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Toward a theory of energy exchange between molecules and light pulses

V. A. Morozov, Yu. V. Gutop, P. P. Shorygin

Published Feb 1, 1986• 0 citations
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Abstract

This paper examines the energy redistribution between a pulse of incident light, a molecule, and a pulse of secondary radiation by considering the transformation of light in a closed system: the radiation field and the molecule. The analysis is carried out using Hamiltonians. The energy balance and the shape of short secondary radiation pulses during the transformation of sufficiently weak light pulses are determined basically by the fast energy exchange between the molecule and the radiation field. The energy transferred from radiation field modes to the molecule and back to these modes is much larger than the energy dissipated by the molecule into the other modes of the field.

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This paper examines the energy redistribution between a pulse of incident light, a molecule, and a pulse of secondary radiation by considering the transformation of light in a closed system: the radiation field and the molecule. The analysis is carried out using Hamiltonians. The energy balance and the shape of short secondary radiation pulses during the transformation of sufficiently weak light pulses are determined basically by the fast energy exchange between the molecule and the radiation field. The energy transferred from radiation field modes to the molecule and back to these modes is much larger than the energy dissipated by the molecule into the other modes of the field.
Abstract The expressions for the pulse shapes of secondary radiation in the frequency range of Rayleigh scattering and resonance fluorescence and in the range of Raman scattering and shifted resonance fluorescence are obtained on the basis of the quantum treatment of transformation of light pulses, the resonance conditions for Raman and Rayleigh scattering being considerably different. The characteristic cases of different pulse shapes of Raman and Rayleigh scattering are considered for the condition when the molecules are irradiated by light pulses which are shorter then the lifetime of the excited state of the molecule and are weak enough not to result in saturation.
We present a novel approach to molecular spectroscopy with light pulses of arbitrary strength and duration. The key quantity is the frequency-resolved net energy transfer dE/dω which reveals at which frequencies energy is transferred from the field to the molecule (absorption) or from the molecule to the field (stimulated emission). It is shown that dE/dω can be expressed as the Fourier transform of the cross-correlation function of the molecular polarization P(t) and the time derivative of the applied field, dℰ/dt. In this sense, it is formally equivalent to the absorption cross section under weak-field conditions which, as commonly known, can be represented as the Fourier transform of the autocorrelation function S(t). The time-dependent polarization P(t) is determined by exact integration of the time-dependent Schrödinger equation including the light-matter interaction to all orders. It is shown that under weak-field conditions the expression for dE/dω reduces to the well-known cross section formula in the time-dependent picture of spectroscopy, multiplied by the spectral intensity of the light pulse. Therefore, we consider the expression for the frequency-resolved energy transfer, which is valid for arbitrary electric fields, as the natural extension of the absorption cross section in the weak-field limit. Furthermore, dE/dω is shown to be formally equivalent to the change of the spectral intensity, ΔI(ω), of an optical pulse after transmission through a sample, the latter being derived by solving Maxwell’s equations under well-known approximations. The theory is applied to a simple one-dimensional model with two electronic states and the frequency-resolved energy transfer is investigated as a function of the field strength. For sufficiently strong fields, dE/dω exhibits transitions between essentially all vibrational levels in the ground and all states in the excited electronic manifold. The new expression distinguishes between absorption and emission and that is clearly seen in the spectra.
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.
Three approximation schemes are discussed and compared with the exact solutions for a Hamiltonian describing the interaction of a single-mode quantized radiation field and NNN two-level "molecules," each resonant with the mode frequency. In particular, the approximation of treating the molecules as uncorrelated is found to be accurate when the system energy is several times larger than the cooperation number of the molecular system.
A mathematical modeling of the time evolution of the populations of the states of a five-level molecule during transformation of resonant monochromatic irradiation and spontaneous emission from the highest-energy state excited by a short pulse of light is performed. The formalism of the optical Bloch equations and quantum theory of radiation are applied a composite system consisting of a molecule and a quantized radiation field. The results of simulation of the evolution of the population of the states of the molecule in the case of spontaneous emission are similar for both of these two approaches, but differ significantly in the case of conversion by the molecule of monochromatic radiation. These differences are the greater, the higher the intensity of resonance Rayleigh scattering or (and) relaxed fluorescence, as a result of which the molecule returns to the initial ground state. An explanation of the nature of these differences is given.
The reflected and transmitted energy flux corresponding to the linear response of a quantum well (QW) is calculated analytically for the cases of monochromatic and pulsed incident radiation normal to the QW plane. The light–matter interaction has been taken to all orders of perturbation theory, resulting in the appearance of radiative broadening in the expressions for the secondary fields. Three time scales determine the decay of the response after the pulse excitation while the quantum beats are superimposed on the exponentially decaying contributions at the frequency which (i) equals detuning from the electronic transition or (ii) corresponds to a characteristic excitation in the system.