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Physical Review A

Dynamics of multilevel molecules and pulse propagation beyond rotating wave approximation near two-photon resonance

Ji‐Cai Liu, Chuan‐Kui Wang, Faris Gel’mukhanov

Published Oct 25, 2007• 15 citations
Publisher

Abstract

Dynamics of multilevel molecules and pulse propagation is studied near the two-photon resonance. We have found a strict solution of this problem beyond the rotating wave approximation. Our analytical solution is in close agreement with the strict numerical solution for the $4,{4}^{\ensuremath{'}}$-bis(dimethylamino) stilbene molecule. The compensation of the dynamical Stark shift is studied for fixed-in-space molecules. It is shown that the orientational disorder does not allow complete compensation of the dynamical Stark shift.

DOI
10.1103/physreva.76.043422

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Dynamics of multilevel molecules and pulse propagation is studied near the two-photon resonance. We have found a strict solution of this problem beyond the rotating wave approximation. Our analytical solution is in close agreement with the strict numerical solution for the 4,4\ensuremath′4,{4}^{\ensuremath{'}}4,4\ensuremath′-bis(dimethylamino) stilbene molecule. The compensation of the dynamical Stark shift is studied for fixed-in-space molecules. It is shown that the orientational disorder does not allow complete compensation of the dynamical Stark shift.
The dynamics of populations of the vibrational states in a NO molecule (one-photon absorption) and of the electronic states in a 4,4'-bis(dimethylamino) stilbene molecule (two-photon absorption) is studied versus the frequency, intensity and shape of the laser pulse. We show that specially designed infrared laser pulses can build selective populations of certain vibrational states. A detuning of light frequency from the vibrational resonance qualitatively changes the dynamics of populations. It is found out that the populations of the nonresonant levels follow the pulse shape adiabatically if the detuning significantly exceeds the inverse characteristic time of the change of the pulse. Depopulation of the nonresonant vibrational states leads to a high population of the resonant state at the end of the pulse. Complete breakdown of the standard rotating wave approximation for a two-photon absorption process is observed even for a rather small intensity of the laser pulse. An analytical solution for the interaction of a pulse with a three-level system beyond the rotating wave approximation is obtained, and it is in close agreement with the strict numerical solution of the amplitude equations. Special attention is paid to the population dynamics of randomly oriented molecules. The orientational disorder as well as the vibrations limit the coherent population transfer. Calculations show the strong role of the anisotropy of photoexcitation in the coherent control of populations which can affect the anisotropy of photobleaching.
Using the finite-difference time domain technique(FDTD) for the fields and the predictor-corrector method for the material variables,we solve the Maxwell-Bloch equations beyond the slowly-varying envelope approximation and the rotating-wave approximation.4,4′-bis(dimethylamino) stilbene organic molecule is one type of one-dimensional symmetrical system and its electronic structure and parameters are calculated by density functional theory.The molecule can be simplified as a three-level system.By numerically simulating the propagation of two-color 2π ultrashort laser pulses in a cascade three-level organic molecule system,we analyze the temporal-spatial evolution properties of the ultrashort laser pulses and the population of each energy level under different resonant conditions.
We study the interaction between the ultra-short laser pulses and the one-dimensional symmetrical π conjugated molecular material (4,4′-bis (dimethylamino) stilbene) by solving Maxwell-Bloch equations. This kind of molecular material has strong nonlinear optical properties, and its electronic structures and dipole moments are calculated by use of density functional theory on ab initio level. The numerical results show that the slowly varying envelope approximation and the rotating wave approximation cannot accurately describe the propagation properties of the ultra-short pulse in the molecular medium. In the case of single photon resonance, the two-level model can well describe the interaction between the small area pulse and the molecular system. For large area pulse, due to the existence of strongly secondary excitation to the higher-lying levels, the three-level model should be used. When the amplitude of the incident electric field is kept constant, the third level's population increases with the increase of the pulse area.
The two-level rotating wave approximation for two-photon excitations in dipolar molecules is modified to include the effects of the Bloch-Siegert shift in the two-photon resonance energy. The resulting analytical results are used to establish a criterion for when Bloch-Siegert effects are important and the relevance of these effects are compared for fixed laser-molecule configurations versus orientationally averaged results. Two-level model molecules, with parallel permanent and transition dipoles, are used in this work and the effects of Bloch-Siegert shifts are discussed for resonance profiles, time-dependent populations of the excited state, and time-averaged excitation rates. Bloch-Siegert shifts can have pronounced effects on resonance energies and the shape of resonance profiles and, for example, on the magnitudes and the temporal locations of the maxima in the temporal evolution of the time-dependent properties of the system.
This paper investigates the dynamics of cooperative emissions in a cascade three-level system driven by an ultrashort laser pulse by solving numerically the full-wave Maxwell–Bloch equations. The 4, 4'-bis(dimethylamino) stilbene molecule is used as the model molecule because of its strong two-photon absorption property. The two-colour cooperative emissions are studied as functions of molecular number density and dephasing rate of the dipole coherence. The propagation effects on the evolution of the cooperative radiations are also taken into account. The cooperative radiations are enhanced for large number density of the molecule, while the fast dephasing of the dipole coherence reduces the intensity of the cooperative radiations and delays the emission times or even inhibits the formation of the emissions. The delay time of the radiation decreases with the increase of the molecular number density and the propagation distance.