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Energy transfer enhanced laser cooling in Ho3+ and Tm3+-codoped lithium yttrium fluoride Guang-Zong Dong, Xin-Lu Zhang,* and Li Li College of Science, Harbin Engineering University, Harbin 150001, China *Corresponding author:
[email protected] Received November 30, 2012; revised January 16, 2013; accepted February 10, 2013; posted February 13, 2013 (Doc. ID 180859); published March 14, 2013 We report a theoretical scheme for laser cooling of solids based on energy transfer usually found in rare-earth codoped materials. The cooling scheme enables a large enhancement in the cooling efficiency with regard to the standard anti-Stokes fluorescence cooling. A Ho3 and Tm3 -codoped low-phonon crystal (LiYF4 ) sample is investigated to find that the cooling efficiency increases, and then decreases with the increasing of the resonant absorption. The optimal cooling efficiency is predicted to exceed 5%. The maximum cooling power density could be promoted greatly by applying the codoped cooling scheme. The cooling scheme is also valid for other rare-earth (for example, Tm3 and Er3 , or Er3 and Yb3 ) codoped materials. © 2013 Optical Society of America OCIS codes: 140.3320, 140.6810, 160.4670, 160.5690, 260.2160.
1. INTRODUCTION Laser cooling of solids or anti-Stokes fluorescence cooling (ASFC) has attracted great interest, as it could be the foundation of fabricating compact, vibration-free, and reliable allsolid-state cryocoolers [1]. The idea that materials might be cooled through luminescence upconversion was initially proposed by Pringsheim in 1929 [2]. The object to be cooled is pumped with narrow-banded and unidirectional radiation (laser photons) [3]. If the photons (fluorescence) emitted by the object have a mean frequency (energy) higher than that of the laser photons, cooling could be achieved. Despite the clear cooling principle, experimental realization of ASFC has been restricted by impurity heating [4]. It was not until 1995 that net cooling of a solid was first demonstrated by Epstein et al. in high-purity ytterbium-doped heavy-metal fluoride glass (Yb3 :ZBLANP) [5]. Since then, ASFC has been observed in several solid-state materials doped with trivalent lanthanide ions (Yb3 , Tm3 , and Er3 ) [6–10]. It was found that rareearth-doped crystalline materials have numerous advantages, including high-absorbing cross section and low-phonon energy that enable cooling to cryogenic temperatures [11]. In 2011, Los Alamos National Laboratory obtained a record local cooling temperature of 110 K in Yb3 doped low-phonon LiYF4 crystal [12]. Recently, rare-earth ions with smaller first excited-state energy, such as Ho3 and Dy3 , are considered as promising active ions for high-efficient ASFC [13]. Various techniques have been exploited to improve the cooling performance. Cavities were introduced in the optical refrigeration experiments to enhance the incident laser absorption, so the total cooling power can be largely increased [14,15]. Besides, photon localization effect in nanocrystalline powders also provides a potential in promoting the input absorption [16]. For rare-earth ions with multielectronic energy levels, like Er3 , the second and the higher excited electronic energy levels could be utilized as additional radiation cooling channels [17,18]. More recently, pulsed laser induced superradiance was suggested to be able to accelerate the cooling 0740-3224/13/040939-06$15.00/0
rate intensively, and meanwhile increase the quantum efficiency markedly [19,20]. In addition, Brillouin and Raman scattering have been considered as alternative cooling mechanisms for laser cooling of solids [21,22]. Although the cooling performance of an optical refrigeration system might be improved by employing the proposals mentioned above, the cooling efficiency (the key aspect of optical refrigeration) remains to be promoted for practical applications. In this paper, we propose an efficient cooling scheme based on energy transfer (ET) processes in rare-earth codoped crystals. Particularly, in holmium, thulium-codoped LiYF4 (Ho, Tm: YLF) crystal, the ET processes are induced by interaction between the ground (5 I8 , 3 H6 ) and the first exited (5 I7 , 3 F4 ) energy states of Ho3 and Tm3 ions [23]. The fluorescence photons produced by Tm3 3 F4 → 3 H6 radiative transitions possess higher average energy than that produced by Ho3 5 I7 → 5 I8 radiative transitions. So the Ho3 to Tm3 ET processes followed by 3 F4 → 3 H6 radiative transitions could lead to an enhancement in the cooling efficiency. We refer the above cooling mechanism hereafter as energy transfer enhanced laser cooling (ETLC) of solids. As it will be revealed in the following sections, our cooling scheme uplifts the cooling efficiency significantly with regard to the standard ASFC. In Section 2, we present a rate equation modeling of ETLC and deduce the enhanced cooling efficiency. Section 3 provides simulation results of ETLC systems based on the spectrum data of Ho, Tm: YLF crystals. The factors that influence the cooling performance are discussed. Section 4 is the conclusion.
2. THEORY The major ET processes in Ho3 and Tm3 -codoped YLF crystal are illustrated in Fig. 1. It is important to note that, the third and the second excited electronic energy levels of Ho3 and Tm3 ion could also get involved in the transition processes through ET mechanism. The Ho3 5 I7 → 5 I8 ; Ho3 5 I7 → 5 I5 and the Tm3 3 F4 → 3 H6 ; Ho3 5 I7 → 5 I5 ET processes will © 2013 Optical Society of America
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H5
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3 4 5 6
5
I7 9
10
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1 2 3 4
10
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3 H6 Ho3 Tm3 Fig. 1. (Color online) Energy level schematic of major Tm3 -Ho3 ET processes in a LiYF4 host matrix [24]. The ET upconversion processes of (4), (5), and (8) result in population accumulation on the third excited electronic energy level of Ho3 and Tm3 ions. The transations (dashed arrows) of 5 I5 → 5 I6 , 5 I6 → 5 I7 , 3 H4 → 3 H5 and 3 H5 → 3 F4 are highly nonradiative, which may hinder the cooling output of a Ho-Tm codoped cooling system. 5
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induce population accumulation on the 5 I5 manifolds of Ho3 ions. The Tm3 3 F4 → 3 H6 ; Tm3 3 F4 → 3 H4 ET processes will induce population accumulation on the 3 H4 manifolds of Tm3 ions. Due to that the energy gaps of 5 I5 − 5 I6 , 5 I6 − 5 I7 , 3 H4 − 3 H5 and 3 H5 − 3 F4 are relatively small, the following 5 I5 → 5 I6 , 5 I6 → 5 I7 , 3 H4 → 3 H5 , and 3 H5 → 3 F4 transitions are highly exothermic [24]. Therefore, inhibiting ET upconversion processes is the essential of realizing ETLC. As outcomes of ion-ion interaction, the ET processes depend on the ion concentrations greatly. Analysis on fluorescence spectrum shows that, when the concentrations of Ho3 and Tm3 ion are restricted within relatively low-levels (for example, 0.3% Ho3 , 2% Tm3 -doped YLF crystal), the ET upconversion processes mentioned above could be averted and the Ho3 5 I7 ↔5 I8 ; Tm3 3 H6 ↔3 F4 ET processes become dominant [25]. In this case, the Ho-Tm ETLC that is shown schematically in Fig. 2 could be realized with proper laser excitation. The incident laser photons (hν) are tuned to be resonant for the transitions from the lower 5 I8 manifolds to the higher 5 I7 manifolds. The excited Ho3 ions relax thermally among the manifolds in a time scale of picoseconds with host phonon absorption, and then decay by emitting fluorescence photons at a mean frequency of ν1 . For each excitation/ de-excitation cycle, an average thermal vibration energy of hν1 − hν is removed from the host material with extraction of
ET 5
F4 , n2
3
H6 , n3
I7 , n1
h 5
3
I8 , n0
h
h
2
1
Tm3 Ho3 Fig. 2. (Color online) Schematic of Ho-Tm ETLC. Ho3 ions are pumped at frequency ν (vertical solid arrow on the left). The Ho3 excitations decay by emitting anti-Stokes fluorescence at an average frequency of ν1 (vertical dashed arrow on the left). Ground state Tm3 ions get activated through sharing energy with excited Ho3 ions (double-head arrow), and then decay by emitting anti-Stokes fluorescence at an average frequency of ν2 (vertical dashed arrow on the right). The level labels used in the rate equations are also indicated.
the fluorescence photon. This is the case of standard ASFC usually discussed. Meanwhile, part of the ground-state Tm3 ions get sensitized by absorbing the energy transferred from Ho3 excitations and the surrounding phonon energy (phonon-assisted ET) [26], and then decay by emitting fluorescence photons at a mean frequency of ν2 (ν2 > ν1 ). Since the pump laser is red-edge tuned for Ho3 ion excitation, the absorption of Tm3 ions is negligible (see the absorption spectrums in Section 3). For each excitation/de-excitation cycle of Tm3 ions, an extra thermal vibration energy of hν2 − hν1 will be released. According to the ET theory, the density population dynamic of the electronic energy levels of the above Ho-Tm cooling system can be described as the following equations: dn1 P r − W 1;r n1 − W 1;nr n1 − p13 n1 n3 p02 n0 n2 dt hν 1 − ηe;1 W 1;r n1 ;
(1)
dn2 −W 2;r n2 − W 2;nr n2 p13 n1 n3 − p02 n0 n2 dt 1 − ηe;2 W 2;r n2 ;
(2)
n0 n1 CHo N;
(3)
n2 n3 CTm N;
(4)
where ni i 0; 1; 2; 3 is the population of ith level, as it is shown in Fig. 2. P r is the resonantly absorbed power density at pump frequency ν. W i;r and W i;nr are the radiative decay rate and the nonradiative decay rate, respectively (i 1 for the Ho3 5 I7 → 5 I8 transitions and i 2 for the Tm3 3 F4 → 3 H transitions). p 13 and p02 are the temperature-dependent 6 macroscopic ET rates [23]. ηe;i is the fraction of photons escaping from the crystal [27]. CHo and CTm are the percent concentrations of Ho3 and Tm3 ions, and N is the total number density of Y3 sites that has a value of approximately 1.396 × 1022 ions∕cm3 in YLF crystal [24]. The net power density transferred to the sample is obtained by using the energy conservation law, P net −ηe;1 W 1;r n1;s hν1 − ηe;2 W 2;r n2;s hν2 P r P b ;
(5)
where ni;s is the steady-state population of ith energy level that can be calculated from Eqs. (1)–(4) by setting dn1 ∕dt dn2 ∕dt 0. The background (impurity) absorption P b is nearly independent of pumping frequency and temperature. The first term on the right-hand side of Eq. (5) represents the energy that is taken out of the host by the standard ASFC mechanism of Ho3 ions, and the second term takes into account the cooling contribution of ET processes. The cooling efficiency, which is defined as the ratio of the cooling output to the total absorption is expressed as ηc
−P net η W n ν ηe;2 W 2;r n2;s ν2 ηabs e;1 1;r 1;s 1 − 1; Pr Pb W 1 n1;s W 2 n2;s ν
(6)
where W i ηe;i W i;r W i;nr i 1; 2 is the total effective decay rate that includes both the radiative decay rate with
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consideration of florescence reabsorption and nonradiative decay rate. The absorption efficiency is defined as [27] ηabs
Pr αr ; P r P b αr αb
(7)
where αr σ abs νn0 − n1 is the resonant absorption coefficient that decreases with the increasing of the resonant absorption (σ abs ν is the pump frequency dependent absorption cross section), αb is the background absorption coefficient that can be treated as a constant. Substituting the analytical results of n1;s and n2;s into Eq. (6), a symmetrical expression is obtained: ηc ηabs
ηext;1 ν1 ηext;2 ν2 ηext;1 ν1 − ηext;2 ν2 − 1; 2ν 2νc
(8)
where ηext;i
ηe;i W i;r ; Wi
(9)
is the external quantum efficiency, and P νc r hA
with
AB−
4p13 CTm W 2 N P r P 2 1∕2 ; B− r p02 − p13 hν hν
(11)
and B
p13 CTm W 2 p02 CHo W 1 N W 1 W 2 : p02 − p13
that νc > ν. Indeed, for 0.3% Ho, 2% Tm: YLF crystal sample, calculated result on the characteristic frequency (with transition rates and macroscopic ET rates at 303 K found in [24] and [28]) shows that the value of characteristic frequency is on the order of 2ν.
3. RESULTS AND DISCUSSION In this section, we predict the cooling performance of an ETLC system based on spectrum data and material parameters including radiative decay rates, nonradiative decay rates, and macroscopic ET rates. Two material-depended parameters impact on the cooling efficiency significantly: the absorption efficiency (ηabs ) and the external quantum efficiency (ηext ). To achieve net cooling in a standard ASFC system, ηabs ηext > 0.95 is typically required. For cryogenic temperature cooling of Yb3 -doped YLF crystals, ηabs ηext > 0.99 needs to be insured [29]. It is important to mention that the host material selected for Ho-Tm ETLC should enable Ho ASFC and Tm ASFC in the first place. According to the energy gap law, the nonradiative transition rate reads W nr βe−αEp ;
10
(12)
The appearance of variable νc in the cooling efficiency formula [Eq. (8)] of ETLC is a result of ET mechanism acting on the codoped cooling system. As an important and unique parameter of ETLC, νc determines the cooling efficiency of a codoped cooling system. It can be seen from Eqs. (10)– (12) that, νc , which will be referred next as the characteristic frequency, lies on four pairs of parameters: the inputs (P r and ν), the total effective transition rates (W 1 and W 2 ) that can be treated as constants, the temperature-dependent macroscopic ET rates (p13 and p02 ), and the percent concentrations (CHo and CTm ). The merit of Eq. (8) is that, knowing the basic property of the characteristic frequency of an ETLC system, one will quickly draw a qualitative conclusion of the cooling efficiency from the expression. For instance, if the concentration of Tm3 ion equals to zero, i.e., the Ho3 to Tm3 ET processes do not exist (p13 0), the value of the characteristic frequency then equals to that of the pumping frequency (νc ν). Equation (8) can be reduced to ν ηc jνc ν ηext;1 ηabs 1 − 1: (13) ν This is exactly the cooling efficiency formula of the standard ASFC system. As a general expression of cooling efficiency for the Ho-Tm ETLC system, Eq. (8) shows that the larger the characteristic frequency of an ETLC system is, the larger the corresponding cooling efficiency could be. Previous analysis shows that the ETLC cooling scheme is more efficient than the standard ASFC scheme in principle, so the right-hand side of Eq. (8) should be larger than that of Eq. (13), indicating
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(14)
where Ep is the electronic energy gap, α and β are the characteristic constants that mainly depend on the host material [30]. For YLF crystal, α 3.8 × 10−3 cm and β 3.5 × 107 s−1 [26]. A very useful deduction of the energy gap law on solidstate laser cooling is that, candidate materials for ASFC should satisfy ℏωmax < Ep ∕8, where ℏωmax is the maximum phonon energy of the host material [13]. The energy gaps of Ho3 5 I7 − 5 I8 and Tm3 3 F4 − 3 H6 in YLF crystal correspond to wavenumbers of 4838 cm−1 and 5180 cm−1 , respectively; the maximum host phonon wavenumber is 450 cm−1 [24]. Therefore, both Ho3 and Tm3 ions could be used for ASFC in YLF crystal. By using Eq. (14), the nonradiative decay rates of Ho3 5 I7 → 5 I8 and Tm3 3 F4 → 3 H6 transition in YLF crystal are calculated as 0.36 s−1 and 0.10 s−1 , respectively. The radiative decay rates of these two transitions are 73.10 s−1 and 66.67 s−1 , respectively [24]. Suppose the cooling sample is geometrically optimized so that the fractions of photons escaping the sample approach to unit (ηe;1 ≈ ηe;2 ≈ 1), we obtain from Eq. (9) that the external quantum efficiencies of Ho3 5 I7 → 5 I8 and Tm3 3 F4 → 3 H6 transition in YLF crystal are 0.9949 and 0.9985, respectively. By using the emission spectrum data of Ho3 and Tm3 ions in YLF host matrix, the calculated average fluorescence wavelengths for 5 I7 → 5 I8 and 3 F4 → 3 H6 transitions are found to be 2014 and 1807 nm, respectively (see Fig. 3). The input laser wavelength is desired to be red-tuned as long as it permits relatively highabsorption. As it can be seen from Fig. 3(a), in the red-edge region of the Ho3 absorption spectrum, a subpeak is near 2070 nm. Therefore, it is rational to select 2070 nm as the pumping wavelength for the Ho-Tm ETLC in YLF host matrix. Figure 4(a) shows the cooling efficiencies of 0.3% Ho, 2% Tm YLF crystal sample and 0.3% Ho YLF crystal sample as functions of resonant absorption at pumping wavelength of 2070 nm. As the resonant absorption increases, the absorption efficiency [see Eq. (7)] will decrease, as a result, the cooling efficiency of Ho ASFC drops. On the contrary, the cooling efficiency of Ho-Tm ETLC first increases with the increasing of the resonant absorption, which is advantageous in
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b 2
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1600 1700 1800 1900 2000 Wavelength nm Fig. 3. (Color online) Absorption and emission cross section (π-pol.) of (a) Ho 5 I7 manifold and (b) Tm 3 F4 manifold in YLF host matrix at 303 K [24,31]. The vertical arrows indicate the pumping wavelength.
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prompting the cooling power. In essence, as more Ho3 ions are in the excited state with the increased absorption, the average distance between an excited-state Ho3 ion and a ground-state Tm3 ion shrinks. Consequently, the Ho3 to Tm3 ET is accelerated and more Tm3 ions participate in the cooling cycle. At the resonant absorption of around 0.8 × 108 W∕m3 , the 0.3% Ho, 2% Tm ETLC system possesses a maximum cooling efficiency of 5.08%. We note that the cooling efficiency for the 0.3% Ho ASFC system at the resonant absorption of 0.8 × 108 W∕m3 is only about 1.65%. The highcooling efficiency of Ho-Tm ETLC system is quite remarkable. Moreover, the maximum resonant absorption for cooling (ηc ≥ 0) of the 0.3% Ho, 2% Tm ETLC system is roughly 2 times of that of the 0.3% Ho ASFC system, indicating that the codoped cooling scheme could enhance the cooling power density largely. As it can be seen from Fig. 4(b), at resonant absorption of about 0.7 × 108 W∕m3 , the maximum cooling power density for the 0.3% Ho ASFC system is 0.8 × 106 W∕m3 . Whereas, at resonant absorption of about 1.8 × 108 W∕m3 , the maximum cooling power density for the 0.3% Ho, 2% Tm ETLC system is 8 × 106 W∕m3 , which is 10 times of that of the 0.3% Ho ASFC system. The ET-induced cooling enhancement varies with the sample temperature since the macroscopic ET rates contained in the characteristic frequency are temperature dependent. To make a clear statement, we consider the low-excitation cases, in which less than 5% of the Ho3 ions are pumped to the excited state for the sample mentioned above, B will be more than 20 times larger than P r ∕hν. The right-hand side of Eq. (11) can then be expanded as a power series of P r ∕hν. Neglecting the terms that are higher than second order, Eq. (11) can be approximately expressed as P r p02 CHo W 1 − p13 CTm W 2 ; hν p02 CHo W 1 p13 CTm W 2
(15)
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6 0.3
4
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Tm 3
2 0 0.3
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Cooling Power Density 10 6 W
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0.5 1.0 1.5 2.0 Resonant Absorption 10 8 W 3
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Fig. 4. (Color online) (a) Cooling efficiencies of Ho-Tm ETLC and Ho ASFC in YLF crystal as functions of resonant absorption at 303 K. (b) The cooling power densities of Ho-Tm ETLC and Ho ASFC in YLF crystal as functions of resonant absorption at 303 K. For the 0.3% Ho, 2% Tm: YLF crystal sample, the ET parameters are estimated as p13 6 × 10−24 cm3 · μs−1 and p02 8 × 10−23 cm3 · μs−1 [28]. The incident wavelength is 2070 nm. The background absorption is assumed to be 4.0 × 10−4 cm−1 .
where the condition p02 CHo W 1 − p13 CTm W 2 N ≫ W 1 W 2 has been used in the simplification. Substituting Eq. (15) into Eq. (8), we obtain the cooling efficiency of the ETLC system in low-excitation condition: η ν − ηext;1 ν1 ν ηC ηabs ηext;1 1 − 1 Γηabs ext;2 2 ; ν ν
(16)
where the enhancing factor that marks the ET-induced cooling enhancement is expressed as W C p −1 ΓT; CTm ∕CHo 1 1 Ho 02 : W 2 CTm p13
(17)
It can be seen clearly that the terms in brackets of Eq. (16) represent the standard ASFC of Ho3 ions, and the last term on the right-hand side accounts for the cooling enhancement induced by ET mechanism. Equation (17) shows that, a higher concentration ratio of the acceptor (Tm3 ) ion to the donor (Ho3 ) ion leads to a larger enhancement in the cooling efficiency, the result is expected since an increased Tm3 concentration promotes the interacting probability of a groundstate Tm3 (acceptor) ion with an excited-state Ho3 (donor) ion. On the other hand, to increase the concentration of Ho3 (donor) ion could promote the cooling power density of a Ho-Tm ETLC system. It means that both of the concentrations
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of Ho3 (donor) and Tm3 (acceptor) ion should be increased to obtain a high-cooling power density with a high-cooling efficiency by applying the Ho-Tm codoped cooling scheme. However, there is a problem of adopting cooling samples with high-concentrations. As it has been mentioned in Section 2, the ET upconversion processes could be prompted if the concentrations of Ho3 and Tm3 ion are increased. The transitions from the third and second excited states to the lower excited states are usually exothermic, which could turn the system into a heating one. It is important to mention that, practical concentrations of Ho3 and Tm3 ion for Ho-Tm ETLC in YLF crystal are around 0.3% and 2% or less, respectively [25]. Whereas, the concentration limits might be broken through by applying alternative host material (for example KPb2 Cl5 crystal) with smaller phonon energy compared to YLF crystal, since the multiphonon (nonradiative) transitions from the third and second excited states of Ho3 and Tm3 ion might be hindered. The ratio of p13 to p02 , which is usually referred as the temperature-dependent equilibrium constant, governs the steadystate energy assignment of a Ho-Tm cooling system. By using the approximate expression of the temperature-dependent equilibrium constant derived by Walsh et al. [28], the enhancing factor as a function of temperature is depicted in Fig. 5. It can be seen that the enhancing factor decreases with the decreasing of the temperate. Actually, as the temperature drops, more excited-state Ho3 ions will occupy the lower manifolds of the electronic energy level due to the nature of Boltzmann distribution. The enlarged average energy difference between the excited electronic energy levels of the Tm3 and Ho3 ions weakens the Ho3 to Tm3 ET processes, and consequently the enhancing factor decreases. Despite this, the ET mechanism assists the cooling processes all the way to the minimum achievable temperature [12] of the cooling system since the value of enhancing factor is always positive. So the time scale for solid-state laser cooling could be shortened by applying the codoped cooling scheme. It is worth mentioning that the codoped cooling scheme presented in this paper can also be applied to other rare-earth codoped materials other than Ho, Tm: YLF crystal, given that the selected dopants share similar electronic energy level structure so that ET processes can efficiently occur. For instance, the Tm3 (donor), Er3 (acceptor) codoped materials are favorable options for ETLC, since the first excited states (3 F4 and 4 I13∕2 ) of Tm3 and Er3 ions are close enough in 0.33
T , C Tm C Ho
0.32
C Ho
0.3
C Tm 2
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energy. To point out, the host material should enable ASFC of each dopant in the first place, and the doping concentrations should be restricted within relatively low levels so that the deleterious ET upconversion processes are averted. Another pair of dopants considered for ETLC could be Er3 and Yb3 , since the electronic energy levels of Er3 4 I11∕2 and Yb3 2 I5∕2 are also very close to each other. However, the drawback of Er-Yb ETLC is that the intermediate Er3 4 I11∕2 → 4 I13∕2 transition usually produces large amount of heat that may hinder the cooling processes. Applying low-phonon energy (which is small enough compared to the energy gap of Er3 4 I11∕2 − 4 I13∕2 , so that the nonradiative transition is negligible) host material could solve the heating issue.
4. CONCLUSION In summary, we have presented a scheme for laser cooling of solids based on the ET mechanism between two species of active ion sharing similar electronic energy level structure. It has been theoretically studied by using rate equations. We find that the ETLC has several advantages with regard to the standard ASFC, among which, the uppermost is that the ET cooling mechanism could greatly enhance the cooling efficiency. A 0.3% Ho, 2% Tm: YLF crystal sample is investigated with an incident laser wavelength of 2070 nm. The cooling efficiency of the ETLC system first increases, and then decreases with the increasing of the resonant absorption. The maximum cooling efficiency could exceed 5%. By applying the codoped cooling scheme, the maximum cooling power density could be promoted greatly. The higher the sample temperature is, the larger the ET-induced cooling enhancement will be. The cooling scheme is valid for other rare-earth codoped materials other than Ho, Tm: YLF crystal, given that the host material enables ASFC of each dopant, the interacting electronic energy levels of the two dopants are close enough in energy so that ET processes could efficiently occur, but the doping concentrations should not be too high to induce deleterious ET upconversion processes. This research may find its practical applications in manufacturing highly efficient all-solid-state cryocooler.
ACKNOWLEDGMENTS The authors acknowledge financial support of the Specialized Research Fund for the Program for New Century Excellent Talents in University (grant NCET-11-269), the National Natural Science Foundation of China (grants 11204048, 61275138, 10804022, 60878016), and the Fundamental Research Funds for the Central Universities (grants HEUCFZ1221, HEUCFZ1217).
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REFERENCES 0.30 0.29 0.28 275
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285 290 Temperature K
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Fig. 5. (Color online) Enhancing factor as a function of temperature in low-excitation condition.
1. D. V. Seletskiy, M. P. Hehlen, R. I. Epstein, and M. Sheik-Bahae, “Cryogenic optical refrigeration,” Adv. Opt. Photon. 4, 78–107 (2012). 2. P. Pringsheim, “Zwei Bemerkungen über den Unterschied von Lumineszenz- und Temperaturestrahlung,” Z. Phys. 57, 739–746 (1929). 3. L. Landau, “On the thermodynamics of photoluminescence,” J. Phys. 10, 503–506 (1946). 4. T. Kushida and J. E. Geusic, “Optical refrigeration in Nd-doped yttrium aluminum garnet,” Phys. Rev. Lett. 21, 1172–1175 (1968).
944 5. 6. 7. 8.
9. 10. 11. 12. 13. 14.
15. 16. 17. 18.
J. Opt. Soc. Am. B / Vol. 30, No. 4 / April 2013 R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser-induced fluorescent cooling of a solid,” Nature 377, 500–503 (1995). A. Mendioroz, J. Fernandez, M. Voda, M. Al-Saleh, R. Balda, and A. J. Garcia-Adeva, “Anti-Stokes laser cooling in Yb3 -doped KPb2 Cl5 crystal,” Opt. Lett. 27, 1525–1527 (2002). J. Thiede, J. Distel, S. R. Greenfield, and R. I. Epstein, “Cooling to 208 K by optical refrigeration,” Appl. Phys. Lett. 86, 154107 (2005). C. W. Hoyt, M. Sheik-Bahae, R. I. Epstein, B. C. Edwards, and J. E. Anderson, “Observation of anti-Stokes fluorescence cooling in thulium-doped glass,” Phys. Rev. Lett. 85, 3600–3603 (2000). W. Patterson, S. Bigotta, M. Sheik-Bahae, D. Parisi, M. Tonelli, and R. I. Epstein, “Anti-Stokes luminescence cooling of Tm3 doped BaY2 F8 ,” Opt. Express 16, 1704–1710 (2008). J. Fernandez, A. J. Garcia-Adeva, and R. Balda, “Anti-Stokes laser cooling in bulk erbium-doped materials,” Phys. Rev. Lett. 97, 033001 (2006). M. P. Hehlen, “Crystal-field effects in fluoride crystals for optical refrigeration,” Proc. SPIE. 7614, 761404 (2010). D. V. Seletskiy, S. D. Melgaard, R. I. Epstein, A. D. Lieto, M. Tonelli, and M. Sheik-Bahae, “Local laser cooling of Yb:YLF to 110 K,” Opt. Express 19, 18229–18236 (2011). M. P. Hehlen, “Novel materials for laser refrigeration,” Proc. SPIE. 7228, 72280E (2009). B. Heeg, M. D. Stone, A. Khizhnyak, G. Rumbles, G. Mills, and P. A. DeBarber, “Experimental demonstration of intracavity solid-state laser cooling of Yb3 :ZrF4 -BaF2 -LaF3 -AlF3 -NaF glass,” Phys. Rev. A 70, 021401 (2004). D. V. Seletskiy, M. P. Hasselbeck, and M. Sheik-Bahae, “Resonant cavity-enhanced absorption for optical refrigeration,” Appl. Phys. Lett. 96, 181106 (2010). X. L. Ruan and M. Kaviany, “Enhanced laser cooling of rare-earth-ion-doped nanocrystalline powders,” Phys. Rev. B 73, 155422 (2006). A. J. Garcia-Adeva, R. Balda, and J. Fernandez, “Upconversion cooling of Er-doped low-phonon fluorescent solids,” Phys. Rev. B 79, 033110 (2009). G. Nemova and R. Kashyap, “Laser cooling of Er3 -doped solids,” Opt. Commun. 283, 3736–3739 (2010).
Dong et al. 19. E. K. Bashkirov, “Dynamics of phonon mode in superradiance regime of laser cooling of crystals,” Phys. Lett. A 341, 345–351 (2005). 20. G. Nemova and R. Kashyap, “Alternative technique for laser cooling with superradiance,” Phys. Rev. A 83, 013404 (2011). 21. S. C. Rand, “Raman laser cooling of solids,” J. Lumin. 133, 10–14 (2013). 22. M. Tomes, F. Marquardt, G. Bahl, and T. Carmon, “Quantummechanical theory of optomechanical Brillouin cooling,” Phys. Rev. A 84, 063806 (2011). 23. B. M. Walsh, N. P. Barnes, and B. D. Bartolo, “On the distribution of energy between the Tm 3 F4 and Ho 5 I7 manifolds in Tm-sensitized Ho luminescence,” J. Lumin. 75, 89–98 (1997). 24. B. M. Walsh, N. P. Barnes, M. Petros, J. Yu, and U. N. Singh, “Spectroscopy and modeling of solid state lanthanide lasers: application to trivalent Tm3 and Ho3 in YLiF4 and LuLiF4 ,” J. Appl. Phys. 95, 3255–3271 (2004). 25. M. Faiconieri and G. Salvetti, “Effects of co-dopant concentrations and excitation conditions on the 2 μm fluorescence dynamics in Tm, Ho: YLF crystals,” Appl. Phys. A 59, 253–258 (1994). 26. R. Powell, Physics of Solid-State Laser Materials (SpringerVerlag, 1998). 27. C. W. Hoyt, M. P. Hasselbeck, and M. Sheik-Bahae, “Advances in laser cooling of thulium-doped glass,” J. Opt. Soc. Am. B 20, 1066–1074 (2003). 28. B. M. Walsh, N. P. Barnes, and B. D. Bartolo, “The temperature dependence of energy transfer between the Tm 3 F4 and Ho 5 I7 manifolds of Tm-sensitized Ho luminescence in YAG and YLF,” J. Lumin. 90, 39–48 (2000). 29. D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. D. Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics 4, 161–164 (2010). 30. J. M. F. van Dijk and M. F. H. Schuurmans, “On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f − 4f transitions in rare-earth ions,” J. Chem. Phys. 78, 5317–5323 (1983). 31. B. M. Walsh, N. P. Barnes, and B. D. Bartolo, “Branching ratios, cross sections, and radiative lifetimes of rare earth ions in solids: application to Tm3 and Ho3 ions in LiYF4 ,” J. Appl. Phys. 83, 2772–2787 (1998).
