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physica status solidi (b)

The Shape of a Spectral Hole and Its Temporal Response at Short Burning Times in Two‐, Three,‐ and Four‐Level Systems

Inna Rebane

Published Sep 1, 1991• 4 citations
Publisher

Abstract

Abstract The shape of the spectral hole in an inhomogeneous distribution function of centres over the transition frequency is calculated for the case of a quasimonochromatic burning light pulse which characteristic duration time is comparable to the relaxation times of the excited electronic level. Two‐step spectral hole‐burning in the cases of three‐ and four‐level systems as well as one‐step processes are considered. The temporal responses of the spectral holes as spectral filters on δ‐pulse of light are found.

DOI
10.1002/pssb.2221670132

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Abstract The shape of the spectral hole in an inhomogeneous distribution function of centres over the transition frequency is calculated for the case of a quasimonochromatic burning light pulse which characteristic duration time is comparable to the relaxation times of the excited electronic level. Two‐step spectral hole‐burning in the cases of three‐ and four‐level systems as well as one‐step processes are considered. The temporal responses of the spectral holes as spectral filters on δ‐pulse of light are found.
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).
A theory of spectral hole burning (SHB) by light pulses of an arbitrary shape and duration is proposed. One- and two-step (photon-gated) SHB processes induced by laser pulses in two-, three- and four-level systems are theoretically considered. It is shown that for two-step SHB there exists a possibility of obtaining spectral holes which are narrower than in the one-step SHB with monochromatic light. In case of one- and two-step SHB the dependence of the shape of the hole on the duration of the burning pulse is considered (on two-step SHB the second pulse is Δ-pulse).
The two-step persistent spectral hole burning (PSHB) of a hole in the inhomogeneous distribution function (IDF) of the optical transition frequencies in a three-level system by two successive light pulses, in the case of an exponentially increasing and decreasing first coherent pulse and an infinitely short second pulse is calculated. The compensation effect of the natural linewidth of the first excited level and the parameter describing the exponential decrease of the intensity of the first burning pulse is shown. The time-dependent zero-phonon line (ZPL) in luminescence spectrum in the recording scheme containing the time gate in front of the spectrometer with high resolution in the case of exponential opening and closing of the time gate is calculated. The effect of the compensation of the natural linewidth of the excited level and the parameter describing the exponential increase of the transparency of the time gate is shown.
One-step (0 to 1) spectral hole burning (SHB) is widely used as a method of eliminating inhomogeneous broadening of spectra: the minimal width of the hole in the inhomogeneous distribution function (IDF) of the transition frequency Omega 01 is obtained by SHB with monochromatic light and is determined by the homogeneous linewidth sigma 0 = gamma 1 + Gamma (where gamma 1 and Gamma are the constants of the energetic and the phase relaxation of the (first) excited level respectively). Two-step (0 to 1 to 2) SHB is considered where the selective excitation of the first step is fixed by a photochemical transformation through the second excitation step. If the selective pulse is a coherent and single-sided exponential then, in the case of an extremely short fixing pulse ( delta pulse), on the increase of the time delay T between the selective and fixing pulses, a monotonic narrowing of the spectral hole in the IDF of the frequency Omega 01 takes place up to the limit width Gamma + mod gamma 1 - Delta mod (where Delta is the spectral width of the selective pulse).
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.
The time-dependent theory of the absorption of three light pulses with an arbitrary duration in ladder-type four-level systems is proposed. The pulses are in resonance with the corresponding transitions. By using the time-dependent perturbation theory the spectral and temporal behaviour of the probability that the fourth level is excited at the moment t is found. We calculate and analyse the cases where the frequencies of the maxima of the two of three light pulses are fixed and the maximum of the remaining pules varies. Widths of possible absorption lines depend on different parameters. On the whole, three or four lines may exist, one of them corresponds to coherent contribution and the others do not.