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Acta Physica Sinica

STUDY ON THE FLUORESCENT COOLING BY ENERGY TRANSFER WITHIN INHOMOGENOUS LINE SHAPE IN SOLIDS

QIN WEI-PING, ZHANG JIA-HUA, Huang Shi-Hua, 中国科学院长春物理研究所激发态物理开放研究实验室，长春 130021

Published Jan 1, 1998• 2 citations
Publisher

Abstract

In this paper, a new mechanism of anti-Stokes fluorescent cooling based on the energy transfer among the centers within the inhomogeneously broadened line is proposed. The dependence of relative cooling efficiency on excitation photon energy and temperature is discussed.
DOI
10.7498/aps.47.1397

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Figure 6.1 Anti-Stokes fluorescence emission in a two-level system. Additionally, only a fraction of the absorbed photons result in excitation of coolant atoms. The rest are absorbed by background impurities. With the absorption coefficient of the coolant atoms designated by αc and that of the background by αb, the proportion of absorbed photons that contribute to cooling is h a c b( ) = + (6.3) If the assumption is made that phonon-mediated absorp-tion is proportional to the occupation probability of the phonon mode, namely n k T= (exp[ / ]-1)B -1W , the efficiency becomes h a a aabs c c b/( )= +n n . Then at high temperatures (kBT >> ħΩ)), ηabs varies little with temperature when the background absorp-tion is low (αb/αc << 1). On the other hand at low temperatures, as n Æ 0, ηabs decreases in proportion to n . Hence the absorption efficiency drops dramatically through the important cryogenic re-gime. The overall cooling is determined by the product of the various efficiency factors. h h h n n ËÁ ˆ ¯˜ (6.4) From Eqs. 6.1 and 6.4 it is easy to show that the cooling power density per unit frequency is Pc/V = ηabsηextαtotIv(vfi – v)/v. Here Iv= I0g(v) is the intensity per unit frequency and g(v) is a normalized spectral line shape function. V is the interaction volume. If the bandwidth of the light source equals the full linewidth 2Γ of the optical transition, and the density of atoms in the interaction volume is N/V, the energy loss rate per atom is R = 2ΓηcαtotIv(V/N) = ηcαtotI0(V/N) (6.5) The condition for net cooling can be expressed in a simple way based on Eq. 6.4, since ηc must exceed zero. By assuming that the laser detuning is optimized at the phonon frequency Ω, we can rewrite the numerator using hvft – hv = ħΩ. Furthermore the average phonon energy is ħΩ ≈ kBT near the boundary of the classical regime [15]. Then the condition for laser cooling (ηc > 0) becomes h h next abs B> -1 k T h (6.6) An important limitation of refrigeration based on anti-Stokes fluorescence emerges from this condition by determining the temperature at which the cooling efficiency drops to zero (ηc = 0). By solving Eq. 6.6 as an equality, it is found that a lower bound exists for the attainable temperature. The minimum temperature Tmin that can be reached with anti-Stokes cooling found from Eq. 6.6 is T h ( / ) ( ) ( / ) = + - + Ê ËÁ ˆ ¯˜ n a a h a a 1 (6.7) According to Eq. 6.7, if the quantum efficiency is high (next ≈ 1), the temperature limit for laser cooling by anti-Stokes emission is primarily determined by the frequency of light and the background-to-resonant-absorption ratio. The dependence on these two factors arises because heat input to the system is proportional to incident photon energy and absorptive heating efficiency. Only when the background absorption coefficient vanishes could arbitrarily low temperatures be reached. For the moderate levels of background absorption encountered in practice in solids, this places a severe constraint on temperatures that can be reached by laser cooling. As a simple example of this, the anti-Stokes cooling limit predicted by Eq. 6.7 at a wavelength of 1 micron is Tmin = 145.3 K when the external quantum efficiency is ηext = 0.90 and background absorption coefficient is αb = αc/1000. The lower bound on attainable temperatures can be interpreted in another way. It arises because the cooling rate depends on phonon occupation, a factor that diminishes as temperature decreases. Eventually the rate of anti-Stokes cooling drops below the rate of heating from background impurity absorption and cooling is no longer possible [16]. For 3D refrigeration of solids to be as effective as laser cooling of gases, techniques capable of maintaining high rates of cooling through the cryogenic temperature range are needed. This is discussed further in what follows. In the remainder of this chapter momentum is incorporated into the discussion to investigate whether the fundamental temperature limitation of anti-Stokes fluorescence cooling can be evaded when the dynamics are viewed comprehensively. Judging from the successes of laser cooling of gases, cooling schemes that conserve momentum and energy simultaneously during optical interactions are the most efficient. Yet momentum is disregarded in the anti-Stokes fluorescence method. Other techniques may offer the capability of balancing the momentum and energy requirements more consistently to accommodate phonon dispersion (Fig. 6.2).

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Cooling via efficient emission of anti-Stokes photoluminescence can be utilized to realize novel cooling devices. It has been shown that rare earth-doped materials are good candidates for solid-state laser cooling because of their narrow emission spectra and discrete energy levels. We systematically study laser cooling efficiency of rare earth-doped oxide crystals. The photoluminescence spectrum evidences that the phonon-assisted energy transfer from resonant states to inhomogeneously distributed energy states sensitively depends on temperature. We discuss detailed properties of the cooling efficiency of Yb-doped yttrium aluminum oxide crystals and, furthermore, touch emission properties of their crystal thin films.

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Figure 6.1 Anti-Stokes fluorescence emission in a two-level system. Additionally, only a fraction of the absorbed photons result in excitation of coolant atoms. The rest are absorbed by background impurities. With the absorption coefficient of the coolant atoms designated by αc and that of the background by αb, the proportion of absorbed photons that contribute to cooling is h a c b( ) = + (6.3) If the assumption is made that phonon-mediated absorp-tion is proportional to the occupation probability of the phonon mode, namely n k T= (exp[ / ]-1)B -1W , the efficiency becomes h a a aabs c c b/( )= +n n . Then at high temperatures (kBT >> ħΩ)), ηabs varies little with temperature when the background absorp-tion is low (αb/αc << 1). On the other hand at low temperatures, as n Æ 0, ηabs decreases in proportion to n . Hence the absorption efficiency drops dramatically through the important cryogenic re-gime. The overall cooling is determined by the product of the various efficiency factors. h h h n n ËÁ ˆ ¯˜ (6.4) From Eqs. 6.1 and 6.4 it is easy to show that the cooling power density per unit frequency is Pc/V = ηabsηextαtotIv(vfi – v)/v. Here Iv= I0g(v) is the intensity per unit frequency and g(v) is a normalized spectral line shape function. V is the interaction volume. If the bandwidth of the light source equals the full linewidth 2Γ of the optical transition, and the density of atoms in the interaction volume is N/V, the energy loss rate per atom is R = 2ΓηcαtotIv(V/N) = ηcαtotI0(V/N) (6.5) The condition for net cooling can be expressed in a simple way based on Eq. 6.4, since ηc must exceed zero. By assuming that the laser detuning is optimized at the phonon frequency Ω, we can rewrite the numerator using hvft – hv = ħΩ. Furthermore the average phonon energy is ħΩ ≈ kBT near the boundary of the classical regime [15]. Then the condition for laser cooling (ηc > 0) becomes h h next abs B> -1 k T h (6.6) An important limitation of refrigeration based on anti-Stokes fluorescence emerges from this condition by determining the temperature at which the cooling efficiency drops to zero (ηc = 0). By solving Eq. 6.6 as an equality, it is found that a lower bound exists for the attainable temperature. The minimum temperature Tmin that can be reached with anti-Stokes cooling found from Eq. 6.6 is T h ( / ) ( ) ( / ) = + - + Ê ËÁ ˆ ¯˜ n a a h a a 1 (6.7) According to Eq. 6.7, if the quantum efficiency is high (next ≈ 1), the temperature limit for laser cooling by anti-Stokes emission is primarily determined by the frequency of light and the background-to-resonant-absorption ratio. The dependence on these two factors arises because heat input to the system is proportional to incident photon energy and absorptive heating efficiency. Only when the background absorption coefficient vanishes could arbitrarily low temperatures be reached. For the moderate levels of background absorption encountered in practice in solids, this places a severe constraint on temperatures that can be reached by laser cooling. As a simple example of this, the anti-Stokes cooling limit predicted by Eq. 6.7 at a wavelength of 1 micron is Tmin = 145.3 K when the external quantum efficiency is ηext = 0.90 and background absorption coefficient is αb = αc/1000. The lower bound on attainable temperatures can be interpreted in another way. It arises because the cooling rate depends on phonon occupation, a factor that diminishes as temperature decreases. Eventually the rate of anti-Stokes cooling drops below the rate of heating from background impurity absorption and cooling is no longer possible [16]. For 3D refrigeration of solids to be as effective as laser cooling of gases, techniques capable of maintaining high rates of cooling through the cryogenic temperature range are needed. This is discussed further in what follows. In the remainder of this chapter momentum is incorporated into the discussion to investigate whether the fundamental temperature limitation of anti-Stokes fluorescence cooling can be evaded when the dynamics are viewed comprehensively. Judging from the successes of laser cooling of gases, cooling schemes that conserve momentum and energy simultaneously during optical interactions are the most efficient. Yet momentum is disregarded in the anti-Stokes fluorescence method. Other techniques may offer the capability of balancing the momentum and energy requirements more consistently to accommodate phonon dispersion (Fig. 6.2).
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.
Cooling via efficient emission of anti-Stokes photoluminescence can be utilized to realize novel cooling devices. It has been shown that rare earth-doped materials are good candidates for solid-state laser cooling because of their narrow emission spectra and discrete energy levels. We systematically study laser cooling efficiency of rare earth-doped oxide crystals. The photoluminescence spectrum evidences that the phonon-assisted energy transfer from resonant states to inhomogeneously distributed energy states sensitively depends on temperature. We discuss detailed properties of the cooling efficiency of Yb-doped yttrium aluminum oxide crystals and, furthermore, touch emission properties of their crystal thin films.