Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Saturation Effects and Thermal Balance in Laser-Cooled Solids

Long Cheng

Published Jan 1, 2023• 0 citations
Publisher

Abstract

The role of saturation of background absorption by unintended impurities has been investigated for the first time theoretically and experimentally in the context of laser cooling of crystalline solids and the operation of self-cooled or radiation-balanced lasers. In this thesis it is shown that when saturation of the background takes place at an intensity lower than the saturation intensity of dopant ions responsible for cooling, as in Yb3+:LiYF4, cooling efficiency can be improved by using elevated input intensity. With the same input power, the measured cooling efficiency in 10% Yb3+:LiYF4 crystal was doubled at 1020 nm when the beam radius was reduced by a factor of 10, by partially saturating the background impurity absorption. This is effective not only as a post-growth method of enhancing cooling efficiency but offers a new way of reaching lower temperatures than were previously possible with anti-Stokes fluorescent (ASF) refrigeration. Prior to this work, cooling efficiency was thought to be independent of intensity and crystal purification was considered as the only way to improve the cooling efficiency. It is further demonstrated that background saturation plays a key role in the operation of self-cooled or radiation-balanced lasers. Because radiation-balanced lasers operate under saturated conditions it is essential to include limitations imposed by impurity content of the gain medium. When this is done, quantitative predictions of the required conditions for radiation balance become possible. Laser operation can then be made more efficient and can be extended to new materials which may be relatively impure and uncommon but are well-suited to efficient operation under radiation-balanced conditions by virtue of a special combination of physical characteristics. Radiation-balanced laser operation is achieved in 3% Yb:YAG (1 × 1 × 10 mm3) and is found to result in exceptionally uniform temperature distributions using high resolution thermal imagery. Threshold levels, output power, and input power at the radiation balance point are all shown to be in close agreement with theory. This laser achieved 30.5% laser efficiency (agreed with predictions within 2%), which is the highest efficiency level of any self-cooled laser operated to date. Radiation-balanced lasing is also achieved for the first time in the tungstate crystal 2% Yb3+:KYW (0.9×1.2×10 cm3), despite having very high impurity content as the result of being an uncommon gain medium. The achieved laser efficiency was only 2.2%, as the result of non-optimal optical components, high Yb concentration, high impurity content, crystal polish, excitation wavelength, and output coupling. However, this is the first demonstration of an Yb3+ radiation-balanced laser in the tungstate host. Correction of these deficiencies should enable high quality Gaussian output at the 5 W level with 18% efficiency in existing commercial 1% Yb:KYW samples. Even better performance of this new self-cooled laser could result from improved crystal growth efforts.

DOI
10.7302/7297

Related papers

Temperature dynamics of laser cooling of solids with Yb3+ions

Galina A. Nemova, Raman Kashyap

We consider a theoretical model for laser cooling with anti-Stokes fluorescence of a Yb3+:YAG sample. We have estimated the fluorescence power density removed from the system with spontaneous emission, the power density radiated with stimulated emission as well as the heat power density generated in the system by non-radiative decays from the impurities in the host material. We have investigated the influence of each of these power densities on the cooling process in Yb3+:YAG system. It has been shown how the temperature dependences of the different parameters of the system as well as the concentration of the impurities in the host influence the final temperature of the cooled sample.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 19, 2014•1 citation

Laser cooling under ambient conditions in Yb3+:KYW

Laura B. Andre, Long Cheng, Alexander J. Salkeld +4 more

We report the first observation of laser cooling in 1%Yb3+:KYW and discuss factors that limit the cooling efficiency. Cooling by 10 K from room temperature at atmospheric pressure was achieved in this crystal at a wavelength of 1025 nm using 8 W from a seeded fiber amplifier. The temperature of the sample was measured using a calibrated differential luminescence thermometry method and was verified with a thermal camera. Infrared imagery and 3-D modeling were used to analyze the impact of thermal conduction, thermal convection, black-body radiation, and background impurities. The simulated results agree with experimental measurements confirming that the chief limitation of laser cooling at room temperature and atmospheric pressure is thermal conduction from sample supports. Best results were obtained for samples mounted on silica aerogel. Theoretical improvement of cooling efficiency in vacuum by exploiting impurity absorption saturation is also discussed.

Photonic Heat Engines: Science and Applications•Mar 1, 2019•0 citations

Comparison of Yb3+: YAP with Yb3+: YAG cooling crystals

Chaoyu Wang, Jianping Yin

Abstract YAlO 3 (YAP) shows lower phonon energy than Y 3 Al 5 O 12 (YAG), which implies a lower temperature can be obtained in Yb 3+ -doped YAP according to the single-frequency phonon model. Here, a 2% Yb 3+ : YAP crystal was refrigerated by anti-Stokes fluorescence and compared to YAG crystal with the same doping concentration in experiments. Yb 3+ exhibited a broad spectral cooling range in YAP from 1020nm to 1070nm, which was broader than in YAG from 1020 nm to 1055 nm. A minimum achievable temperature (MAT) dropped to ~ 249.7 K at 1040 nm for Yb 3+ : YAP, which was lower than that of ~ 259.3 K obtained in 2% Yb 3+ : YAG. Further analysis predicted that the cooling limit of two crystals can reach ~167 K for Yb 3+ : YAP and ~171 K for Yb 3+ : YAG from room temperature. This work exhibited the excellent cooling properties of Yb 3+ : YAP compared with Yb 3+ : YAG in experiment and provided a unique perspective for the practical application of high-power Radiation balance lasers (RBLs).

Applied Physics B•Apr 27, 2026•1 citation

Laser cooling in Yb^3+:YAG

Galina A. Nemova, Raman Kashyap

We develop a detailed theoretical model for laser cooling in Yb3+:YAG. The expressions for the fluorescence power density removed from the system with spontaneous emission, the power density radiated with stimulated emission, as well as the heat power density generated in the system by nonradiative decays on the impurities of the host material have been calculated. The influence of each of these power densities on the cooling process has been analyzed. We show, for the first time to our knowledge, how the temperature dependences of the different parameters of the system as well as the concentration of the impurities in the host influence the final temperature of the cooled sample.

Journal of the Optical Society of America B•Jan 22, 2014•20 citations

Chapter 8 Bulk Cooling Efficiency Measurements of Yb-Doped Fluoride Single Crystals and Energy Transfer–Assisted Anti-Stokes Cooling in Co-Doped Fluorides

Azzurra Volpi, Alberto Di Lieto, M. Tonelli

To overcome the ETU-induced heating and realize efficient and enhanced laser cooling in Ho3+-doped solids, in Section 4.3, we will provide a modified excitation scheme based on ground-state absorption (GSA) of 5I8 Æ 5I7 at around 2.07 μm and ESA of 5I5 Æ 5F5 at around 2.28 μm. Compared with the conventional pumping scheme, the co-pumping scheme ameliorates the cooling performance significantly through alleviating the upconversion-quenching-induced heat [12], that is, the heat-producing 5I5 Ho3+ions are pumped to the 5F5 state by the laser at 2.28 μm. Fortunately, the 5F5 Ho3+ ions barely transit to the lower nearby state and tend to decay radiatively. Therefore, major heat produced in the conventional laser cooling of Ho3+-doped solids is avoided, and both cooling efficiency and cooling power density can be improved. In Section 4.4, we broaden the research domain of optical refrigeration to rare earth ion co-doped systems. Specifically, when Ho3+–Tm3+ co-doped YLiF4 crystals are pumped at around 2.07 μm, Ho3+ ions will populate at the 5I7 manifold. Meanwhile, Tm3+ ions will also be sensitized by absorbing energy transferred from 5I7 Ho3+ ions. Since the average energy of fluorescence photons generated by Tm3+3F4 Æ 3H6 radiative transitions is higher than that generated by Ho3+5I7 Æ 5I8 radiative transitions, energy transfer (ET) from Ho3+ to Tm3+ ions will induce annihilation of host phonons, and bring enhancement in both the cooling efficiency and the cooling power. Therefore, this cooling mechanism is referred next as energy transfer-enhanced laser cooling (ETLC) of solids [11]. 4.2 Conventional Laser Cooling of Holmium- The main upconversion process and the anti-Stokes fluorescence cooling (ASFC) processes of Ho3+-doped fluoride crystals are illustrated in Fig. 4.1. The ground-state (5I8) Ho3+ ions are pumped to the first excited state (5I7) with laser excitations of energy hν (solid red arrow on the left) and then relax thermally among the Stark levels in a timescale of picoseconds with host phonon absorption. Part of the Ho3+5I7 ions de-excite by emitting fluorescence photons of mean energy hν10 (solid blue arrow, ν10 > ν), which accounts for the ASFC process. The rest of the 5I7 Ho3+ ions de-excited and transfer their energy to the neighboring 5I7 Ho3+ ions, causing population accumulation at the third excited state (5I5) with host phonon absorption (solid green arrows). Comparison between the energy mismatch and the host phonon energy (for YLiF4 crystal host, ħω ≈ 450 cm-1) indicates that about two host phonons are annihilated for each ETU process (see Table 4.1).

Pan Stanford Publishing eBooks•Aug 31, 2016•0 citations

Chapter 10 Fluoride Glasses and Fibers

Mohammed Saad

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).

Pan Stanford Publishing eBooks•Aug 31, 2016•0 citations
The role of saturation of background absorption by unintended impurities has been investigated for the first time theoretically and experimentally in the context of laser cooling of crystalline solids and the operation of self-cooled or radiation-balanced lasers. In this thesis it is shown that when saturation of the background takes place at an intensity lower than the saturation intensity of dopant ions responsible for cooling, as in Yb3+:LiYF4, cooling efficiency can be improved by using elevated input intensity. With the same input power, the measured cooling efficiency in 10% Yb3+:LiYF4 crystal was doubled at 1020 nm when the beam radius was reduced by a factor of 10, by partially saturating the background impurity absorption. This is effective not only as a post-growth method of enhancing cooling efficiency but offers a new way of reaching lower temperatures than were previously possible with anti-Stokes fluorescent (ASF) refrigeration. Prior to this work, cooling efficiency was thought to be independent of intensity and crystal purification was considered as the only way to improve the cooling efficiency. It is further demonstrated that background saturation plays a key role in the operation of self-cooled or radiation-balanced lasers. Because radiation-balanced lasers operate under saturated conditions it is essential to include limitations imposed by impurity content of the gain medium. When this is done, quantitative predictions of the required conditions for radiation balance become possible. Laser operation can then be made more efficient and can be extended to new materials which may be relatively impure and uncommon but are well-suited to efficient operation under radiation-balanced conditions by virtue of a special combination of physical characteristics. Radiation-balanced laser operation is achieved in 3% Yb:YAG (1 × 1 × 10 mm3) and is found to result in exceptionally uniform temperature distributions using high resolution thermal imagery. Threshold levels, output power, and input power at the radiation balance point are all shown to be in close agreement with theory. This laser achieved 30.5% laser efficiency (agreed with predictions within 2%), which is the highest efficiency level of any self-cooled laser operated to date. Radiation-balanced lasing is also achieved for the first time in the tungstate crystal 2% Yb3+:KYW (0.9×1.2×10 cm3), despite having very high impurity content as the result of being an uncommon gain medium. The achieved laser efficiency was only 2.2%, as the result of non-optimal optical components, high Yb concentration, high impurity content, crystal polish, excitation wavelength, and output coupling. However, this is the first demonstration of an Yb3+ radiation-balanced laser in the tungstate host. Correction of these deficiencies should enable high quality Gaussian output at the 5 W level with 18% efficiency in existing commercial 1% Yb:KYW samples. Even better performance of this new self-cooled laser could result from improved crystal growth efforts.
We consider a theoretical model for laser cooling with anti-Stokes fluorescence of a Yb3+:YAG sample. We have estimated the fluorescence power density removed from the system with spontaneous emission, the power density radiated with stimulated emission as well as the heat power density generated in the system by non-radiative decays from the impurities in the host material. We have investigated the influence of each of these power densities on the cooling process in Yb3+:YAG system. It has been shown how the temperature dependences of the different parameters of the system as well as the concentration of the impurities in the host influence the final temperature of the cooled sample.
We report the first observation of laser cooling in 1%Yb3+:KYW and discuss factors that limit the cooling efficiency. Cooling by 10 K from room temperature at atmospheric pressure was achieved in this crystal at a wavelength of 1025 nm using 8 W from a seeded fiber amplifier. The temperature of the sample was measured using a calibrated differential luminescence thermometry method and was verified with a thermal camera. Infrared imagery and 3-D modeling were used to analyze the impact of thermal conduction, thermal convection, black-body radiation, and background impurities. The simulated results agree with experimental measurements confirming that the chief limitation of laser cooling at room temperature and atmospheric pressure is thermal conduction from sample supports. Best results were obtained for samples mounted on silica aerogel. Theoretical improvement of cooling efficiency in vacuum by exploiting impurity absorption saturation is also discussed.
Abstract YAlO 3 (YAP) shows lower phonon energy than Y 3 Al 5 O 12 (YAG), which implies a lower temperature can be obtained in Yb 3+ -doped YAP according to the single-frequency phonon model. Here, a 2% Yb 3+ : YAP crystal was refrigerated by anti-Stokes fluorescence and compared to YAG crystal with the same doping concentration in experiments. Yb 3+ exhibited a broad spectral cooling range in YAP from 1020nm to 1070nm, which was broader than in YAG from 1020 nm to 1055 nm. A minimum achievable temperature (MAT) dropped to ~ 249.7 K at 1040 nm for Yb 3+ : YAP, which was lower than that of ~ 259.3 K obtained in 2% Yb 3+ : YAG. Further analysis predicted that the cooling limit of two crystals can reach ~167 K for Yb 3+ : YAP and ~171 K for Yb 3+ : YAG from room temperature. This work exhibited the excellent cooling properties of Yb 3+ : YAP compared with Yb 3+ : YAG in experiment and provided a unique perspective for the practical application of high-power Radiation balance lasers (RBLs).
We develop a detailed theoretical model for laser cooling in Yb3+:YAG. The expressions for the fluorescence power density removed from the system with spontaneous emission, the power density radiated with stimulated emission, as well as the heat power density generated in the system by nonradiative decays on the impurities of the host material have been calculated. The influence of each of these power densities on the cooling process has been analyzed. We show, for the first time to our knowledge, how the temperature dependences of the different parameters of the system as well as the concentration of the impurities in the host influence the final temperature of the cooled sample.
To overcome the ETU-induced heating and realize efficient and enhanced laser cooling in Ho3+-doped solids, in Section 4.3, we will provide a modified excitation scheme based on ground-state absorption (GSA) of 5I8 Æ 5I7 at around 2.07 μm and ESA of 5I5 Æ 5F5 at around 2.28 μm. Compared with the conventional pumping scheme, the co-pumping scheme ameliorates the cooling performance significantly through alleviating the upconversion-quenching-induced heat [12], that is, the heat-producing 5I5 Ho3+ions are pumped to the 5F5 state by the laser at 2.28 μm. Fortunately, the 5F5 Ho3+ ions barely transit to the lower nearby state and tend to decay radiatively. Therefore, major heat produced in the conventional laser cooling of Ho3+-doped solids is avoided, and both cooling efficiency and cooling power density can be improved. In Section 4.4, we broaden the research domain of optical refrigeration to rare earth ion co-doped systems. Specifically, when Ho3+–Tm3+ co-doped YLiF4 crystals are pumped at around 2.07 μm, Ho3+ ions will populate at the 5I7 manifold. Meanwhile, Tm3+ ions will also be sensitized by absorbing energy transferred from 5I7 Ho3+ ions. Since the average energy of fluorescence photons generated by Tm3+3F4 Æ 3H6 radiative transitions is higher than that generated by Ho3+5I7 Æ 5I8 radiative transitions, energy transfer (ET) from Ho3+ to Tm3+ ions will induce annihilation of host phonons, and bring enhancement in both the cooling efficiency and the cooling power. Therefore, this cooling mechanism is referred next as energy transfer-enhanced laser cooling (ETLC) of solids [11]. 4.2 Conventional Laser Cooling of Holmium- The main upconversion process and the anti-Stokes fluorescence cooling (ASFC) processes of Ho3+-doped fluoride crystals are illustrated in Fig. 4.1. The ground-state (5I8) Ho3+ ions are pumped to the first excited state (5I7) with laser excitations of energy hν (solid red arrow on the left) and then relax thermally among the Stark levels in a timescale of picoseconds with host phonon absorption. Part of the Ho3+5I7 ions de-excite by emitting fluorescence photons of mean energy hν10 (solid blue arrow, ν10 > ν), which accounts for the ASFC process. The rest of the 5I7 Ho3+ ions de-excited and transfer their energy to the neighboring 5I7 Ho3+ ions, causing population accumulation at the third excited state (5I5) with host phonon absorption (solid green arrows). Comparison between the energy mismatch and the host phonon energy (for YLiF4 crystal host, ħω ≈ 450 cm-1) indicates that about two host phonons are annihilated for each ETU process (see Table 4.1).
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).