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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Laser cooling in extended solids, taking into account the collective processes

Eugene K. Bashkirov

Published Jul 11, 2006• 0 citations
Publisher

Abstract

The kinetics of the extended model of crystal doped by rare-earth ions in regime of anti-Stokes laser cooling has been considered taking into account the collective radiation effects. The system of master equations for impurities and pseudo-local phonons has been obtained. As would be expected, the collective radiation effects causes an acceleration in relaxation depletion of the phohon mode and therefore an increase of crystal cooling efficiency.

DOI
10.1117/12.696836

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 23, 2012•4 citations
The kinetics of the extended model of crystal doped by rare-earth ions in regime of anti-Stokes laser cooling has been considered taking into account the collective radiation effects. The system of master equations for impurities and pseudo-local phonons has been obtained. As would be expected, the collective radiation effects causes an acceleration in relaxation depletion of the phohon mode and therefore an increase of crystal cooling efficiency.
The method of elimination of boson operators is used to theoretically analyze the possibility and optimal conditions of superradiance regime of laser cooling of crystals and glasses doped with rare-earth ions. A set of kinetic equations governing the processes of laser cooling and optical superradiance in a multilevel system is derived for the pulsed regime. It is demonstrated that the efficiency of laser cooling in this regime is proportional to a factor N2(lambda) 2KnS, where N is the number of active impurity centers, (lambda) is the superradiance wavelength, K is the number of superradiance channels, and nS is the number of superradiance events per second.
We present a theoretical scheme for laser cooling of rare-earth-doped solids with optical superradiance (SR), which is the coherent, sharply directed spontaneous emission of photons by a system of laser-excited rare-earth ions in the solid-state host (glass or crystal). We consider an Yb+{}^{+}+-doped ZnF4{}_{4}4​-BaF2{}_{2}2​-LaF3{}_{3}3​-AlF3{}_{3}3​-NaF (ZBLAN) sample pumped at a wavelength 1015 nm, with a rectangular pulsed source with a power of \ensuremath{\sim}433 W and a duration of 10 ns. The intensity of the SR is proportional to the square of the number of excited ions. This unique feature of SR permits an increase in the rate of the cooling process in comparison with the traditional laser cooling of the rare-earth-doped solids with anti-Stokes spontaneous incoherent radiation (fluorescence). This scheme overcomes the limitation of using only low phonon energy glasses for laser cooling.
The enhanced laser cooling performance of rare-earth-ion-doped nanocrystalline powders is predicted, compared to the bulk material, using Yb3+:Y2O3{\mathrm{Yb}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Yb3+:Y2​O3​ as the model material. This is achieved by enhancing the off-resonance, phonon-assisted absorption, which is proportional to the three factors considered in this paper: the dopant concentration, the pumping field energy, and the excitation coefficient. Using the energy transfer theory for concentration quenching, the optimum concentration corresponding to the maximum cooling power is found to be considerably larger than the currently used value, suggesting noticeable enhancement effects for laser cooling. The pumping field energy is enhanced in random nanopowders compared with bulk crystals under the same irradiation, due to the multiple scattering of photons. Photons are thus localized in the medium and do not propagate through, increasing the photon absorption of the pumping beam (and it is shown that the reabsorption of the fluorescence is negligible). Using molecular dynamics simulations, the phonon density of states (DOS) of the nanopowder is calculated, and found to have broadened modes, and extended small tails at low and high frequencies. The second-order electronic transition rate for the anti-Stokes luminescence is calculated using the Fermi golden rule, which includes the influence of this phonon DOS, and is shown to have enhancement effects on the laser cooling efficiency using nanopowders. It is finally concluded that these three enhancement mechanisms are essentially to increase the population of the three participating carriers (electron, photon, and phonon) in the interacting volume, and this also points out directions for enhancing laser cooling performance in bulk materials.
Theoretical schemes for laser cooling with nanoparticles have been presented and comprehensively investigated. It is shown that specially designed samples based on nanoparticles can be used to improve the process of laser cooling of solids. One of the proposed schemes is based on lead salt colloidal quantum dots (QDs) doped in a glass host. The second one is based on Tm3+ doped oxy fluoride glass ceramic. It has been shown that lead salt colloidal QDs doped in a glass host can operate as artificial atoms. Very short (microsecond range) radiative lifetimes of the excited 1Sh level of PbSe QDs in comparison with the relatively long (millisecond) radiative lifetime of rare-earth (RE) ions allows the cooling process to be accelerated and to use new hosts with relatively high maximum phonon energy, which have so far been considered not suitable for cooling with RE ions. It has been shown that the second sample, which is based on Tm3+ doped oxy fluoride glass ceramic provides the unique combination of high chemical and mechanical stability of the oxide glass, which is important for a number of applications, and the low phonon energy of the fluoride nano-crystals, which trap a majority of Tm3+ ions participating in the cooling process. This is highly beneficial for laser cooling of solids, since the effective embedding of rare-earth ions in the crystalline phase with low phonon energy provides a high quantum efficiency for the 3F4 → 3H6 transition involved in the cooling cycle in the Tm3+ ions, which is a key parameter for laser cooling of solids.