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Laser Cooling of Solids

Mansoor Sheik‐Bahae, Richard I. Epstein

Published Mar 7, 2007• 14 citations
OpenAlex

Abstract

Publisher Summary This chapter focuses on the concept of laser cooling of a solid, which may occur when the average energy of the photons emitted by the solid is larger than the energy of the ones it absorbs. More formally, the anti-Stokes emission, which occurs at frequencies larger than that of the pump laser, must dominate the Stokes emission that occurs at smaller frequencies. A crucial additional requirement is that the nonradiative decay rates of the laser-pumped states be negligible in comparison to their radiative decay rates. For the sake of specificity, these states will be taken to be those of a set of isolated ions embedded within an insulating host, although in general they could equally well be those of gas-, liquid-, or solid-phase neutral atoms or molecules, or even those of the energy bands of intrinsic semiconductors. Outside the realm of impurity-doped insulators, recent experiments with semiconductors make net anti-Stokes fluorescence cooling of these materials appear achievable. A long-term idea for improving laser cooling of solids takes advantage of photonic band gap materials. The idea is to fabricate a refractive-index structure within the cooling element that would establish a three-dimensional photonic gap immediately below the pump frequency. In this way, emission at Stokes frequencies falling within the gap would be inhibited, thereby enhancing the cooling power derived from the anti-Stokes emission.

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Publisher Summary This chapter focuses on the concept of laser cooling of a solid, which may occur when the average energy of the photons emitted by the solid is larger than the energy of the ones it absorbs. More formally, the anti-Stokes emission, which occurs at frequencies larger than that of the pump laser, must dominate the Stokes emission that occurs at smaller frequencies. A crucial additional requirement is that the nonradiative decay rates of the laser-pumped states be negligible in comparison to their radiative decay rates. For the sake of specificity, these states will be taken to be those of a set of isolated ions embedded within an insulating host, although in general they could equally well be those of gas-, liquid-, or solid-phase neutral atoms or molecules, or even those of the energy bands of intrinsic semiconductors. Outside the realm of impurity-doped insulators, recent experiments with semiconductors make net anti-Stokes fluorescence cooling of these materials appear achievable. A long-term idea for improving laser cooling of solids takes advantage of photonic band gap materials. The idea is to fabricate a refractive-index structure within the cooling element that would establish a three-dimensional photonic gap immediately below the pump frequency. In this way, emission at Stokes frequencies falling within the gap would be inhibited, thereby enhancing the cooling power derived from the anti-Stokes emission.
The laser cooling of vibrational states of solids has been achieved through photoluminescence in rare-earth elements, optical forces in optomechanics, and the Brillouin scattering light-sound interaction. The net cooling of solids through spontaneous Raman scattering, and laser refrigeration of indirect band gap semiconductors, both remain unsolved challenges. Here, we analytically show that photonic density of states (DoS) engineering can address the two fundamental requirements for achieving spontaneous Raman cooling: suppressing the dominance of Stokes (heating) transitions, and the enhancement of anti-Stokes (cooling) efficiency beyond the natural optical absorption of the material. We develop a general model for the DoS modification to spontaneous Raman scattering probabilities, and elucidate the necessary and minimum condition required for achieving net Raman cooling. With a suitably engineered DoS, we establish the enticing possibility of refrigeration of intrinsic silicon by annihilating phonons from all its Raman-active modes simultaneously, through a single telecom wavelength pump. This result points to a highly flexible approach for laser cooling of any transparent semiconductor, including indirect band gap semiconductors, far away from significant optical absorption, band-edge states, excitons, or atomic resonances.
Laser cooling of solids is also called anti-Stokes fluorescent cooling, it is a new optical cooling technology in recent years. We propose a two-level model to analyze the absorption and stimulated-emission processes between the Yb3+2F7/2 ground-state manifold and the 2F5/2 excited-state manifold, and discuss several parameters that influence the cooling power, and find some ways to improve the cooling power. The influences of the doped concentration, pumping power and the effective pump-spot area on cooling are particularly analyzed. At the same time, we make computer simulation about the cooling process and obtain the temperature as a function of the cooling time, which is similar to the experimental results. So this shows that our model is reasonable.
A theoretical scheme for laser cooling thulium doped solids with optical superradiance is presented. The superradiance is coherent, sharply directed spontaneous emission of photons by an ensemble of excited ions in the solid-state host, the properties of which are much different from the conventional, incoherent anti-Stokes fluorescence radiating through all directions. In this paper, we consider a thulium doped ZBLAN sample pumped with continuous-wave laser at 1.9 μm and pulse laser at 1.8 μm. The induced anti-Stokes superrandiance at 1.8 μm removes the matrical phonons energy much effectively and quickly, because of the intensity of superradiance proportional to the square of the number of excited Tm ions. The numerical evaluations of the superradiance cooling performance, especially in the net cooling power and the cooling efficiency, is discussed.
The material metrics for optimal laser cooling of ion-doped solids are derived using atomic and molecular dynamics properties of the constituents. The anti-Stokes process is modeled as an optical phonon coupling of the bound electron, followed by a photon absorption. The transition dipole moment is estimated using a simplified charge-displacement model and the Judd--Ofelt theory of rare-earth ions both suggesting that transitions with high-energy gaps and similar angular momentum states should be used. The electron-phonon coupling is interpreted as a derivative of electronic energy with respect to displacement of the nearest neighboring ligands whose stretching mode frequency is approximated using the molecular data. The Debye-Gaussian model is used for the phonon density of states of diatomic crystal. Then, the Fermi golden rule is used for photon-induced, phonon-assisted electronic transition probability and applied to the cooling rate equation by defining a phonon-assisted transition dipole moment. Based on the material metrics, an example blend is investigated for its cooling performance and a general guide is proposed for selection of better performing laser cooling hosts. Furthermore, the cooling rate limits are discussed and three distinct characteristic times are identified with the photon-induced, phonon-assisted transition time controlling the rate. The metrics guide the selection of host materials for optimal cooling, and predict a noticeable increase in the absorption rate when using a blend of cation atoms.
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 established approach to laser cooling of solids relies on anti-Stokes fluorescence, for example from rare earth impurities in glass. Although successful, there is a minimum temperature to which such a process can cool set by the electronic level spacing in the impurity. We propose an alternative method which does not suffer from this limitation. Our approach relies on the formation of dressed states under strong laser driving, which generates a spectrum in which the gaps can be tuned to optimize the heat absorption. This allows for a cooling cycle which operates at any temperature with a power comparable to the maximum dictated by thermodynamic principles. While this cooling cycle will compete with heating due to non-radiative decay and other mechanisms, it could in principle allow laser cooling to temperatures which are unachievable with anti-Stokes fluorescence.