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The Journal of Chemical Physics

Interpretation of dispersive hole-burning kinetics

Ranko Richert

Published Feb 15, 1987• 14 citations
Publisher

Abstract

Nonexponential decay of an ensemble of first-order processes are modeled assuming distributions of rate-controlling parameters to be responsible for dispersive kinetics. Some problems of deriving microscopic properties from experimental decay data are illustrated focusing on hole-burning kinetics on the basis of the two-level system model. This approach is compared with reasonings leading to the logarithmic decay law.

DOI
10.1063/1.452173

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Nonexponential decay of an ensemble of first-order processes are modeled assuming distributions of rate-controlling parameters to be responsible for dispersive kinetics. Some problems of deriving microscopic properties from experimental decay data are illustrated focusing on hole-burning kinetics on the basis of the two-level system model. This approach is compared with reasonings leading to the logarithmic decay law.
High inhomogeneous broadening of impurity spectra in amorphous media reflects one type of dispersion, characteristic for disordered systems: dispersion of electronic transition frequency. In principle, there can exist a pronounced dispersion of other parameters: homogeneous line width (Γ), Debay-Waller factor (α), hole burning efficiency (ϕ), etc. The problem of the burning efficiency dispersion (BED) was extensively discussed in the recent years ([1-6] and references therein). The nonexponentiality of the burning kinetics was treated in some publications [1-3,6] as an evidence of such dispersion. But burning kinetics is always nonexponential in strongly inhomogeneously broadened systems, if a burning laser line width Δνl is much less then Γ. That was found experimentally and treated theoretically in one of the first publications on a hole burning [7] (see, also [8]). All other sources of the nonexponentiality are, in fact, additional to this one. So, it’s not easy to attain experimentally the BED parameters on such background. The procedure of a numerical fit ting of the burning kinetic with BED, developed in [4,5], is correct, but it looks unreliable due to many fitting parameters.
The dispersive kinetics of nonphotochemical burning and spontaneous filling of the zero-phonon hole of Cresyl Violet in polyvinyl alcohol at 1.6 K are analyzed in terms of the standard external two-level system (TLSezt) model for probe–glass systems and a distribution function for the tunnel frequency derived from a normal distribution function for the tunnel parameter λ. Average values for the relaxation rates for burning and filling are determined. It is shown that the dominant mechanism for filling is not global spectral diffusion but rather antihole reversion. A high degree of positive correlation between the rates of burning and filling associated with the TLSext is found. A new methodology that permits a more physically reasonable interpretation of spontaneous hole-filling kinetics is described. It is based on the hypothesis that only a fraction of burned sites, on reversion to the ground state, yield sites with resonance frequencies that lie within the hole profile.
In this paper theories are given, describing photophysical and photochemical hole burning experiments on molecular mixed crystals at low temperature. Population saturation hole burning is treated for a two-level system where the lower level is the ground state. Hole burning due to a triplet state acting as a population bottle neck is also described by a steady-state density matrix theory. Connection is made with optical free induction decay. To obtain T2 (the decay time of the off-diagonal elements of the density matrix), which is the main goal of these hole burning experiments, a linear extrapolation method is discussed. For photochemical hole burning a time-dependent density matrix treatment is given. Using this theory numerical simulations were performed of the experimental results obtained by Völker and co-workers for porphin in n-octane at low temperature. Good agreement with experiment is obtained. For this case extrapolation methods are discussed in order to obtain reliable T2 values. A time-dependent kinetic theory is used to simulate the photochemical hole burning experiments on dimethyl-s-tetrazine in durene and s-tetrazine in benzene. This theory accounts for the recently revealed two-photon character of these photodissociations. It is shown that despite this complication the hole full width at half-maximum may still equal twice the homogeneous width of the So-S1 transition.
The dynamics of laser hole burning in a three-dimensional system of fixed isotropically oriented oscillators is simulated. The kinetic curves obtained are analyzed using methods of solving the inverse problem. The contribution of orientational effects to the total dispersion is studied and a quantitative characteristic of this contribution in the form of the standard deviation is obtained. The influence of the broadening of impurity centers on the dispersion of the burning kinetics of persistent and dynamical holes is studied. It is shown how some experimental instrumental factors can distort the results of the analysis of kinetic curves. On the basis of spectral and fluorescence experimental kinetic data, a method for determining the rate constants of the hole burning is proposed.
Investigations in the field of quantum optics very often requires a molecular simulation of transport phenomena. This paper presents a discrete kinetic model to deal with the quantum optical problem of hole burning. Based on a full discretization of the velocity space, Boltzmann-like equations are established to govern the temporal evolution of heavily disturbed Maxwell distributions of optically excited particles diffusing in a buffer gas. These model equations involve elastic collisions and the interaction of photons with three-level atoms by taking into account the Doppler effect. Important features of the developed model are the realistic simulation of the relaxation process and the existence of a stable and unique equilibrium solution.
Excited state absorption measurements have usually to be modelled for the determination of the population densities in the different occupied excited states. Rate equations can be used for this purpose if the described experimental conditions are fulfilled. The photophysical hole burning (PPHB) effect may then be considered in an elementary way. Finally the decay rates of the different states and the holes can be determined. Fast routines for solving the system of differential equations are given allowing for an easy interactive analysis of the measurements on personal computers. The behaviour of the solutions for the two simplest models is discussed. The experimental results of PPHB measurements on crystal violet in 2-propanol were modelled using this formalism.