Calculation of vibrational level populations in multiphoton absorption processes

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Abstract
A simple procedure is described for computing steady-state excited vibrational state populations for multiphoton absorption processes in many-level systems. The procedure utilizes techniques already in the literature, i.e., expansion of the density matrix as a Fourier series in the frequency of the monochromatic radiation field, and introduction of linewidths and thermal relaxation by the addition of empirical terms to the density matrix time-development equation. Numerical computations can be carried out quickly on idealized systems, using commercially available band matrix inversion routines. A sample calculation for a 10-level, nine-photon process is presented.