Perturbation treatment of pump–probe laser–molecule interactions: An application to the fluorescence from the S1 state of α-NPO

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Abstract
Time‐dependent perturbation theory, together with a (minimal) molecular model consisting of three energy levels (S0,S1,S3), is used to investigate the spectroscopy and the dynamics of fast time resolved, two‐photon, two‐color, pump–probe experiments, involving the direct S0→S1 two‐photon excitation of α‐NPO. In particular the theory is used to examine the Θ‐dependence of the fluorescence signal from the S1 state, where Θ is the angle between the polarization vectors of the pump and probe lasers, for fixed (zero) time delay between the laser pulses. It is predicted, in contradistinction to the cos2 Θ dependence of the fluorescence signal from the S2 state of azulene arising from the sequential two‐photon S0→S1→S2 transition, that the signal from the S1 state of α‐NPO can vary between pure cos2 Θ and pure cos4 Θ dependencies and that secondary maxima in the signal, as a function of Θ, can occur for certain laser intensities. Also reported is a new series of experiments for α‐NPO, motivated by the theory, that yields results for the fluorescence intensity of the S1 state, as a function of Θ and laser intensity, in agreement with the theoretical predictions. Comparison of experiment and theory is used to estimate the relative orientations of the relevant transition and permanent dipole moments, and the transition moment between the S1 and S3 states of α‐NPO. The important role played by the permanent dipoles of the S0 and S1 states, and the importance of including averages over the relative laser phase, the jitter in the time‐delay, and the orientations of the absorbing molecules, is emphasized in the theoretical analysis of the problem.