Indeed, the literature is replete with calculations based on two-level approximations to simplify the optical properties of complex molecular systems. On the other hand, the coherence features that arise through adoption of the celebrated Bloch equations are limited to exact two-level systems and are rarely applicable to the optical response of complex molecular media. 

Analytical (Closed Form) Results for Coherent Multiphoton Excitation... 

Although analytically solvable models for coherent multiphoton excitation are neither computational nor of direct relevance for realistic chemical systems, they are nevertheless of general interest for the theory and also they can serve as a reference, against which numerical calculations and other types of approximation can be tested. We therefore briefly discuss here some of the analytical results. 

A somewhat more interesting model, for which closed analytical expressions for multiphoton excitation are available, is the harmonic oscillator of frequency S2, excited by a laser field of frequency a>. We quote here the results from Ref. 66 with a phase = 0 of the field, an average frequency E and a resonance defect A given by equations (75) and (76) ... 

---