On the optimization, and the intensity dependence, of the excitation rate for the absorption of two-photons due to the direct permanent dipole moment excitation mechanism

A model two-level dipolar molecule, and the rotating wave approximation and perturbation theory, are used to investigate the optimization and the laser intensity dependence of the two-photon excitation rate via the direct permanent dipole mechanism. The rate is proportional to the square of the laser intensity I only for small intensities and times when perturbation theory is applicable. An improvement on perturbation theory is provided by a small time RWA result for the rate which is not proportional to I2; rather it is proportional to the square of an effective intensity Ieff. For each laser intensity the optimum RWA excitation rate as a function of time, for low intensities, is proportional to I, not I2, and for high intensities it is proportional to Ieff. For a given two-photon transition the laser-molecule coupling optimizes for an intensity Imax which, for example, leads to a maximum possible excitation rate as a function of time. The validity of the RWA results of this paper, and the importance of including the effects of virtual excited states, are also discussed briefly.