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APPLIED PHYSICS LETTERS 96, 181106 共2010兲 Resonant cavity-enhanced absorption for optical refrigeration D. V. Seletskiy,a兲 M. P. Hasselbeck, and M. Sheik-Bahae Department of Physics and Astronomy, University of New Mexico, USA 共Received 15 February 2010; accepted 26 March 2010; published online 6 May 2010兲 A 20-fold increase over the single path optical absorption is demonstrated with a low loss medium placed in a resonant cavity. This is applied to laser cooling of ytterbium-doped fluorozirconate glass resulting in 90% absorption of the incident pump light. A coupled-cavity scheme to achieve active optical impedance matching is analyzed. © 2010 American Institute of Physics. 关doi:10.1063/1.3397989兴 The benefits of absorption enhancement in an optical cavity were appreciated shortly after the invention of the laser.1 The effective interaction length increases as a consequence of beam trapping inside a stable resonator. Techniques such as cavity ring-down spectroscopy exploit this nonresonantly to achieve 10−10 absorbance in gaseous media.2,3 Resonantly enhanced absorption has been shown to increase the electronic bandwidth of infrared detectors and to provide spectral tuning of the response.4 In this letter, we use a resonant cavity to increase pump light absorption for optically cooling a glass sample. A 20-fold increase over singlepass absorption is observed, corresponding to 90% absorption on resonance. We describe low-power laser cooling experiments and propose a dynamically tunable three-mirror cavity, suitable for high-power cavity cooling. Laser cooling in solids occurs by anti-Stokes luminescence, i.e., conversion of coherent pump photons into higher energy luminescence photons.5,6 The extra energy of the emitted photon is supplied by phonon absorption. If excited state relaxation is mainly radiative, net cooling of the high purity medium occurs. Since the first demonstration,7 laser cooling has been shown in a variety of rare-earth ions doped into amorphous and crystalline hosts.8,9 The cooling power of an optical refrigerator is Pcool = Pabs共extf / − 1兲, where Pabs is the absorbed optical power, is the pump frequency, f is the mean luminescence frequency, and ext is the external quantum efficiency.8,10 To attain net cooling 共i.e., Pcool ⬎ 0兲, pumping must take place at frequencies smaller than the mean luminescence frequency, where absorption is inherently weak. The interaction length can be increased in a nonresonant cavity, where the sample is placed between two dielectric mirrors with pump light admitted through a small entrance hole in the input mirror.11,12 Cooling of Yb:ZBLAN 共ZrF4 – BaF2 – LaF3 – AlF3 – NaF兲 glass by 90° 共Ref. 13兲 and Yb-doped yttrium-lithium fluoride crystal by 145° 共Ref. 14兲 has been demonstrated with this scheme. In a resonant cavity enhancement 共RCE兲 arrangement, pump light couples to cavity modes interferometrically. This avoids complications associated with an entrance hole in a multipass setup, alleviating pump scatter 共mirror heating兲, and leakage from the trap. RCE also provides scalability since the cavity mode-volume can be matched to the sample size. Reducing the size allows for miniaturization and ima兲 Author to whom correspondence should be addressed. Electronic mail: [email protected]. 0003-6951/2010/96共18兲/181106/3/$30.00 proves the performance of an optical refrigerator because the dominant radiative heat load scales linearly with surface area. The RCE can also be implemented by placing the absorber inside a laser resonator.15,16 This is complicated for refrigeration since the temperature-dependent round-trip loss in the cooling medium will affect the lasing threshold. Ignoring parasitic losses, the maximum absorption of the resonant cavity occurs when the reflectivity of the input mirror 共RI兲 satisfies RI = RB exp共−2␣L兲, where RB is the back mirror reflectivity and ␣ is the absorption coefficient in the intracavity absorber of length L.4 The equation expresses optical impedance matching 共OIM兲 for a lossy cavity.17 In the Gires–Tournois limit,18 the pump absorption on resonance is given by A=1− 冉冑 R I − e −␣L 1 − e−␣L冑RI 冊 2 , 共1兲 and approaches unity at the OIM condition. For our macroscopic-size sample, i.e., 2nL / Ⰷ 1, positioning in the cavity is not critical.19 Details of the experiment are described elsewhere.20 The pump is a continuous-wave ytterbium doped yttrium aluminum garnet 共Yb:YAG兲 disk laser 共ELS Versadisk兲 at 1030 nm 共Fig. 1兲. Its longitudinal mode spectrum is monitored by a high-resolution Fabry–Perot cavity. After Faraday isolators 共⬃60 dB rejection兲 and spatial mode-matching optics, the pump beam enters an optical cavity placed inside a vacuum chamber. The intracavity absorber is 2% Yb3+-doped ZBLAN glass with geometry similar to Ref. 13. A cavity mirror is deposited on the back facet 共RB ⬎ 0.999兲; the front facet is antireflection coated 共R ⬍ 0.2%兲. Losses at both fac- FIG. 1. 共Color online兲 Schematic of the cooling setup. Pump laser tuned to the absorption tail excites anti-Stokes luminescence 共blue wavy lines兲 that leads to cooling of the sample. A combination of piezodriving 共PD兲 circuit, lock-in amplifier 共LA兲, and proportional-integral-derivative circuit 共PID兲 allows for active stabilization of the cavity length. A thermal camera 共TC兲 is used to monitor the cooling process. 96, 181106-1 © 2010 American Institute of Physics Downloaded 14 Dec 2011 to 64.106.63.195. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions 181106-2 Appl. Phys. Lett. 96, 181106 共2010兲 Seletskiy, Hasselbeck, and Sheik-Bahae FIG. 2. 共Color online兲 共a兲 Resonant 89% absorption of the cavity plotted on a semi-log scale. 共b兲 Impedance matching curves 关Eq. 共1兲兴 along with the experimentally measured RCE factor ␥ as a function of RI on a semilog scale. ets are negligible compared to the single-pass absorbance 关A1 = 1 − exp共−␣L兲 = 4.5⫾ 0.5%兴. An input mirror RI = 94% is housed in a piezoactuated mount, allowing for cavity length scan and stabilization. The RI value is chosen to attain nearly optimal OIM 关Eq. 共1兲兴 at room temperature. The sample is supported by thin quartz fibers to minimize conductive heat load from the chamber. The radiative load is reduced approximately three-fold by placing the sample inside a tightly fitted 共partial兲 shell with a low-emissivity coating.13 A reflectivity signal 共Rc兲 is used to estimate the resonant absorption of the cavity. Since transmission and losses are minimized by design, we deduce absorption A from energy conservation as follows: A = 1 − Rc. The Rc is normalized by reflection from a perfect mirror, placed before the cavity. On-resonant absorption of 89⫾ 3% is obtained during cavity length scan 关Fig. 2共a兲兴. Using the experimental values of RI and ␣L, 93% of the ideal absorption 关Eq. 共1兲兴 is achieved. The discrepancy is partially due to imperfect modematching, seen from fringe asymmetry 关Fig. 2共a兲兴. We define an RCE factor ␥ by the ratio of on-resonance absorption to A1 and measure it for varying values of RI. Good agreement with 关Eq. 共1兲兴 is obtained within the uncertainty of the ␣L value 关shaded region in Fig. 2共b兲兴. An enhancement of ⬃20 is obtained near the OIM condition. In cooling experiments, the cavity is kept on resonance by an active stabilization scheme. Collected luminescence 共Fc, Fig. 1兲 is used as an error-generating signal in the feedback loop. The cavity length is dithered by small-amplitude voltage Vd. By mixing Fc and Vd signals in a lock-in filter the leading and trailing edges of a cavity fringe are differentiated. This allows generation of a feedback signal via a proportional-integral-derivative 共PID兲 circuit. The black-body radiation of the sample is imaged by a microbolometer thermal camera to provide a noncontact temperature measurement. Averaged pixel counts from a time series of images 关Fig. 3共a兲兴 yield temperature, as per separate calibration. A low-power experiment is performed by irradiating the sample with 1 W of pump at t = 0 min and blocking at t = 40 min to avoid saturation of the thermal camera image 关Fig. 3共b兲兴. Fitting the data to ⌬T共t兲 = ⌬T f 关1 − exp共−t / 兲兴 yields a final temperature difference of ⌬T f = −3.2⫾ 0.1 K with respect to ambient with a thermal time constant = 45 min. For small input power, this result can be linearly scaled to account for imperfect efficiencies in absorption 共90%兲, stabilization 共60%兲, and radiation shielding 共30%兲. A temperature drop of 3.2⫻ 关0.9⫻ 0.6⫻ 0.3兴−1 = 20 K / W is FIG. 3. 共Color online兲 共a兲 Top view thermal image of cavity on resonance: sample 共dark rectangle兲 cools with respect to the ambient 共gray兲, while thermal radiation shell heats 共light gray structure around the sample兲 due to fluorescence absorption. 共b兲 Measured temperature evolution of RCE laser cooling with corresponding exponential fit. projected, on par with the best cooling performance of ⬃22 K / W in Yb:ZBLAN glass.13 Sample-to-sample impurity variations can account for the remaining discrepancy.21 Our experiment is limited to small input powers due to optical-feedback-induced longitudinal mode instability of the pump laser. A monitoring cavity shows pronounced multimode operation of the pump laser at input levels ⬎1 W. For high power cooling, dynamic OIM becomes an important consideration, since resonant absorption A can be maximum only at a particular value of the temperaturedependent absorption coefficient 关Eq. 共1兲兴. One solution is to under-couple the cavity at the starting room temperature to satisfy the OIM condition at the steady-state temperature. A more general solution is to implement a continuously tunable reflectivity, which was recently shown in a fiber-based cavity.22 Here, we propose a free-space optics solution in the form of a coupled cavity geometry to allow for dynamic OIM. Consider a three-mirror cavity, with two mirrors of equal reflectivity R1, followed by an absorbing sample and a third mirror R2. The half-round trip phases of the first and second 共absorbing兲 subcavities are 1,2. Within the adiabatic approximation,23 the OIM condition can be generalized to the following: R11共1兲 = F sin2共1兲 = R2e−2␣L , 1 + F sin2共1兲 共2兲 where F = 4R1 / 共1 − R1兲2. Coupling between the two cavities causes Eq. 共2兲 to be satisfied only for a particular value of 2. Resonant reflectivity of the first cavity 共R11兲 acts as a tunable input coupler to maximize the absorption. The maximum reflectivity given by Eq. 共2兲 sets the minimum absorbance that allows for impedance matching as follows: 冉冑 冊 共␣L兲min = ln 1 + R1 2 R1 共3兲 for R2 = 1. We are interested in relatively small values of ␣L, so the minimum reflectivity R1 that satisfies the OIM condition is R1 ⬇ 1 − 冑8␣L. This means that a range of intracavity loss values ␣L no less than 0.125共1 − R1兲2 can be actively impedance matched. As an example, having ␣L ⬃ 10−9 requires a reflectivity of R1 ⱖ 0.9999. When the resonant absorption is extremely small, however, losses at the cavity mirrors can no longer be ignored in the analysis. The proposed technique of dynamic OIM is general, with possible applications outside of laser cooling in solids. Backgroundfree, narrow-band, and ultrasensitive photoacoustic spectroscopy is envisioned, where a signal can be monitored as a function of subcavity phases. Downloaded 14 Dec 2011 to 64.106.63.195. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions 181106-3 In summary, we used a resonant cavity to obtain nearly 90% absorption in a laser cooling sample, corresponding to 20-fold enhancement over single-pass absorbance. A ⬃3° temperature drop was obtained with low-power pumping. This result is comparable with the performance of state-ofthe-art glass-host coolers. We propose a coupled cavity scheme to achieve active optical impedance-matching in high-power laser cooling experiments. We acknowledge helpful dialog with Dr. Richard I. Epstein. This work was supported by an AFOSR MultiUniversity Research Initiative Grant No. FA9550-04-1-0356 entitled Consortium for Laser Cooling in Solids. A. Kastler, Appl. Opt. 1, 17 共1962兲. A. 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Greenfield, J. Thiede, J. Distel, and J. Valencia, J. Opt. Soc. Am. B 20, 1066 共2003兲. 13 J. Thiede, J. Distel, S. R. Greenfield, and R. I. Epstein, Appl. Phys. Lett. 86, 154107 共2005兲. 14 D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. D. Lieto, M. Tonelli, and M. Sheik-Bahae, Nat. Photonics 4, 161 共2010兲. 15 B. Heeg, G. Rumbles, A. Khizhnyak, and P. A. DeBarber, J. Appl. Phys. 91, 3356 共2002兲. 16 B. Heeg, M. D. Stone, A. Khizhnyak, G. Rumbles, G. Mills, and P. A. DeBarber, Phys. Rev. A 70, 021401 共2004兲. 17 A. E. Siegman, Lasers 共University Science, Mill Valley, California, 1986兲, p. 423. 18 The back mirror reflectivity RB is approximated as unity. 19 J. A. Jervase and Y. Zebda, IEEE J. Quantum Electron. 34, 1129 共1998兲. 20 D. V. Seletskiy, M. P. Hasselbeck, M. Sheik-Bahae, R. I. Epstein, S. Bigotta, and M. Tonelli, Proc. SPIE 6907, 69070B 共2008兲. 21 M. P. Hehlen, R. I. Epstein, and H. Inoue, Phys. Rev. B 75, 144302 共2007兲. 22 J. H. Chow, I. C. Littler, D. S. Rabeling, D. E. McClelland, and M. B. Gray, Opt. Express 16, 7726 共2008兲. 23 R. J. Lang and A. Yariv, Phys. Rev. A 34, 2038 共1986兲. 10 Downloaded 14 Dec 2011 to 64.106.63.195. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions