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Molecular Physics

Modelling excited state absorption (ESA) measurements including the photophysical hole burning effect with rate equations

Ralf Menzel

Published Sep 1, 1989• 5 citations
Publisher

Abstract

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.

DOI
10.1080/00268978900102031

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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.
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.
Theory based on a configuration coordinate model is presented to clarify solute–solvent relaxation effect on the line shape of a time-resolved hole-burning spectrum. The time-resolved hole-burning spectrum is affected by both a hole created in a ground-state population and an excess excited-state population. The solute–solvent relaxation causes thermalization in both populations and then the shift and broadening of the spectrum is expected observable. The line shapes of three typical cases are mainly considered: (1) The excited state is assumed to have an infinitely long lifetime; (2) the excited state has a finite lifetime, the population being assumed to relax toward an electronic state other than the ground state, and (3) the population created in the excited state relaxes to the ground state, where a hole-filling effect is taken into account. Results obtained by numerical calculations show that a time evolution of the ground-state hole is clearly observed when the low-energy tail of the absorption band is excited under the condition that the population decay to the other electronic state is very fast. Further, it is predicted that the hole-filling effect causes a considerable deformation of the spectral shape when the solvent relaxation rate is comparable to the excited-state population decay rate.
We report a theoretical investigation of effective four-photon absorption (4PA) process and propose a two-step 4PA model of three-photon- induced excited-state absorption (ESA). Based on three-level rate-equation theory, we find an analytical result for the effective 4PA coefficient that depends on the three-photon absorption (3PA) cross-section, excited-state photophysical properties, and laser pulse duration. We present the analytical theory of the z-dependent nonlinear transmission for straightforwardly yet unambiguously evaluating the 3PA and effective 4PA coefficients simultaneously.
Laser induced hole burning in optical absorption bands of low temperature solids has been investigated with emphasis on mechanisms for population hole burning, the interactions with the environment which limit the hole widths and the use of hole burning for ultra high resolution spectroscopy. Hole burning was observed in a wide range of solids including organic and organometallic molecules in crystals and rare earth ions in crystals and glasses. The mechanisms for hole burning also varied widely and a new mechanism involving optically induced nuclear spin flips of near neighbor nuclei was discovered. Examples of hole burning in new classes of materials are presented here for the first time, namely inorganic glasses (silicate glasses containing Nd(3+), Pr(3+) or Eu(3+)) and undoped stoichiometric compounds (e.g., EuP5O14). Hole recovery was used to determine nuclear spin lattice relaxation rates in praseodymium doped crystals. For allowed optical transitions (e.g., singlet states of zinc porphyrin, dibromoindigo and color centers in alkali halides) the hole widths at 2K are limited by population decay to approximately 50 MHz. For longer lived optical levels in crystalline materials, e.g., those containing rare earth ions, the hole widths are narrower (less than 10 MHz) and are limited by dynamical interactions with surrounding nuclei. In amorphous materials such as europium doped silicate glass, hole widths are much broader, being limited by low frequency tunneling motions. Hole burning measurements were complemented by time domain coherent transient (photon echo, and optical free decay) measurements of homogeneous linewidths which enabled us to measure optical resonances as narrow as 760 Hz in Eu(3+):Y2O3.
A large number of signal-processing protocols are based on recording a spectral pattern via spectral hole-burning in an inhomogeneously broadened absorption profile. We present a simulation method specifically designed for periodic excitation sequences leading to the creation of a spectral pattern. This method is applicable to any multilevel atomic structure. The atomic variables’ coherent dynamics are solved for a single temporal excitation step. The result is expressed as an equivalent population transfer rate. This way, the whole sequence is described as a matrix product and the steady state of the system under periodic excitation is easily derived. The propagation through the atomic medium is fully decoupled from the temporal evolution. We apply this method to the engraving of a spectral grating in a large-absorption Tm:YAG sample for wideband spectral analysis.
Abstract A two‐step spectral hole burning (SHB) is considered, where the selective excitation of the first step is fixed by a photochemical transformation through the second excitation step. It is shown that in a three‐level system excited by two consecutive pulses, the kinetics of the forming spectral hole differs essentially from the one on stationary irradiation. In the case of a short second pulse the shape of the hole in the inhomogeneous distribution function (IDF) of the purely electronic line frequency Ω01 is dependent on the time interval T between the first and second excitation steps and under certain conditions a hole can be obtained which is narrower than in the one‐step SHB with monochromatic light. It is considered how the hole in IDF is manifested in the absorption and two‐step pulse excitation spectra. It is shown that the hole in the absorption spectrum may be narrower than 2γ1 and in the two‐step pulse excitation, −γ1 (γ1 is the energy relaxation constant of the first excited level).