Abstract
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.
Highlights
Molecules with permanent dipoles make good candidates for suitable target molecules for the absorption of two identical photons since they offer two mechanisms for two-photon excitation, the “usual” virtual state mechanism[1] and the direct permanent dipole mechanism.[2,3] The latter requires both a transition dipole and a non-zero permanent dipole moment difference between the initial and final states of the two-photon excitation process
Continuous wave (CW) laser-molecule interactions are considered as an example and the rotating wave approximation (RWA),[7,8] the rotating wave perturbation approximation (RWPA), and perturbation theory[1,2,3] calculations are employed in the discussion
That t = PER(res)/2 corresponds to the maximum population of the excited state is related to the condition for a π-pulse;[19,20] this value of t does not correspond to the maximum excitation rate for a given laser intensity
Summary
Molecules with permanent dipoles make good candidates for suitable target molecules for the absorption of two identical photons since they offer two mechanisms for two-photon excitation, the “usual” virtual state mechanism[1] and the direct permanent dipole mechanism.[2,3] The latter requires both a transition dipole and a non-zero permanent dipole moment difference between the initial and final states of the two-photon excitation process. In this paper the optimization of the direct permanent dipole moment two-photon excitation mechanism is discussed through the use of a simple but instructive two-level (giant) dipole molecular model. In general the laser dependence of the two-photon excitation rate is not quadratic and this has implications on the utility of the use of the concept of two-photon cross sections.
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