A theory of visible/UV multiphoton processes in molecules. I. Resonance effect on three-photon absorption

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Abstract
Using a transition operator formalism, an expression for three-photon transitions is derived. The transition operator formalism makes it possible to take into account the effects of population decays and pure dephasings occurring in the relevent vibronic states on the cross sections of the resonance multiphoton processes. It is shown that for a two-photon resonant (2+1) process, the cross section can approximately be divided into two terms, one is called sequential term which cannot be taken into account by using the lowest order time-dependent perturbation theory, and the other which can be derived from simultaneous three-photon cross section under constraint of a resonant condition for the second photon absorption. Assuming the adiabatic approximation for the molecular states, analytical expressions for the cross sections for the three-photon absorptions are derived in the displaced harmonic oscillator model of the molecules. An analytical expression taken into account the temperature effect is given for the simultaneous three-photon absorption cross section.