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Journal of Physics B Atomic Molecular and Optical Physics

Absorptive and dispersive processes in a two-level molecule with intramolecular coupling and non-zero permanent dipole moment

Máximo García-Sucre, Emilio Squitieri, José Luis Paz, Vladimiro Mújica

Published Oct 28, 1994• 16 citations
Publisher

Abstract

We investigate linear and non-linear absorptive and dispersive properties for a homogeneously broadened molecular two-level system including simplified versions of vibrational structure and intramolecular coupling. The Born-Oppenheimer electronic energy curves for this simplified molecular model consist of two intercrossing harmonic oscillators potentials with different force constants. These electronic states are coupled and inclusion of the intramolecular coupling within a vibronic model renders the corresponding coupled states. We have analysed the influence of the intramolecular coupling parameters on the optical response of the system up to third-order in the external field. The critical quantities for this analysis are the transition and permanent dipole moments (both in magnitude and relative sign) which depend strongly on the intramolecular coupling. Some simple exact results are derived for the important case of exact degeneracy. Finally, the relevance of the optical response of the change in force constants associated with the two uncoupled states is examined.

DOI
10.1088/0953-4075/27/20/013

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Journal of Nonlinear Optical Physics & Materials•Jun 1, 2015•2 citations
We investigate linear and non-linear absorptive and dispersive properties for a homogeneously broadened molecular two-level system including simplified versions of vibrational structure and intramolecular coupling. The Born-Oppenheimer electronic energy curves for this simplified molecular model consist of two intercrossing harmonic oscillators potentials with different force constants. These electronic states are coupled and inclusion of the intramolecular coupling within a vibronic model renders the corresponding coupled states. We have analysed the influence of the intramolecular coupling parameters on the optical response of the system up to third-order in the external field. The critical quantities for this analysis are the transition and permanent dipole moments (both in magnitude and relative sign) which depend strongly on the intramolecular coupling. Some simple exact results are derived for the important case of exact degeneracy. Finally, the relevance of the optical response of the change in force constants associated with the two uncoupled states is examined.
We consider the Four-Wave mixing (FWM) signal and the effects of the pump beam on the nonlinear optical responses of a two-level system where intramolecular coupling is modelled by two coupled harmonic electronic potentials, displaced both in their equilibrium minimum position and energy. We investigate the modifications introduced in the FWM signal, considering a simple representation for the vibrational structure and including molecular electronic states with nonzero permanent dipole moments. The critical quantities for this analysis are the transition and permanent dipole moments, which depend strongly on the intramolecular coupling. Our results show how both absorption and dispersion are affected by the vibronic coupling.
Motivation. Polyatomic molecules can be described by a two–level system represented by two crossed harmonic potential curves (including vibrational levels) in order to study their nonlinear signal response. The variation of the coupling parameter has an important influence on the behavior of the dipole moments and, consequently, on the polarization on the new coupled–state basis. Method. The calculation method employed is based on the Liouville formalism for the density matrix, where the conventional optical Bloch equations are solved in Fourier space to obtain the density matrix elements associated to the polarization of the system. Changes in the coupling parameters V0 (energetic difference between the minima of the potential curves), S (height to which the vibronic coupling occurs) and v (coupling parameter) produce modifications in the behavior of the dipole moments and Polarization on the coupled system. In this communication, two studies are presented: (a) variation of the parameters S and v, while keeping V0 constant and, (b) variation of S and V0, while keeping v constant. In order to study the effects of these changes, the rotating–wave approximation is neglected, which permits us to analyze the processes that occur out of the resonance region. Moreover, the permanent dipole moments of the states in the uncoupled basis are included. Results. First case (variation of S and v): an important increment of dipole moments and polarization magnitude values were observed for low values of v and high values of S. Second case (variation of S and V0): an abruptly increment in the polarization magnitude were found at high values of S and low values of V0. Conclusions. The observed changes in the nonlinear response are associated to modifications in the overlap integral and consequently to the dipole moments of the states in the new coupled basis.
We calculate the third-order nonlinear absorption and dispersion (self-phase-modulation and cross-phase modulation) of a homogeneously broadened two-level molecular system with permanent dipole moments interacting with (1) an optical field of frequency \ensuremath{\omega}, and (2) two optical fields of frequency ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$, i.e., the susceptibilities ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-\ensuremath{\omega};\ensuremath{\omega},-\ensuremath{\omega},\ensuremath{\omega}) and ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-${\mathrm{\ensuremath{\omega}}}_{1}$;${\mathrm{\ensuremath{\omega}}}_{1}$,-${\mathrm{\ensuremath{\omega}}}_{2}$,${\mathrm{\ensuremath{\omega}}}_{2}$). Sharp features in the nonlinear absorption and dispersion appear whenever one- or two-photon resonance conditions are met. Only features corresponding to one-photon resonance arise if the difference between the permanent dipole moments of the levels, \ensuremath{\Delta}\ensuremath{\mu}, vanishes. The ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-\ensuremath{\omega};\ensuremath{\omega},-\ensuremath{\omega},\ensuremath{\omega}) spectrum has two features, one at frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{b}\mathit{a}}$ dominated by contributions proportional to ${\mathrm{\ensuremath{\mu}}}_{\mathit{a}\mathit{b}}^{4}$, where ${\mathrm{\ensuremath{\mu}}}_{\mathit{a}\mathit{b}}$ is the transition dipole moment of the two levels with transition frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{b}\mathit{a}}$, and the other at frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{b}\mathit{a}}$/2 dominated by contributions proportional to (\ensuremath{\Delta}\ensuremath{\mu})2{)}^{2})2${\mathrm{\ensuremath{\mu}}}_{\mathit{a}\mathit{b}}^{2}$. Sharp features in ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-${\mathrm{\ensuremath{\omega}}}_{1}$;${\mathrm{\ensuremath{\omega}}}_{2}$,-${\mathrm{\ensuremath{\omega}}}_{2}$,${\mathrm{\ensuremath{\omega}}}_{1}$) appear when ${\mathrm{\ensuremath{\omega}}}_{2}$ is near ${\mathrm{\ensuremath{\omega}}}_{\mathit{b}\mathit{a}}$,${\mathrm{\ensuremath{\omega}}}_{1}$,${\mathrm{\ensuremath{\omega}}}_{1}$+${\mathrm{\ensuremath{\omega}}}_{\mathit{b}\mathit{a}}$, and \ensuremath{\Vert}${\mathrm{\ensuremath{\omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{\mathit{b}\mathit{a}}$\ensuremath{\Vert}.
We have studied the effects of the changes in the intramolecular coupling parameters S (height) to which the vibronic coupling occurs), V0 (energetic difference between the minima of the potential curves) and v (coupling parameter), considering a two levels system described by two crossed harmonic potential curves. This work has been divided into two particular cases: a) simultaneous changes in S and v and b) simultaneous changes in S and V0. In the first case we have observed an important increment of the polarization values for low values of v. In the particular case of resonance peak, an important increment of polarization values is observed with the increment of v. In the second case, an abruptly increasing in polarization values is observed to high values of S and low values of Vo. In the particular case of resonance peak we observed the contrary behaivor of the precedent case: a notable decreasing of the polarization values is observed with the increasing in v. These changes are associated to the modifications in the overlapping integral and consequently in the dipole moments of the states in the new coupled basis.
A study has been made of the effect of relaxation times on the four-wave mixing (FWM) signal response in frequency space for a two-level system where intramolecular coupling is explicitly taken into account within a vibronic model. The model is a generalization of the conventional two-level approach in that it includes a simplified description of the molecular structure and the explicit consideration of permanent dipole moments. Significant changes in both the intensity and shape of the peaks of the FWM spectrum are observed, due mainly to changes in the ratio between the longitudinal and transversal relaxation times, T 1/T 2.
A study of the effects of relaxation times on the Four-Wave Mixing (FWM) signal response in frequency space for a two-level system is presented where the collisional effects of the solvent and the presence of the electromagnetic field are considered. The model is a generalization of the conventional two-level approach in that it includes a simplified description of the molecular structure associated with the non-zero permanent dipole moments. Significant changes in both the FWM-intensity and nonlinear optical properties are observed, due mainly to changes in the ratio between the longitudinal and transversal relaxation times.