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physica status solidi (b)

Theory of Absorption and Dispersion Profiles of Molecular Transitions in Dense Media

H. Paeeschke, K.‐E. Süsse, D.‐G. Welsch, B. Wilhelmi

Published Aug 1, 1977• 2 citations
Publisher

Abstract

Abstract Starting from quantum theoretical principles the phase relaxation is described of a molecule localized in a dense medium by an integro‐differential equation. Using this equation, which leads to a non‐exponential phase decay, general formulas are derived for calculating the absorption and dispersion profiles of vibronic and vibrational transitions of the guest molecule. In detail the calculations are performed for the case that the acoustic phonons of the medium are responsible for the phase relaxation. Especially it is shown, that in comparison with the Lorentz profile the wings of a real absorption profile become steeper with increasing ratio between dephasing rate y and Debye frequency wD‐ Only for γ/wD ≪ 1 the absorption profiles are expected to be Lorentz profiles. The dispersion is found to increase with increasing ratio γ/wD. Both the real absorption and dispersion curves are asymmetric ones.

DOI
10.1002/pssb.2220820228

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Journal of Experimental and Theoretical Physics•Jun 1, 2024•0 citations
Abstract Starting from quantum theoretical principles the phase relaxation is described of a molecule localized in a dense medium by an integro‐differential equation. Using this equation, which leads to a non‐exponential phase decay, general formulas are derived for calculating the absorption and dispersion profiles of vibronic and vibrational transitions of the guest molecule. In detail the calculations are performed for the case that the acoustic phonons of the medium are responsible for the phase relaxation. Especially it is shown, that in comparison with the Lorentz profile the wings of a real absorption profile become steeper with increasing ratio between dephasing rate y and Debye frequency wD‐ Only for γ/wD ≪ 1 the absorption profiles are expected to be Lorentz profiles. The dispersion is found to increase with increasing ratio γ/wD. Both the real absorption and dispersion curves are asymmetric ones.
In this paper we consider some features of vibrational relaxation of a guest molecule in a host matrix. The model system involves a harmonic molecule interacting with a harmonic medium. The molecule-medium coupling was handled by the rotating wave approximation considering linear terms in the intramolecular displacements and high terms in the medium displacements. Three specific models for the molecule-medium coupling were considered, which involve single phonon decay, vibron-phonon decay and multiphonon decay. Within the framework of the random phase approximation the Heisenberg equations of motion for the system could be expressed in terms of a unified scheme which is valid for both single phonon and multiphonon processes. Explicit solutions were derived utilizing the Wigner-Weisskopf approximation. This generalized formalism was applied for the study of the time evolution of the distribution, the cooling and the heating processes of the oscillator by a thermal field and for the coupling between vibrational relaxation and infra-red emission.
It is shown that, in general, the interaction between relaxing quantum systems and radiation is described by non-Markov transport equations for the density matrix ρ p and the relaxation matrix depends on the properties of the radiation. The usual Markov-type equations for ρ p are obtained from these equations if γτ c ≪1 and (∊ 2 +4 V 2 ) 1/2 τ c ≪1 (γ is the width of the investigated transition in a quantum system, rc is the correlation time of the perturbations causing relaxation, e is the frequency detuning, and V is the energy of the interaction between the system and the radiation field). When the second inequality is disobeyed, the relaxation process deviates strongly from the Markov type. In the case of small values of V , this results in a non-Lorentzian profile of the absorption lines characterized by a steep descent in the wings. In the range of high values of V , when 2 V τ c 1, the whole relaxation process becomes greatly modified: the dependence of the relaxation coefficients on V becomes strong and a coupling appears between the relaxations of the diagonal and the nondiagonal elements of the density matrix. This is manifested, in particular, in the saturation effect: the term describing saturation in the expression for the polarizability changes considerably and the expression for the line width loses the component due to the adiabatic (elastic) perturbation.
The dephasing of a high-frequency intramolecular vibrational mode in a molecular crystal is successively investigated by the cumulant perturbation expansion method as in the preceding papers in this series, I and II. The dephasing of the high-frequency mode is brought on by the thermal excitation of a low-frequency mode in the same molecule as in I and II. In this paper, however, the intramolecular vibrational modes are expressed by the bands of the exciton waves traveling through the crystal (in I and II, the intramolecular vibrational modes are expressed by the localized excitation in one molecule). The calculation shows that the spectrum becomes considerably broad as the temperature increases, while the narrowing is observed as the band widths of the exciton waves increases.
We model the response of a molecular medium to an intense pulse of light. We begin by reducing the Maxwell-Bloch equations for a multilevel molecular model system to a set of simplified propagation equations. We thereby obtain expressions for the frequency, temperature, and field intensity dependence of the ground and excited electronic state absorption cross sections, and the emission cross section, as well as the temperature dependence of the decay rate of the excited state. The phenomena of saturation, excited-state absorption, optically induced dichroism and birefringence, vibronic energy transfer, induced molecular alignment, decay of the matter-field interaction energy, and rotational diffusion are considered within the general formalism for describing the propagation of an intense pulse of light in the molecular medium. We find that the cross section for absorption (emission) of a photon is not identical to the cross section for molecular excitation (deexcitation) via the matter-field interaction. This is explained in terms of an energy balance between the matter, radiation, the matter-radiation interaction, and the bath responsible for the broadening of the molecular transitions. The inequality of these cross sections determines whether the system supplies or draws energy from the thermal bath. The rise in the vibrational temperature of molecules subjected to an intense short pulse is shown to significantly affect propagation of the pulse. The alignment of the molecular system resulting from saturation of the ground-state transition by a polarized laser pulse and the effects of the orientational dependence of the matter-field interaction including effects of rotational diffusion are determined. As an example of the formalism we consider pulse propagation in a Rhodamine 6G solution. We fit the parameters of the model to determine the frequency dependence of the ground- and excited-state absorption cross sections and the emission cross section and compare with experimentally determined cross sections. We describe the propagation of a pulse whose temporal width is comparable to the rotational diffusion time of the molecules in the dye solution and calculate polarization pulse probe signals.
Abstract In the framework of the consistent microscopic theory, universal analytic expressions describing absorption of laser pulses of an arbitrary duration in an optically dense medium have been derived, and their limiting cases have been considered. For the Gaussian and Lorentzian spectral profiles, simple expressions have been obtained for the absorption coefficient as a function of dimensionless parameters (optical thickness of the medium, the pulse duration and carrier frequency). Based on the performed calculations, the effect of the optical thickness of the medium on the dependences of the absorption coefficient on the pulse parameters has been revealed.