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Chemical Physics Letters

Validity of the rotating wave approximation for high-order molecular multiphoton processes

Israel Schek, Martin L. Sage, Joshua Jortner

Published May 1, 1979• 34 citations
Publisher
DOI
10.1016/0009-2614(79)87006-2

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The interaction of two continuous wave electric fields (lasers) with a two-level molecule, that has a nonzero difference d, between the permanent dipoles of the two states involved in a multiphoton two-color transition, is studied in the rotating wave approximation and by using exact methods. Analytical rotating wave approximation results for the time-dependent populations of the molecular states and for the resonance profiles are derived and used to help discuss the effects of permanent dipole moments in the two-color absorption problem. Several examples of multiphoton, two-color, two-level resonance profiles calculated in the rotating wave approximation and by using exact techniques, are employed for illustrative purposes. They are used to help quantify the conditions for the validity of the two-color rotating wave approximation, which are considerably more restrictive than the analogous conditions for the one-color rotating wave approximation with d≠0, and to illustrate the interpretive and predictive nature of the rotating wave approximation results. For example, there are many multiphoton, two-color transitions that are available if a molecule possesses permanent dipoles (d≠0). The analytic rotating wave approximation expression for the molecule-two laser coupling can often be used to reliably estimate the field parameters of the two lasers that are required to optimize a given transition relative to others.

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Enhanced high-order-harmonic generation and wave mixing via two-color multiphoton excitation of atoms and molecules

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We consider harmonics generation and wave mixing by two-color multiphoton resonant excitation of three-level atoms and molecules in strong laser fields. The coherent part of the spectra corresponding to multicolor harmonics generation is investigated. The obtained analytical results on the basis of a generalized rotating wave approximation are in a good agreement with numerical calculations. The results applied to the hydrogen atoms and homonuclear diatomic molecular ions show that one can achieve efficient generation of moderately high multicolor harmonics via multiphoton resonant excitation by appropriate laser pulses.

arXiv:1606.01705•Physical Review A•Jul 29, 2016•6 citations
The interaction of two continuous wave electric fields (lasers) with a two-level molecule, that has a nonzero difference d, between the permanent dipoles of the two states involved in a multiphoton two-color transition, is studied in the rotating wave approximation and by using exact methods. Analytical rotating wave approximation results for the time-dependent populations of the molecular states and for the resonance profiles are derived and used to help discuss the effects of permanent dipole moments in the two-color absorption problem. Several examples of multiphoton, two-color, two-level resonance profiles calculated in the rotating wave approximation and by using exact techniques, are employed for illustrative purposes. They are used to help quantify the conditions for the validity of the two-color rotating wave approximation, which are considerably more restrictive than the analogous conditions for the one-color rotating wave approximation with d≠0, and to illustrate the interpretive and predictive nature of the rotating wave approximation results. For example, there are many multiphoton, two-color transitions that are available if a molecule possesses permanent dipoles (d≠0). The analytic rotating wave approximation expression for the molecule-two laser coupling can often be used to reliably estimate the field parameters of the two lasers that are required to optimize a given transition relative to others.
A rotating-wave approximation (RWA) for the single-photon and multiphoton resonance profiles for a two-level molecule interacting with both sinusoidal and static electric fields is derived. Included is a useful expression for the coupling between the molecule and the applied sinusoidal field which exhibits the effects of both diagonal dipole matrix elements (permanent dipole moments) and the applied static electric field. Comparisons of the RWA results with exact two-level calculations provide qualitative information concerning the validity of the RWA as a function of molecular and field parameters. These examples are also used to illustrate the interpretive nature of the RWA results for the resonance profiles and some of the effects of permanent dipoles and static fields on the profiles. Of particular interest are examples involving Boltzmann rotationally averaged spectra as a function of temperature where it is shown that minima in the spectra occurring for high temperatures can be reduced or removed completely if the temperature or applied static field is reduced.
We consider harmonics generation and wave mixing by two-color multiphoton resonant excitation of three-level atoms and molecules in strong laser fields. The coherent part of the spectra corresponding to multicolor harmonics generation is investigated. The obtained analytical results on the basis of a generalized rotating wave approximation are in a good agreement with numerical calculations. The results applied to the hydrogen atoms and homonuclear diatomic molecular ions show that one can achieve efficient generation of moderately high multicolor harmonics via multiphoton resonant excitation by appropriate laser pulses.