A computationally simple theory of multiple photon excitation of polyatomic molecules: Dependence of the energy distribution on molecular properties

Abstract

We present a simple and universal method to calculate multiple photon excitation (MPE) of polyatomic molecules in the collisionless case. The excited molecules are described with two variables: the absorbed energy and the width of the distribution function. The system of equation for these parameters is closed, and it is possible to integrate it in quadratures. It is shown that energy distribution formed is completely defined by the spectral properties of the molecule and the average occupation number for the resonance mode, the latter being computable unambiguously. The same quantities of clear physical significance can be used for determination of stimulated emission and absorption cross sections to be used in master equations. The approach developed in the present work enables one to calculate the width of the distribution function at MPE with account for the anharmonic shift and broadening of the absorption spectrum. In the case of a constant absorption cross section it is shown that the width is given to a good accuracy by the universal formula. δ = ( n̄ 2/ s + n̄) 1 2 , where n̄ is the number of quanta absorbed, and s is the number of vibrational degrees of freedom. Comparison with the Boltzmann distribution shows that a broader distribution is generated at the MPE, if the laser frequency is higher than the mean frequency of the molecular vibrations: the distribution is narrower than the Boltzmann distribution in the opposite case.