On the effects of permanent molecular dipole moments in two-photon molecular excitations: an analytic generalized rotating wave approximation treatment including both the direct permanent dipole and the virtual state excitation mechanisms

Abstract

One of the purposes of this paper is to develop an analytical many-level generalized rotating wave approximation (GRWA), including the effects of permanent dipoles, for the excitation of many-level molecules through the simultaneous absorption of two photons. Included are expressions for the two-photon laser–molecule coupling C, and its two components Cd and Cv corresponding to the direct permanent dipole and the virtual state excitation mechanisms, respectively, and related observables such as the time-dependent populations of the initial and final states of the excitation process and resonance profiles. This GRWA treatment also includes an energy shift parameter ε, which causes shifts in the position of the resonance energy as the laser intensity increases. The effects of permanent dipoles are very different in Cv and ε versus Cd. These effects have been discussed previously for Cd using analytic two-level RWA approaches. The analytical results for Cv and ε obtained here are new as is their use in discussing the influence of permanent dipoles in the parts of the two-photon excitation process involving virtual states. In the absence of permanent dipoles Cd is zero whereas Cv and ε are not; they equal the corresponding perturbation theory results. The GRWA and perturbative results are related by Bessel function damping functions which, for dipolar molecules, damp out the divergence of the perturbative results as the laser intensity increases. Illustrative examples are given for a two-photon excitation involving a model chromophore which has a significant virtual state contribution through both the laser–molecule coupling and the energy shift parameter.