FLOQUET THEORY AND QUASI-ENERGY METHODS FOR INTENSE FIELD MOLECULAR MULTIPHOTON EXCITATION AND DISSOCIATION

Abstract
(1) A non-perturbative quasi-vibration-rotational energy method has been developed for the treatment of the quantum dynamics of non-linear high-order multiphoton excitation of molecules in the presence of intense laser and static electric fields.¹ The Floquet theory is applied to the single and multiphoton excitations of the HF molecule. Non-linear effects such as power broadening, dynamics Stark shift, Autler-Townes multiplet splitting, hole burning and S-hump behaviors, etc., are observed and discussed in terms of quasi-energy diagrams. Many of the salient features in the spectral line shapes may be qualitatively understood in terms of an analytical three-level model. The addition of a dc electric field removes the restriction of the rotational dipole selection rule and causes significant intermixing of the bare molecular vibrator states. Due to the greater number of strongly coupled nearby states in the dc field, non-linear effects such as those mentioned above appear at a much lower ac field strength than they would in the absence of the dc field. The introduction of an external dc field there for estrongly enhances the multiphoton excitation probabilities and results in a much richer spectrum. (2) A practical and nonperturbative complex quasi-vibrational energy method is developed² for studying molecular photodissociation processes in the presence of (weak or intense) electromagnetic fields, using only square-integrable (L²) functions. By means of the complex coordinate transformation and L² discretization of the vibrational continua, the complex quasivibrational energies (QVE) of the Floquet Hamiltonian can be determined by standard non-Hermitian eigenvalue analysis. The real parts of the QVE's provide the ac Stark-shifted vibronic energies, whereas the imaginary parts are related to the photodissociation transition rates. The theory has been applied to the direct photodissociation of H₂⁺ (lsσ_g-2pσ_u) in both weak and strong fields.² Extension of the method to multiphoton dissociation of H₂⁺, HF and SO₂ is in progress, This research is supported in part by the United States Department of Energy, Division of Chemical Sciences, under contract NO. DE-AC02-80ER10748, and by the Alfred P. Sloan Fellowship. Acknowledgment is also made to the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this work.