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Journal of the Optical Society of America B

Excited-state dynamics including radiative diffusion in quasi-three-level laser crystals: application to Yb^3+-doped Y3Al5O12

A. Brenier

Published Sep 28, 2006• 12 citations
Publisher

Abstract

I present a model devoted to linking the properties of a quasi-three-level laser crystal to microscopic parameters. The role of the radiative diffusion is taken into account with a sample-size-dependent parameter, including the total internal reflections, allowing both radiative and nonradiative diffusions to be treated equally. The radiation self-trapping aspect is quantified with the number η′imp of imprisoned photons engendered by one absorbed pump photon. The losses toward the traps that are not always well known are described with the dipole-dipole interaction, giving a microscopic interpretation of the heat dispensed in the sample from the pump. One prediction is that the excited-state decay of the donor subsystem is exponential, in agreement with experiment. The main experimental data, which are the excited-state intrinsic and extrinsic lifetimes τ and τ′ and the extrinsic fractional thermal loading ξ′, can be calculated by adjusting a small number of parameters. This number can be reduced by use of spectroscopy. I have shown that this model can be applied with a reasonable success to Yb3+-doped Y3Al5O12.

DOI
10.1364/josab.23.002209

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I present a model devoted to linking the properties of a quasi-three-level laser crystal to microscopic parameters. The role of the radiative diffusion is taken into account with a sample-size-dependent parameter, including the total internal reflections, allowing both radiative and nonradiative diffusions to be treated equally. The radiation self-trapping aspect is quantified with the number η′imp of imprisoned photons engendered by one absorbed pump photon. The losses toward the traps that are not always well known are described with the dipole-dipole interaction, giving a microscopic interpretation of the heat dispensed in the sample from the pump. One prediction is that the excited-state decay of the donor subsystem is exponential, in agreement with experiment. The main experimental data, which are the excited-state intrinsic and extrinsic lifetimes τ and τ′ and the extrinsic fractional thermal loading ξ′, can be calculated by adjusting a small number of parameters. This number can be reduced by use of spectroscopy. I have shown that this model can be applied with a reasonable success to Yb3+-doped Y3Al5O12.
Radiation trapping causes significant lengthening of the measured fluorescence lifetimes in solid samples, which leads to overestimating them. Self-absorption inside solid-state samples is considerably enhanced by successive total internal reflections at the sample/air interface. A simple method for quantitative estimation of radiation trapping in solid-state materials within the frame of the Holstein-Biberman equations is presented. This method is based on the assumption that the radiation propagation follows paths with many total internal reflections; it can be applied to many resonant two-level systems such as Er3+{\mathrm{Er}}^{3+}Er3+-, Yb3+{\mathrm{Yb}}^{3+}Yb3+-, or Ho3+{\mathrm{Ho}}^{3+}Ho3+-doped materials. The equations are solved for a pulsed excitation localized in a finite volume inside the sample. In our modeling approach, we take into account the initial geometric population distribution and the imaging setup. We derive analytical expressions of the measured decays, which give the deformation of the measured curves compared with the ideal exponential decay. We investigate the effect of the fraction of self-trapped light on the decay modification. We then show that the ratio between the pumping volume, the collected volume, and the sample dimension changes the measured decay significantly.
This research is an outgrowth of earlier experiments that demonstrated bistable luminescence in heavy metal halide crystals doped with trivalent ytterbium ions. This type of instability has importance as a fundamentally new physical phenomenon with a potential application for fast all-optical switching as well as a limitation on compact solid state laser performance. In this thesis, the investigation of luminescent instabilities is extended to bistable energy transfer processes in crystals and to the observation of bistable blackbody emission in rare earth nanopowders. High resolution laser spectroscopy was used to study bistable luminescence and energy transfer in Yb,Er:CsCdBr3 crystals at cryogenic temperatures. For the first time, it was found that bistable behavior associated with Yb 3+ ions was transferred to Er 3+ through resonant energy transfer. Bistability of the resulting sensitized luminescence caused sufficiently dramatic changes in the crystal dynamics so as to change the color of emission from yellow to green. This color changing phenomenon is fully explained in the present work and is referred to as chromatic switching. Temperature is a critical variable that is known to govern luminescent instabilities in all current theories. Therefore, in a search for new systems with luminescent instabilities at high temperatures, materials with extreme thermal properties were investigated as part of this research. Yb,Er:Y 2O3 nanopowders were selected for this purpose. Nanopowders exhibit greatly reduced thermal conductivity and were verified during the course of this work to cause enhanced absorption as the result of multiple scattering. Significant spectral differences between Yb,Er:Y2O 3 nanopowders and single crystals also emerged. Measurements of erbium upconversion luminescence versus pump intensity in resonance with the ytterbium absorption transition revealed striking new optical phenomena: strong luminescent quenching, intense bistable blackbody emission, and the formation of single crystal micro-tubes directly from powder samples. A simple theoretical model was successfully developed to explain all these optical effects by a detailed balance approach to thermal transport that explicitly included erbium and ytterbium atomic level occupation probabilities, blackbody radiation and radiation trapping. Calculations of nanopowder sample luminescence accurately reproduced experimentally observed quenching, the onset of blackbody emission, bistability and details of hysteresis loops. The model also predicted that absorbed powers of less than 15 mW could melt yttria nanopowders (melting point = 2410°C), again in agreement with experiments. This work is expected to enable new approaches to laser processing of ceramics and laser machining of reflective metals, notably aluminum, using low power lasers.
We study the internal state dynamics of optically trapped polyatomic molecules subject to room-temperature blackbody radiation. Using rate equations that account for radiative decay and blackbody excitation between rovibrational levels of the electronic ground state, we model the microscopic behavior of the molecules' thermalization with their environment. As an application of the model, we describe in detail the procedure used to determine the blackbody and radiative lifetimes of low-lying vibrational states in ultracold CaOH molecules, the values of which were reported in previous work [C. Hallas et al., Phys. Rev. Lett. 130, 153202 (2023)]. Ab initio calculations are performed and are found to agree with the measured values. Vibrational-state lifetimes for several other laser-coolable molecules, including SrOH and YbOH, are also calculated.
A vibronic model of laser cooling for crystals doped with Yb3+ ions is proposed. The model involves the stimulated Raman adiabatic passage pumping through dipole-allowed 4f–5d transitions, electron transitions between Stark-split sublevels due to vibronic interaction, and anti-Stokes fluorescence from the excited ion state. Dynamics of the cooling process are described by the density matrix formalism. It is shown that the cooling power in the case of vibronic interaction is higher at least by a factor of 3.4 compared to the case of electron–phonon interaction. In the proposed model, an increase in the cooling power yields deeper and faster refrigeration of a crystal doped with Yb3+ ions. Estimations show that, on cooling by the stimulated Raman adiabatic passage pumping, the temperature of a crystal with an irradiated volume of 2.12×10−4 cm3 can reach 64 K in a time of 2 s. In the proposed model, the cooling temperature is 30 K lower and the cooling process is 100 times faster compared to the traditional model of direct pumping. The estimates are applicable to present-day materials of technologically attainable purity.
In this paper, quantum mechanical calculations of cooling characteristics for the Yb3+: YLF system with use of the vibronic model of laser cooling are presented. Dynamics of the laser cooling process for the seven-level system of an Yb ion is described by the density-matrix formalism. Dependences of the cooling characteristics on the pump intensity are obtained for various temperatures and absorption coefficients of impurity ions. It is shown that the pump intensity, at which the net cooling power has a maximum, depends on temperature. Thus, choosing the intensities, which correspond to the net cooling power maximum over the entire temperature range, we achieve a lower sample temperature at a shorter time than in the case of using a constant intensity throughout the cooling process. Calculations are performed for the parameters of the Yb3+:YLF system.
In this work we expose a recently developed theoretical model for the analysis of the measurements obtained with the so-called pinhole method, for the determination of the upper level lifetime in materials where the superimposition between fluorescence and absorption spectra determines significant radiation trapping effect. Under fairly general conditions the fluorescence decay curve after a pulsed excitation of the sample obtained with this experimental set-up can be conveniently described by a double exponential functional form. The faster of the two decay times is close to the intrinsic fluorescence lifetime, with a difference that can be calculated with geometrical considerations. The theoretical results were tested with a suitably designed experiment, where the upper level lifetime of the laser transition of some Yb doped samples were investigated, obtaining results that are consistent with literature data and in good agreement with the theoretical results as for the temporal dependence of the fluorescence decay.