Open Access
Add to BibSonomyAbstract
We report for the first time the experimental demonstration of optical cooling of a bulk crystal at atmospheric pressure. The use of a fiber Bragg grating (FBG) sensor to measure laser-induced cooling in real time is also demonstrated for the first time. A temperature drop of 8.8 K from the chamber temperature was observed in a Yb:YAG crystal in air when pumped with 4.2 W at 1029 nm. A background absorption of 2.9 × 10−4 cm−1 was estimated with a pump wavelength at 1550 nm. Simulations predict further cooling if the pump power is optimized for the sample’s dimensions.
© 2013 Optical Society of America
1. Introduction
Laser-induced cooling of solids (LICOS) is the refrigeration of solid state matter by anti-Stokes fluorescence (ASF), when the solid is pumped with a wavelength of lower energy than the mean fluorescence wavelength. Cooling through ASF was predicted in 1929 by Pringsheim [1], but the first observation of LICOS was achieved only in 1995 by Epstein et al. [2]. Since, bulk cooling has been demonstrated down to 119 K [3], lasers with near-zero heat generation have also been proposed [4–6], and demonstrated [7, 8], cooling of semiconductor nanobelts has been demonstrated [9], and new materials for LICOS, such as quantum dots [10], nanoparticles [11], have been suggested.
The potential applications of laser cooling in solids are in conventional refrigeration, self-cooled lasers, electronics, an additional mechanism of heat removal in LED lighting, in which the longevity of the LED is critically dependent on the operating temperature, as well as for sensors in space applications. The cooling of a 5 μg load was demonstrated in high vacuum down to 165 K [12], and cooling of Yb:YAG was demonstrated by 8.9 K also in vacuum [13]. Despite laser cooling in vacuum being easily applicable for space applications, for earth-based devices its use can be a major constraint in the cost and design of instruments. In the present work we evaluate and demonstrate LICOS under atmospheric pressure, with a temperature drop close to that observed in vacuum.
The measurement of the temperature in LICOS experiments can be difficult due to the transparency of some materials at the detected wavelength [14], and competing optical effects induced by the pump, which can affect the thermal emissivity [15] and the refractive index [16], thus affecting the transduced signal from different optical techniques [17]. In addition free-space optical methods may require complex optical alignment, or pump modulation [18]. A direct and reliable thermometric method relies on a contact sensor [14]. In the present work we report the use of a fibre Bragg grating (FBG), transparent and of low mass, to directly measure the temperature of the sample as it cools. While this technique was originally proposed for laser cooling by our group [19], this is the first time it has been applied to quantitatively measure LICOS.
Most of the literature on LICOS concentrates on the materials properties, pump wavelength and environmental conditions, but a few have taken into account the effects of saturation [20–22], which can play a significant role in choosing the optimal geometry of an optical cooler. Here, simulations are presented, which consider such effects and show how the sample’s dimension and pump power scale to obtain the maximum temperature drop of the sample.
2. Theory
We describe Yb:YAG as a two-level system with absorption, spontaneous and stimulated-emission processes between the ground, 2F7/2, and the excited 2F5/2 manifolds. The optical power which leaves the sample as fluorescence, minus the absorbed laser power, which corresponds to the cooling power is given by [23],
where Ppump, αr, Ls, ηe, αb and λp are respectively, the pump power, resonant absorption coefficient, sample’s length, external quantum efficiency (EQE), background absorption coefficient and the pump wavelength. λf = ∫λIf(λ)dλ/∫If(λ)dλ is the external mean fluorescence wavelength, where If(λ) is the spectral power density of the measured fluorescence [24]. The term in the square brackets is the fraction of the pump power which is absorbed by the sample. The first two terms of the product in parentheses is the fraction of absorbed photons, which will generate an escaped fluorescence photon, multiplied by the ratio of the mean energy of the fluorescence photons and the energy of the pump photons. The absorption of the pump photons can be modeled using the rate equations for a two-level system in the steady-state condition, when ∂N1/∂t = ∂N2/∂t = 0, where N1 and N2 are the populations of the ground and excited manifolds, respectively, N1 + N2 = NT is the concentration of active ions, and t is the time. Thus the resonant absorption coefficient is given bywhere Is = hcγeff/(λpσa), and Aeff, h, c, γeff, σe and σa are the pump effective mode area, Planck’s constant, speed of light in vacuum, effective decay rate of the excited manifold, emission cross section and absorption cross section, respectively. Equation (2) is entirely equivalent to Eq. (4) in [21]. However, in order to point out and distinguish the effects of saturable absorption clearly, we use Eq. (2).If the sample of thermal emissivity ε and surface area Asurf enclosed by a black-body, is allowed to exchange heat with its environment, the heat load dependence on the temperature difference between the sample Ts and the environment Tr is [25],
where σB, hcv, k, L and Act are the Stefan-Boltzmann constant, convective heat transfer coefficient, solid’s link thermal conductivity, length and cross-sectional area, respectively. The first term on the right side of Eq. (3) is the load of thermal radiation exchange with the enclosure. The second term is the load from contact of the sample with the air (1st part) and with the sample holder (2nd part), which depends on a series of material parameters and also on the topology. In both convective and conductive heat transfers, the load is proportional to the module of the temperature difference ΔT = Ts - Tr, so it increases linearly as the sample cools down. Radiative heat load also increases with ΔT, but as the sample cools down the rate of heat load increment decreases, and the heat load approaches its asymptotic value at Ts = 0 K. Equating cooling power, Pcool, and heat load power, Pload, one can calculate the temperature of the sample, Ts.3. Spectroscopy and thermometry
A commercially available ultra-high purity, 3 at.% Yb3+:YAG crystal of square cross section of edge d = 1 mm, 10 mm long, Brewster-cut, purchased from Scientific Materials Corp. was used for the experiments. The absorption spectrum was measured using a Perkin-Elmer Lambda 19 spectrophotometer in the range 400 nm - 2500 nm [Fig. 1(a)]. The fluorescence spectrum [Fig. 1(b)] was measured using a Ando AQ6317B optical spectrum analyser, with the sample pumped at 940 nm.
Fig. 1 Absorption (a) and emission (b) spectra of the Yb:YAG crystal. The inset in (a) is a zoomed-in detail of the most important wavelength region 850 nm to 1060 nm. (b) shows the normalized fluorescence spectral density, and the vertical dashed line shows the calculated mean fluorescence wavelength.
From the fluorescence spectrum a mean fluorescence wavelength λF = 1010(1) nm was calculated. This result is in line with the theoretical prediction [26], and previous works [27–29], considering that they should be at slightly shorter wavelengths due to absence of reabsorption. However another work [13], using a crystal from the same company, has measured λF = 995 nm. In order to explain the later discrepancy, the sideways fluorescence spectra were also measured at different depths of the crystal and had it corrected for reabsorption. The analysis show that the reabsorption should account for a maximum red-shift of 2 nm in our 1 mm thick sample, but does not explain why the ours and others’ results [27–29], differ from [13].
To measure the temperature during pumping, a 1 mm long, 125 μm diameter silica FBG made in our lab was placed in contact on the top surface of the crystal. The FBG used was fabricated using a 213 nm laser [30], using the Talbot interferometer technique [31]. As the temperature of the sensor changes, it undergoes a refractive index change which induces a shift, ΔλB = λBξΔT in its Bragg wavelength, λB. ξ is the FBG thermo-optic coefficient [31]. ΔλB is calculated from the reflected and transmitted power of a narrow linewidth laser connected to the FBG through an optical circulator [Fig. 2 and Fig. 3].
Fig. 2 Experimental setup for laser heating and cooling measurements. The pump source used is a Ti:Sapphire laser or alternatively a Yb:KGW laser for higher power. The pump power is controlled by rotating a half-wave plate (HWP) before it is p-polarized in a Glan-Thompson prism (GTLp) and spatially filtered with a pin-hole (PH). A servo-motor controller (SRV) drives the TC and shutter position, and an electronic cold junction compensator (CJ) is used as a reference for the TC.
Fig. 3 Measured reflection/transmission power spectra from the FBG before the cooling experiment, in red. In blue: representation of the shifted spectra after a temperature drop, and the corresponding power change measured by the power meters when the fiber is interrogated at a single wavelength λI (in green).
There are numerous methods to interrogate the Bragg reflection wavelength of an FBG. For calibration, a broadband source is connected to an optical circulator, with the second port connected to the FBG. The reflection is directed to the circulator’s third port and measured by an Ando AQ6317B optical spectrum analyser, controlled by a personal computer (PC). For measurements of ΔλB during cooling, the Bragg wavelength within the FBG’s bandwidth is measured. The circulator’s input port is connected to a narrow linewidth laser source at wavelength λI and the reflected, PR and transmitted, PT powers, respectively, are measured by optical power meters, interrogated by a PC. A MATLAB code in the PC controls the instruments and determines the corresponding ΔλB from the calibration curves PR (λ), PT(λ), the chosen value λI and the measured PR and PT.
Both temperature sensors were calibrated in an environmental chamber, a TestEquity Half CubeTM 105, while the temperature was independently recorded using a platinum resistance thermometer, interrogated in a 4-wire scheme using a workbench multimeter, Agilent 34401A controlled by the PC through a GPIB interface.
The Bragg wavelength shift is 9.9 pm/K. With a Bragg reflection bandwidth of 616 pm, the total measurement range is 62 K. This can be increased if the probe laser is tuned continuously as the Bragg wavelength shifts, or by the use of a broadband source, as used in the calibration procedure. The lowest temperature which can be easily measured by a bare FBG seems to be 75 K [32], however to our knowledge there is no limiting factor beyond this value. A microthermocouple (TC) is used as reference and to measure the chamber temperature. Both temperature sensors were calibrated in a controlled environment with the temperature monitored by a platinum resistor thermometer. Their readings are also compared in situ, with the TC touching the sample when the pump is switched off, showing agreement of the measured temperature. The TC cannot measure cooling, due to the absorption of the fluorescence. If it were transparent, a fragile 10 mm long, 50 μm diameter TC would constitute the same heat load as the FBG.
4. Cooling experiments
4.1 System characterization
The sample is supported by four 1 cm long, 125 μm diameter silica fibers, which are held by eight steel posts of 1 mm diameter, attached to a small aluminum plate. In air, these fibers and the FBG act as fins, contributing to an estimated best case heat load of 22.8 μW/K or a worst case of 68.4 μW/K. The holder was placed inside an aluminum chamber whose inner walls are painted with matt black paint and the temperature difference ΔT between the crystal and the chamber is calculated from the chamber temperature measured with the TC and the sample temperature measured with the FBG. The sample was pumped remotely [Fig. 2], at different power levels [Fig. 4(a)] at the optimal pump wavelength of 1030 nm [13], using the Ti:Sapphire laser. The laser has been previously tuned around this wavelength and this optimal value is confirmed for the present measurement. In the left of Fig. 4(a) the FBG measurement shows a transient at the relatively low pump power of 17 mW, with a resolution of ~10 mK, which corresponds to a Bragg wavelength measurement of 0.1 pm. The principal limitation comes from the probe wavelength stability, nominally 5 pm/h. The power stability is not a concern since both the reflection and the transmission of the FBG are measured together.
Fig. 4 Cooling dynamics of the sample under CW . (a) Temperature dynamics as a function of time, as the laser power is switched on and off. (b) Fitted exponential curve (red) to a section of the item (a), when the laser switches on. The curves correspond to the axes of same color.
From Fig. 4(b), the thermal coupling time constant was calculated to be τt = 29.4(1) s. An overall heat transfer coefficient heff which accounts for the sample’s emissivity ε and heat transfer coefficient hcv can be approximated as heff = hcv + 4σB εTr3, compromising the heat load accuracy by less than 1%. Since the radiative load is not linear [Eq. (3)], the error on the load power can be up to 10% for a temperature drop of 100 K and should be taken into account at much lower temperatures. The thermal parameters of the Yb:YAG crystal are summarized in Table 1. A lumped-capacitance model for the sample’s thermal behavior, estimates heff = Ch/(τtAsurf) = 22 W.m−2.K−1, where Ch is the sample’s heat capacity. That means that the crystal specific heat load Asurfheff = 924 μW/K, i.e. the fiber supports have a potential maximum contribution of 7.4% of the sample’s load.
Table 1. Thermal parameters of the Yb:YAG crystal used in the experiment
Owing to the FBG sensitivity, the sample’s background absorption was measured directly through heat generation. Since the wavelength 1550 nm is far from the resonant absorption band of Yb3+:YAG, and it is inside a small transparency window of Er3+:YAG – which could be a contaminant in the crystal, this wavelength was chosen to pump the sample for the measurement of background absorption. The same setup as shown in Fig. 2 was used for this measurement, but with a YPG ELR-70-1550-LP 1550 nm ytterbium-erbium fiber laser as the source of optical power. When using an input power of 2170 mW an equilibrium temperature difference of 688 mK in the sample was observed. From Eq. (1) and Eq. (3), and the thermal parameters shown in Table 1, a background absorption coefficient of αb = 2.89 × 10−4 cm−1 is calculated. For instance Epstein [13], reported a αb = 2.2 × 10−4 cm−1 in a 2.3% Yb:YAG crystal. Our results of αb in a crystal sample of higher concentration of Yb from the same supplier, indicate that the impurity related background absorption scales with the concentration of Yb2O3.
4.2 Optimal cooling
In order to observe the maximum temperature drop under the high thermal load from the environment, the crystal was pumped with 4.2 W from a commercial Yb:KGW laser. The laser emits 10 ps pulses at 1029 nm at a repetition rate of 600 kHz, which can be regarded as effectively continuous wave for the possible phenomena in our system. The Gaussian beam diameter at the sample is 2w0 ~0.67 mm. We do not believe there was any upconversion processes at play, owing to the absence of any visible blue-green emission using either laser. In the single pass configuration the chamber heated by 1.68 K [Fig. 5(a)] from which a temperature drop of 8.8 K of the crystal is achieved [Fig. 5(b)], for 1.0(1) W of absorbed power. A double pass arrangement could not be implemented with our high power laser as it broke down. However, we did note the increase in the cooling power with a double pass arrangement using the lower power Ti:Sapphire laser.
Fig. 5 Temperature dynamics as the laser pump power is increased from 0 W up to 4.2 W. (a) The chamber temperature variation, measured by the thermocouple. (b) The difference between the temperature of the Yb:YAG crystal measured by the FBG and the chamber temperature.
From Eq. (3), one can calculate an 8.8 K drop corresponding to a heat load of 8.0 mW. Since this is the equilibrium temperature, the heat load is equal to the cooling power. Using this heat load in Eq. (1), with σe (1029 nm) = 2.0 × 10−20 cm2 [34], the external quantum efficiency can be calculated: ηe = 0.9914.
From Eq. (1) and Eq. (2) it can be noticed that the cooling power is not limited by the environment, but due to the choice of material and pump characteristics. However the temperature drop will depend on the material and environment thermal and geometrical characteristics [Eq. (3)], which also will influence the cooling power [Eq. (2)].
Although in a less controlled environment, and with a higher background absorption, the temperature drop of our sample was only 0.1 K less than the result obtained in vacuum [13]. In that work a sample of 1 cm2 cross section was used, and the crystal’s dimension was relevant; the smaller the crystal, the smaller is the heat load from the environment. However, as pointed out by [21, 22], saturation effects can occur so there is an optimal pump power, which depends on the sample’s geometry, in addition to its specific physical properties. If one allows 1% loss of the pump power due to truncation, the pump beam radius should be w0 = 0.67d/2. At the same time the active area of the sample should be overfilled in order to reduce saturation. Thus in the discussion below it is implicit that the sample diameter is always coupled to the beam radius as d = 2w0/0.67. The Eq. (1) and Eq. (2) set a limit on how large a sample can be made in order to achieve a maximum temperature drop, as a function of the pump power. Below this limit absorption saturation dominates and the cooling efficiency drops as the pump power is increased, or as the sample cross-sectional area decreases.
Below we solve Pcool(Ts,Ppump) = Pload(Ts) for Ts, for a range of values of ηe as a function of the length of the sample edge d, for a 4.2 W pump power [Fig. 6(a)], and for a fixed ηe = 0.9914, for a range of pump powers [Fig. 6(b)]. It was used the experimental values of σa(1029 nm, 300 K) = 6.8 × 10−22 cm2 and λf (1029 nm, 300 K) = 1010 nm from this work, σe(1029 nm, 300 K) = 2.0 × 10−20 cm2 from [34], while the temperature dependence was estimated from the data in [13], as σa(T) = σa(300 K)[1 + 0.005ΔT K−1]. σe(λp, T) = kσeRC(λp, T), where σeRC(λp, T) = σa(λp, T)Zuexp[hc(1/λZL – 1/λp)/(kT)] is the McCumber formula [35], and k = σe(300 K)/σeRC(300 K) is a correction due to the use of the the McCumber relation with λp relatively far from λZL = 964.7 nm, and Zu = 1.13 [36].
Fig. 6 Calculated steady-state temperature of Yb:YAG in air as a function of the sample edge dimension d. (a) For different EQEs, when pumped with 4.2 W at 1029 nm. (b) For a EQE = 0.9914, for different pump powers. In black: the optimal d for the corresponding pump power.
Figure 6 allows the determination of the optimal d = 0.43 mm, at which we should observe the minimum ΔT = −12.1 K for the available pump power of 4.2W. As for our sample, it can be seen that the power for which d is optimal should be 20.8 W, at which ΔT = −21.3 K. If the power is further increased, one can see in Fig. 6(b) that the temperature can drop even more, e.g. ΔT(d = 1.0mm, 30W) = −23.8 K, however the pump power and d are not matched: ΔT(d = 1.2mm, 30W) = −24.3 K. For d smaller than the optimal value, the cooling efficiency decreases dramatically.
The sample parameters obtained with the use of an FBG are very close to the values reported in the literature. Despite our sample being pumped in a single pass scheme, and thermally coupled radiatively to the chamber walls, a temperature difference of 8.8 K was attained for a 1.0 W of absorbed power in air, compared to the 8.9 K drop for a 1.8 W of absorbed power observed by [13], in vacuum. The difference arises from the fact that our sample is closer to having the optimum dimensions: although we do not have the sample dimensions of the previous reports [13], the theoretical model can be made to fit our experimental results using experimentally derived parameters, showing that our experimental results are in keeping with the simulations.
The influence of the sample geometry on its potential thermal load highlights the importance of reducing the sample cross-section to achieve low temperatures. Obviously the coupled pump beam radius has an upper limit determined by the sample’s cross section. Therefore the amount of the absorbed pump power which will cool the sample is also limited. These considerations allow the remarkable drop in the temperature in air rather similar to what has been previously achieved in vacuum [13], although it is important to notice that the simulations show that further optimization can lead to even lower temperatures.
Despite the relatively small temperature drop achieved in our measurements, we have shown the possibility of remote cooling with light delivered by optical fibers, as well as the possibility of using an in situ sensor to sense the temperature without significantly affecting the outcome. We believe our demonstration the first to show this possibility of remote pumping, although we are aware of recent work [37], on research related to a fiber based solution. Our own previous work [38–40], has proposed and focused on this means of light delivery and cooling. With larger pump power, multi-pass arrangements, or with better optimised geometries, the FBG load will become still more insignificant, but remain useable over a wide wavelength range.
5. Conclusion
Bulk optical cooling in air at atmospheric pressure is reported. A commercially available 3%-doped Yb:YAG crystal was maintained at −8.8 K from the chamber temperature, despite unrestricted radiative and convective loads being present. The results are in good agreement with theoretical prediction and in line with previous reports.
Using a contact technique, the temperature drop of the samples was monitored in situ during pumping using a fiber Bragg grating, which is transparent to the ASF and pump radiation. This overcomes most of the difficulties in laser cooling measurements, which traditionally rely on cumbersome calibration methods or optical alignment. Also the dynamic range of the technique can be easily switched by changing the interrogation system while keeping the sensor in the sample. The technique can be readily implemented with commercially available equipment, and is the first system, which can be used as an active temperature measurement scheme in real-life laser cooling devices and experiments.
This works demonstrates the use of the laser material, Yb:YAG, being optically cooled in real-world conditions, and monitored by a simple FBG measurement technique. Our work shows the applicability of laser cooling technology in practical commercial devices, which are subject to a non-ideal environment, and presents a theoretical model and simulations which can be used as a starting point for the design of such devices.
Acknowledgments
We thank Mathieu Gagné for the fabrication of the FBGs used for the temperature sensor. RK acknowledges support from the Natural Sciences and Engineering and Research Council (NSERC) of Canada’s Strategic grants program, NSERC’s Discovery Grants program, Canada Council for the Arts’ Killam Research Fellowships program, and the Government of Canada’s Canada Research Chairs program.
References and links
1. P. Pringsheim, “Zwei bemerkungen über den unterschied von lumineszenz- und temperaturstrahlung,” Z. Phys. A-Hadron. Nucl. 57, 739–746 (1929).
2. 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(6549), 500–503 (1995). [CrossRef]
3. S. D. Melgaard, D. V. Seletskiy, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Optical refrigeration to 119 K, below National Institute of Standards and Technology cryogenic temperature,” Opt. Lett. 38(9), 1588–1590 (2013). [CrossRef] [PubMed]
4. S. R. Bowman, “Lasers without internal heat generation,” IEEE J. Quantum Electron. 35(1), 115–122 (1999). [CrossRef]
5. G. Nemova and R. Kashyap, “Athermal continuous-wave fiber amplifier,” Opt. Commun. 282(13), 2571–2575 (2009). [CrossRef]
6. G. Nemova and R. Kashyap, “Radiation-balanced amplifier with two pumps and a single system of ions,” J. Opt. Soc. Am. B 28(9), 2191–2194 (2011). [CrossRef]
7. S. R. Bowman, N. W. Jenkins, B. Feldman, and S. O'Connor, “Demonstration of a radiatively cooled laser,” in Summaries of PapersPresented at theConf. Lasers Electro-Opt., 2002)
8. S. R. Bowman, S. P. O'Connor, S. Biswal, N. J. Condon, and A. Rosenberg, “Minimizing heat generation in solid-state lasers,” IEEE J. Quantum Electron. 46(7), 1076–1085 (2010). [CrossRef]
9. J. Zhang, D. Li, R. Chen, and Q. Xiong, “Laser cooling of a semiconductor by 40 kelvin,” Nature 493(7433), 504–508 (2013). [CrossRef] [PubMed]
10. G. Nemova and R. Kashyap, “Laser cooling with lead-salt colloidal quantum dots doped in a glass host,” Proc. SPIE 8275, 82750B2-8275B8 (2012).
11. G. Nemova, E. Soares de Lima Filho, S. Loranger, and R. Kashyap, “Laser cooling with nanoparticles,” Proc. SPIE 8412,84121P1–84121P14 (2012).
12. D. V. Seletskiy, S. D. Melgaard, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of a semiconductor load to 165 K,” Opt. Express 18(17), 18061–18066 (2010). [CrossRef] [PubMed]
13. R. I. Epstein, J. J. Brown, B. C. Edwards, and A. Gibbs, “Measurements of optical refrigeration in ytterbium-doped crystals,” J. Appl. Phys. 90(9), 4815–4819 (2001). [CrossRef]
14. N. J. Condon, S. R. Bowman, S. P. O’Connor, R. S. Quimby, and C. E. Mungan, “Optical cooling in Er3+:KPb2Cl5.,” Opt. Express 17(7), 5466–5472 (2009). [CrossRef] [PubMed]
15. V. K. Malyutenko, V. V. Bogatyrenko, and O. Y. Malyutenko, “Radiative cooling by light down conversion of InGaN light emitting diode bonded to a Si wafer,” Appl. Phys. Lett. 102(24), 241102 (2013). [CrossRef]
16. J. R. Silva, L. C. Malacarne, M. L. Baesso, S. M. Lima, L. H. C. Andrade, C. Jacinto, M. P. Hehlen, and N. G. C. Astrath, “Modeling the population lens effect in thermal lens spectrometry,” Opt. Lett. 38(4), 422–424 (2013). [CrossRef] [PubMed]
17. D. V. Seletskiy, S. D. Melgaard, R. I. Epstein, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Precise determination of minimum achievable temperature for solid-state optical refrigeration,” J. Lumin. 133, 5–9 (2013). [CrossRef]
18. D. Seletskiy, “Fast differential luminescence thermometry,” Proc. SPIE 7228, 72280K1-72280K5 (2009).
19. E. de Lima Filho, M. Gagné, G. Nemova, M. Saad, S. R. Bowman, and R. Kashyap, “Sensing of laser cooling with optical fibres,” in 7th International Workshop on Fibre Optics and Passive Components, (2011), pp. 1–5. [CrossRef]
20. X. Luo, M. D. Eisaman, and T. R. Gosnell, “Laser cooling of a solid by 21K starting from room temperature,” Opt. Lett. 23(8), 639–641 (1998). [CrossRef] [PubMed]
21. G. Nemova and R. Kashyap, “Optimization of the dimensions of an Yb3+:ZBLANP optical fiber sample for laser cooling of solids,” Opt. Lett. 33(19), 2218–2220 (2008). [CrossRef] [PubMed]
22. T. R. Gosnell, “Laser cooling of a solid by 65K starting from room temperature,” Opt. Lett. 24(15), 1041–1043 (1999). [CrossRef] [PubMed]
23. M. Sheik-Bahae and R. I. Epstein, “Optical refrigeration,” Nat. Photonics 12(12), 693–699 (2007). [CrossRef]
24. R. Kashyap and G. Nemova, “Laser induced cooling of solids,” Phys. Status Solidi C 8(1), 144–150 (2011). [CrossRef]
25. R. Siegel and J. R. Howell, Thermal Radiation Heat Tranfer, Series in Thermal and Fluids Engineering (Hemisphere Publishing Corporation / McGraw-Hill Book Company, 1981).
26. D. C. Brown and V. A. Vitali, “Yb:YAG kinetics model including saturation and power conservation,” IEEE J. Quantum Electron. 47(1), 3–12 (2011). [CrossRef]
27. S. Chénais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30(4), 89–153 (2006). [CrossRef]
28. S. R. Bowman and C. E. Mungan, “New materials for optical cooling,” Appl. Phys. B 71(6), 807–811 (2000). [CrossRef]
29. T. Y. Fan, “Heat generation in Nd:YAG and Yb:YAG,” IEEE J. Quantum Electron. 29(6), 1457–1459 (1993). [CrossRef]
30. M. Gagné and R. Kashyap, “New nanosecond Q-switched Nd:VO4 laser fifth harmonic for fast hydrogen-free fiber Bragg gratings fabrication,” Opt. Commun. 283(24), 5028–5032 (2010). [CrossRef]
31. R. Kashyap, Fiber Bragg Gratings (Academic Press, 2009).
32. D. Sengupta, M. S. Shankar, P. Kishore, P. S. Reddy, R. Prasad, P. V. Rao, and K. Srimannarayana, “An FBG sensor for strain and temperature discrimination at cryogenic regime,” in Asia Communications and Photonics Conference and Exhibition, (Optical Society of America, 2011), paper 831106. http://www.opticsinfobase.org/abstract.cfm?URI=ACP-2011-831106 [CrossRef]
33. P. Shi, B. Bai, L. Zhang, L. Li, and Y. Xin, “Semianalytical thermal analysis of the heat capacity of YAG laser rods,” Appl. Opt. 48(35), 6701–6707 (2009). [CrossRef] [PubMed]
34. L. D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications,” IEEE J. Quantum Electron. 29(4), 1179–1191 (1993). [CrossRef]
35. D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136(4A), A954–A957 (1964). [CrossRef]
36. F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG,” IEEE J. Quantum Electron. 37(1), 135–144 (2001). [CrossRef]
37. D. T. Nguyen, R. Thapa, D. Rhonehouse, J. Zong, A. Miller, G. Hardesty, N. H. Kwong, R. Binder, and A. Chavez-Pirson, “Towards all-fiber optical coolers using Tm-doped glass fibers,” Proc. SPIE 8638, 86380G1–86380G9. [CrossRef]
38. G. Nemova and R. Kashyap, “High efficiency solid state laser cooling in Yb3+:ZBLANP fiber with tilted fiber Bragg grating structures,” Phys. Status Solidi C 6(S1), S248–S250 (2009). [CrossRef]
39. G. Nemova and R. Kashyap, “Fiber amplifier with integrated optical cooler,” J. Opt. Soc. Am. B 26(12), 2237–2241 (2009). [CrossRef]
40. G. Nemova and R. Kashyap, “Raman fiber amplifier with integrated cooler,” J. Lightwave Technol. 27(24), 5597–5601 (2009). [CrossRef]
