Complex Wave Function Reconstruction and Direct Electromagnetic Field Determination from Time-Resolved Intensity Data

We present a reference-free robust method for the nondestructive imaging of complex time-evolving molecular wave functions using as input the time-resolved fluorescence signal. The method is based on expanding the evolving wave function in a set of bound stationary states and determining the set of complex expansion coefficients by calculating a series of Fourier integrals of the signal. As illustrated for the A(1)Sigma(+)(u) electronic state of Na-upsilon the method faithfully reconstructs the time-dependent complex wave function of the nuclear motion. Moreover, using perturbation theory to connect the excitation pulse and the material expansion coefficients, our method is used to determine the electromagnetic field of the excitation pulse, thus providing a simple technique for pulse characterization that obviates the additional measurements and iterative solutions that beset other techniques. The approach, which is found to be quite robust against errors in the experimental data, can be readily generalized to the reconstruction of polyatomic vibrational wave functions.