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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␩ext␯f / ␯ − 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
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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.
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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. O’Keefe and D. A. G. Deacon, Rev. Sci. Instrum. 59, 2544 共1988兲.
J. Ye and J. L. Hall, Phys. Rev. A 61, 061802 共2000兲.
4
M. S. Ünlü, K. Kishino, J.-I. Chyi, L. Arsenault, J. Reed, S. N. Mohammad, and H. Morkoç, Appl. Phys. Lett. 57, 750 共1990兲.
5
P. Pringsheim, Z. Phys. 57, 739 共1929兲.
6
L. Landau, J. Phys. 共USSR兲 10, 503 共1946兲.
7
R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E.
Mungan, Nature 共London兲 377, 500 共1995兲.
8
M. Sheik-Bahae and R. I. Epstein, Nat. Photonics 1, 693 共2007兲.
9
R. I. Epstein and M. Sheik-Bahae, Optical Refrigeration 共Wiley, Wein1
2
3
Appl. Phys. Lett. 96, 181106 共2010兲
Seletskiy, Hasselbeck, and Sheik-Bahae
heim, 2009兲, Chap. 1, p. 1–31.
C. E. Mungan, M. I. Buchwald, B. C. Edwards, R. I. Epstein, and T. R.
Gosnell, Phys. Rev. Lett. 78, 1030 共1997兲.
11
C. W. Hoyt, M. Sheik-Bahae, R. I. Epstein, B. C. Edwards, and J. E.
Anderson, Phys. Rev. Lett. 85, 3600 共2000兲.
12
C. W. Hoyt, M. P. Hasselbeck, M. Sheik-Bahae, R. I. Epstein, S. 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
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