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

Collective effects application in laser cooling of solids

S. V. Petrushkin, Самарцев Виталий Владимирович

Published Nov 15, 2001• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.447960

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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.
Laser cooling of rare-earth doped solids has been demonstrated across a wide range of material platforms, inspiring the development of simple phenomenological models such as the four-level model to elucidate the universal properties of laser cooling under various operating conditions. However, these models usually require the input of full absorption spectra that must be provided experimentally or by additional complicated atomic modeling. In this Letter, we propose that a four-level model, when extended to admit effective energy levels adaptive to the pumping photon energy, can accurately predict the cooling efficiency as a function of temperature and pumping frequency using only few inputs such as the absorption coefficient measured at a single frequency and temperature. Our model exploits the quasi-equilibrium properties of the excitation of rare-earth ions for the determination of the effective four energy levels. The model is validated against published experimental results for a span of materials including ytterbium/thulium-doped glass and crystals. With the verified model, we derive explicit expressions for the optimal frequency and the operating bandwidth of pumping lasers. Our model significantly simplifies the modeling process of laser cooling and is expected to stimulate further development of optical refrigeration.