U.S. patent application number 13/469635 was filed with the patent office on 2012-12-13 for methods for laser cooling of fluorescent materials.
This patent application is currently assigned to CORPORATION DE L'ECOLE POLYTECHNIQUE DE MONTREAL. Invention is credited to Raman KASHYAP, Galina NEMOVA.
Application Number | 20120312028 13/469635 |
Document ID | / |
Family ID | 47291974 |
Filed Date | 2012-12-13 |
United States Patent
Application |
20120312028 |
Kind Code |
A1 |
KASHYAP; Raman ; et
al. |
December 13, 2012 |
METHODS FOR LASER COOLING OF FLUORESCENT MATERIALS
Abstract
Methods for cooling fluorescent material are provided. A first
method includes providing a sample of the material having an
elongated direction of light propagation, exhibiting fluorescence
at a mean fluorescence wavelength and capable of emitting
superradiant pulses with a formation delay time. The method then
involves generating a pump pulsed laser beam having a wavelength
longer than the mean fluorescence wavelength, a pump power at which
superradiant pulses are emitted and a pulse duration shorter than
the formation delay time. The pulses are directed onto the sample
along the direction of light propagation to produce the
superradiant pulses in an anti-Stokes process inducing a cooling of
the sample. A second laser cooling method includes a combination of
a traditional anti-Stokes cooling cycle and an upconversion cooling
cycle, wherein the two cooling cycles act cooperatively to cool the
sample.
Inventors: |
KASHYAP; Raman; (Baie
D'Urfe, CA) ; NEMOVA; Galina; (Montreal, CA) |
Assignee: |
CORPORATION DE L'ECOLE
POLYTECHNIQUE DE MONTREAL
Montreal
CA
|
Family ID: |
47291974 |
Appl. No.: |
13/469635 |
Filed: |
May 11, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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61484784 |
May 11, 2011 |
|
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Current U.S.
Class: |
62/3.1 |
Current CPC
Class: |
F25B 23/00 20130101 |
Class at
Publication: |
62/3.1 |
International
Class: |
F25B 21/00 20060101
F25B021/00 |
Claims
1. A method for cooling a fluorescent material, the method
comprising the steps of: a) providing a sample of the fluorescent
material, the sample having an elongated light propagation
direction, the fluorescent material exhibiting fluorescence at a
mean fluorescence wavelength and being capable of entering a
superradiance regime wherein superradiant pulses are emitted with a
formation delay time; b) generating a pump laser beam comprising
laser pulses, the generating comprising the substeps of: i)
selecting a pump wavelength of the pump laser beam that is longer
than the mean fluorescence wavelength of the fluorescent material;
ii) selecting a pump power of the pump laser beam so as to reach
the superradiance regime of the fluorescent material; and iii)
selecting a pulse duration of the laser pulses that is shorter than
the is formation delay time of the superradiant pulses; and c)
directing the laser pulses of the pump laser beam onto the sample
of the fluorescent material along the elongated light propagation
direction thereof so as to produce the superradiant pulses in an
anti-Stokes process inducing a cooling of the sample.
2. The method according to claim 1, comprising a step of mounting
the sample of the fluorescent material in a vacuum chamber prior to
directing the laser pulses thereonto.
3. The method according to claim 1, wherein the fluorescent
material is a solid material comprising a host material doped with
ions of a rare-earth element.
4. The method according to claim 3, wherein the host material is
one of a glass and a crystal.
5. The method according to claim 4, wherein the host material is
selected from the group consisting of a fluoride glass, a
fluoro-chloride glass, an oxide crystal, a fluoride crystal and a
chloride crystal.
6. The method according to claim 3, wherein the rare-earth element
is selected from the group consisting of ytterbium, thulium and
erbium.
7. The method according to claim 1, wherein the sample of the
fluorescent material is shaped as a cylinder.
8. The method according to claim 1, wherein the sample of the
fluorescent material is shaped as a rectangular parallelepiped.
9. The method according to claim 1, wherein the sample of the
fluorescent material is a sphere supporting whispering-gallery
modes.
10. The method according to claim 3, further comprising adjusting a
temperature of the sample of the solid material so as to adjust a
threshold value for a number of excited ions in the host material
beyond which the solid material enters in the superradiance
regime.
11. A method for cooling a fluorescent material, the method
comprising the steps of: a) providing a sample of the fluorescent
material, the fluorescent material having an absorption spectrum
comprising at least one absorption band, each of the at least one
absorption band having a corresponding maximum absorption
wavelength; b) illuminating the sample of the fluorescent material
with a first pump laser beam having a first pump wavelength that is
longer than the corresponding maximum absorption wavelength of one
of the at least one absorption band, so as to generate an
anti-Stokes cooling cycle; and, simultaneously, c) illuminating the
sample of the fluorescent material with a second pump laser beam
having a second pump wavelength, the second pump wavelength being
selected for exciting electrons of the fluorescent material so as
to generate an upconversion cooling cycle, wherein the anti-Stokes
and the upconversion cooling cycles act cooperatively to induce a
cooling of the sample of the fluorescent material.
12. The method according to claim 11, comprising a step of mounting
the sample of the fluorescent material in a vacuum chamber prior to
steps b) and c).
13. The method according to claim 11, wherein the fluorescent
material is a solid material comprising a host material doped with
ions of a rare-earth element.
14. The method according to claim 13, wherein the host material is
one of a glass and a crystal.
15. The method according to claim 14, wherein the host material is
selected from the group consisting of a fluoride glass, a
fluoro-chloride glass, an oxide crystal, a fluoride crystal and a
chloride crystal.
16. The method according to claim 13, wherein the rare-earth
element is selected from the group consisting of ytterbium, thulium
and erbium.
17. The method according to claim 11, wherein the upconversion
cooling cycle comprises an excited state absorption process and a
cooperative energy-transfer upconversion process.
18. The method according to claim 13, wherein the solid material is
a potassium-lead chloride crystal doped with trivalent erbium
ions.
19. The method according to claim 18, wherein the first pump
wavelength is selected so that the anti-Stokes cooling cycle
comprises .sup.4I.sub.15/2 and .sup.4I.sub.13/2 absorption bands of
the potassium-lead chloride crystal doped with erbium, and wherein
the second pump wavelength is selected so that the upconversion
cooling cycle comprises .sup.4I.sub.15/2, .sup.4I.sub.13/2 and
.sup.4H.sub.912 absorption bands.
20. The method according to claim 19 wherein the first and second
pump wavelengths are equal to about 1567 and 860 nanometers,
respectively.
Description
FIELD OF THE INVENTION
[0001] The present invention relates to the field of light-matter
interaction, and more particularly concerns laser cooling
methods.
BACKGROUND OF THE INVENTION
[0002] Laser cooling of solids, also referred to as optical
refrigeration, optical cooling or anti-Stokes fluorescence cooling,
is a fast-developing area in the field of optical science and laser
physics. Apart from being of fundamental scientific interest, this
topic addresses the relevant technological problem of designing and
constructing laser-pumped optical coolers.
[0003] The idea of cooling solids by anti-Stokes fluorescence was
proposed by Peter is Pringsheim in 1929 [see P. Pringsheim, Z.
Phys. vol. 57, p. 739, (1929)]. It has been shown that in some
materials, excited atoms emit light having wavelength shorter than
that of the light illuminating the material, and that the excess
energy is supplemented via thermal (phonon) interactions with the
excited atoms [see R. W. Wood, Phil. Mag. Vol. 6, p. 310, 1928].
This process was named anti-Stokes fluorescence, in contrast to the
process of Stokes fluorescence in which the wavelength of the
emitted photons is larger than the wavelength of the absorbed
ones.
[0004] Since anti-Stokes fluorescence involves the emission of
photons having energy larger than the energy of the photons that
are absorbed, it may cause the removal of thermal energy (i.e.
phonons) from the illuminated material and, as a result, lead to
its refrigeration. Hence, anti-Stokes fluorescence has the
potential to provide a basis for obtaining entirely solid-state
optical coolers with the added benefits of being compact and free
of mechanical vibrations, moving parts or fluids. Furthermore, such
optical coolers offer several anticipated advantages over
thermoelectric and mechanical coolers.
[0005] For example, optical refrigerators share the benefit of low
mechanical vibrations with thermoelectric coolers based on the
Peltier effect, but do not require physical contact with a heat
sink in order to expel heat from the material to be cooled.
Additionally, although thermoelectric coolers may be more effective
than anti-Stokes optical coolers at temperatures above 190 K, the
minimum cold side of thermoelectric coolers is limited to about 180
K whereas anti-Stokes optical coolers may cool materials at
temperatures as low as about 90 K [see R. Frey et al. J. Appl.
Phys. vol. 87, p. 4489 (2000)]. Furthermore, while mechanical
coolers such as the Stirling cycle cooler can reach temperatures of
the order 10 K, they remain large, expensive, and cause vibrations
that may not be suitable in many applications. In comparison,
anti-Stokes optical coolers can be based on reliable laser diode
systems disposed is remote from the cooler, thereby generating low
electromagnetic interference in the cooling area.
[0006] An observation of net radiation cooling of a solid by
anti-Stokes fluorescence was reported in 1995 with an
ytterbium-doped fluorozirconate
ZrF.sub.4--BaF.sub.2--LaF.sub.3-AlF.sub.3--NaF--PbF.sub.2 (ZBLANP)
glass [see R. I. Epstein et al., Nature vol. 377, p. 500 (1995)].
In this experiment a Yb.sup.3+-doped sample of ZBLANP having the
shape of a rectangular parallelepiped of volume 43 mm.sup.3 was
laser-pumped at a wavelength of 1015 nm and cooled to 0.3 K below
room temperature via anti-Stokes fluorescence cooling. Since this
experimental demonstration, laser-induced cooling of solids has
been observed in a range of glasses and crystals doped with the
rare-earth ions ytterbium (Yb.sup.3+), thulium (Tm.sup.3+) and
erbium (Er.sup.3+) [see M. P. Hehlen, Proc. SPIE vol. 7228, p.
72280E (2009) and references therein].
[0007] Cryogenic operation in an all-solid-state refrigerator was
reported in 2010 by the research group of Mansoor Sheik-Bahae from
the University of New Mexico [see D. V. Seletskiy et al. Nature
Photon. vol. 4, p. 161 (2010)]. In this study, a laser cooling of
an ytterbium-doped LiYF.sub.4 from ambient temperature to a
temperature of about 155 K with a cooling power of 90 mW was
demonstrated, thereby establishing a new milestone in the field of
optical refrigeration. In particular, this temperature constitutes
a considerable improvement in comparison with the temperatures
reached with glasses and crystals doped with Tm.sup.3+ and
Er.sup.3+ ions.
[0008] It should be noted that in all the experiments mentioned
above, fluorescence (i.e. incoherent radiation), is involved in the
cooling process. Furthermore, all excited ions in the doped host
materials radiate independently from and without interacting with
each other.
[0009] In this regard, in 1954, when lasers had not yet been
invented, R. H. Dicke theoretically predicted a phenomenon of
collective spontaneous emission of coherent radiation by an
ensemble of excited particles coupled by radiation and noise field
[see R. H. Dicke, Phys. Rev. vol. 93, p. 99 (1954)]. This
collective emission was named superradiance (SR).
[0010] The experimental history of superradiance began in 1973,
when it was observed in a gas of hydrogen fluoride (HF) [see N.
Skribanovitz et al. Phys. Rev. Lett. vol. 30, p. 309 (1973)].
Experiments on superradiance in solids were carried out in the
early 1980s, using O.sub.2.sup.- centers in KCI crystals [see R.
Florian et al. Solid State Commun. vol. 42, p. 55 (1982); R.
Florian et al., Phys. Rev. A vol. 28, p. 2709 (1984)] and impurity
pyrene molecules in di-phenyl crystals [see P. V. Zinov'ev et al.
Sov. Phys. JETP vol. 58, p. 1129 (1983); Zh. Eksp. Teor Fiz. vol.
85, p. 1945 (1983), in Russian]. In 1999, Zuikov and colleagues
reported the experimental observation of superradiant pulses in a
crystal doped with rare-earth ions (Pr.sup.3+:LaF.sub.3) [see V. A.
Zuikov et al. Laser Phys. vol. 9, p. 951 (1999)]. This study was a
proof-of-principle experiment, which simply aimed to achieve
superradiance in a rare-earth-doped crystal without any intention
of cooling it.
[0011] More recently, it has been proposed and theoretically
demonstrated that superradiance may be employed to intensify laser
cooling of solids in the anti-Stokes regime [see S. V. Petrushkin
and V. V. Samartsev, Laser Phys. vol. 11, p. 948 (2001); E. K.
Bashkirov, Phys. Lett. A vol. 341, p. 345 (2005); S. N. Andrianov
and V. V. Samartsev, Laser Phys. vol. 7, p. 314 (1997)]. In these
studies, two-level impurity ions with resonance frequency
.omega..sub.0 were pumped with two optical pump fields: a
continuous-wave (CW) laser field with frequency
.omega..sub.1<.omega..sub.0, and a pulsed laser field with
frequency .omega..sub.0. As can be seen from FIG. 1 (PRIOR ART),
only the CW pump laser, with a .omega..sub.1<.omega..sub.0,
contributes in exciting the two-level ions with simultaneous is
absorption of phonons from the host material and thus in cooling
the system. On the other hand, since its frequency coincides with
the resonance frequency of the two-level ion system, the pulsed
laser is not involved in the cooling process, but merely promotes
ions from the ground state to the excited state of the two-level
system without absorption of phonons.
[0012] In the configuration shown in FIG. 1 (PRIOR ART), the pulsed
laser thus serves as a catalyst in triggering the onset of the
superradiance regime by accelerating the radiative relaxation rate
of the ions. Indeed, the ions excited by the pulsed laser (i.e.
without absorption of phonons) become correlated with the ions
excited by the CW laser (i.e. with absorption of phonons), which
results in an ensemble of correlated excited ions that relaxes to
the ground state at an accelerated radiative rate in a superradiant
fashion. However, in the process, the pulsed laser may generate
phonons, which heat the system and therefore counteract the cooling
effect provided by the CW laser. It will thus be understood that
optical cooling of the material should involve a net decrease in
the phonon population, that is, that the number of absorbed phonons
per unit time should exceed that of emitted phonons.
[0013] Recently, an alternative cooling cycle based on the
phenomenon of upconversion was proposed and theoretically described
[see A. J. Garcia-Adeva et al., Phys. Rev. B, vol. 79, p. 033110
(2009)]. More particularly, the alternative cooling cycle
considered therein exploits the efficient infrared-to-visible
upconversion process that is often found in rare-earth-doped
low-phonon-energy host materials characterized by reduced
multiphonon transition rates. In this case, the pump level acts as
an intermediate photon reservoir from which excited-state
absorption takes place.
[0014] Potassium-lead chloride crystal (KPb.sub.2Cl.sub.5) was
synthesized in 1993 [see K. Nitsch et al., J. Cryst. Growth vol.
131, p. 612 (1993)]. It possesses high chemical is resistance,
satisfactory mechanical properties, and is only slightly
hygroscopic. Moreover, due to its low-energy phonon spectrum
(maximum phonon energy of about 203 cm.sup.-1) and associated low
non-radiative relaxation rates, KPb.sub.2Cl.sub.5 crystal emerges
as an interesting candidate for optical cooling applications. In
this regard, samples of erbium-doped potassium-lead chloride
(Er.sup.3+:KPb.sub.2Cl.sub.5) have been cooled following either a
traditional anti-Stokes cooling cycle [see N.J. Condon et al., Opt.
Express vol. 17, p. 5466 (2009)] or an upconversion-based cooling
cycle [see J. Fernandez et al., Phys Rev. Lett. vol. 97, p. 033001
(2006)].
[0015] In the first case, a sample of Er.sup.3+:KPb.sub.2Cl.sub.5
was cooled via a traditional cooling cycle involving the
.sup.4I.sub.15/2.fwdarw..sup.4I.sub.13/2 transition pumped at
wavelengths longer than 1557 nm, that is, 17 nm longer than the
mean fluorescence wavelength of 1540 nm. As a result of the
refrigeration process, the sample was cooled by only 0.01 K below
ambient temperature. In the second case, an
Er.sup.3+:KPb.sub.2Cl.sub.5 sample was cooled with
infrared-to-visible upconversion involving the
.sup.4I.sub.15/2.fwdarw..sup.4I.sub.9/2.fwdarw..sup.2H.sub.9/2
transitions at pump wavelengths exceeding the mean fluorescence
wavelength of 852.5 nm, wherein the .sup.4I.sub.9/2 level acts as
an intermediate electron reservoir from which the excited state
absorption process takes place. In this experiment the temperature
of the sample dropped by 0.7.+-.0.1 K. Hence, it should be
emphasized that the cooling efficiency was very low for both the
traditional and the upconversion-based cooling cycles.
[0016] In view of the above considerations, there exists a need for
more efficient methods for laser cooling of materials, which
alleviate at least some of the drawbacks of the prior art.
SUMMARY OF THE INVENTION
[0017] According to a first aspect of the invention, there is
provided a method for cooling a fluorescent material. The method
includes the steps of: [0018] a) providing a sample of the
fluorescent material, the sample having an elongated is light
propagation direction, the fluorescent material exhibiting
fluorescence at a mean fluorescence wavelength and being capable of
entering a superradiance regime wherein superradiant pulses are
emitted with a formation delay time; [0019] b) generating a pump
laser beam including laser pulses. The generating includes the
substeps of: [0020] i) selecting a pump wavelength of the pump
laser beam that is longer than the mean fluorescence wavelength of
the fluorescent material; [0021] ii) selecting a pump power of the
pump laser beam so as to reach the superradiance regime of the
fluorescent material; and [0022] iii) selecting a pulse duration of
the laser pulses that is shorter than the formation delay time of
the superradiant pulses; and [0023] c) directing the laser pulses
of the pump laser beam onto the sample of the fluorescent material
along the elongated light propagation direction thereof so as to
produce the superradiant pulses in an anti-Stokes process inducing
a cooling of the sample.
[0024] In some embodiments, the fluorescent material is a solid
material including a host material doped with ions of a rare-earth
element.
[0025] Advantageously, the above laser cooling method provides, due
in part to the high radiative relaxation rate of the superradiant
pulses, an improved anti-Stokes cooling cycle that is more
efficient and capable of reaching lower temperatures than
traditional cooling cycles based on incoherent anti-Stokes
fluorescence.
[0026] Moreover, in embodiments wherein the fluorescent material is
a rare-earth-doped host material, the laser cooling method relaxes
the constraints on the use of low-phonon-energy materials as host
materials by allowing the use of materials having higher phonon
energy, which have been thus far considered unsuitable as
rare-earth-doped hosts for traditional laser cooling
applications.
[0027] Further advantageously, contrary to previous known methods
employing superradiance to intensify laser cooling of solids in the
anti-Stokes regime, the laser cooling method above may be realized
by using a single pulsed pump laser beam at a pump wavelength
longer than a mean fluorescence wavelength of the solid material to
be cooled. Indeed, in methods known in the art, both a CW and a
pulsed pump laser sources are employed, whereby the latter generate
phonons that heat the material, thus reducing the efficiency of the
cooling cycle. The above method helps circumventing this
problem.
[0028] According to another aspect of the invention, there is
provided a method for cooling a fluorescent material. The method
includes the steps of: [0029] a) providing a sample of the
fluorescent material, the fluorescent material having an absorption
spectrum including at least one absorption band, each of the at
least one absorption band having a corresponding maximum absorption
wavelength; [0030] b) illuminating the sample of the fluorescent
material with a first pump laser beam having a first pump
wavelength that is longer than the corresponding maximum absorption
wavelength of one of the at least one absorption band, so as to
generate an anti-Stokes cooling cycle; and, simultaneously, [0031]
c) illuminating the sample of the fluorescent material with a
second pump laser beam having a second pump wavelength, the second
pump wavelength being selected for exciting electrons of the
fluorescent material so as to generate an upconversion cooling
cycle, wherein the anti-Stokes and the upconversion cooling cycles
act cooperatively to induce a cooling of the sample of the
fluorescent material.
[0032] In some embodiments, the fluorescent material is a solid
material including a host is material doped with ions of a
rare-earth element.
[0033] Advantageously, by combining a traditional anti-Stokes
cooling cycle and an upconversion cooling cycle, the method
according to this aspect of the invention helps overcoming the
self-termination effects that may be present in either of the two
cooling cycles when used on its own.
[0034] Other features and advantages of the present invention will
be better understood upon reading of preferred embodiments thereof
with reference to the appended drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0035] FIG. 1 (PRIOR ART) illustrates a laser cooling method with
superradiance that employs both a continuous-wave laser pump and a
pulsed laser pump to generate cooling.
[0036] FIG. 2 (PRIOR ART) is a schematic energy diagram
illustrating a process of laser cooling according to which the
absorption of a pump photon by the material is followed by rapid
thermalization within the excited state with the absorption of
phonons and subsequent emission of anti-Stokes fluorescence.
[0037] FIG. 3 is a flow chart of a method for laser cooling of a
fluorescent material according to an embodiment of the
invention.
[0038] FIG. 4 is a schematic energy diagram of a laser cooling
method with superradiance is according to an embodiment of the
invention.
[0039] FIG. 5 is a schematic representation of a sample of a ZBLAN
host material doped with Yb.sup.3+ illuminated by the laser pulses
of a pump laser beam and emitting superradiant pulses, according to
an embodiment of the invention.
[0040] FIG. 6 (PRIOR ART) shows the spectra of absorption and
emission cross-sections of Yb.sup.3+ ions in a ZBLAN host material
at room temperature. The inset schematic energy diagram
illustrating anti-Stokes cooling.
[0041] FIG. 7 is graph comparing the cooling rate as a function of
the pump power P.sub.p provided by a laser cooling method according
to an embodiment of the invention (solid line) and by a traditional
anti-Stokes cooling cycle (dotted line).
[0042] FIG. 8 is a graph showing the normalized power of a
superradiant pulse as a function of time according to an embodiment
of the invention.
[0043] FIG. 9 is a graph showing the formation delay time
.tau..sub.D of a superradiant pulse as a function of the pump power
of a pump laser beam with laser pulses having a pulse duration
.tau..sub.p=10 ns, according to an embodiment of the invention.
[0044] FIG. 10 is a graph showing the time of correlation
self-formation .tau..sub.c of a superradiant pulse as a function of
the pump power of a pump laser beam with laser pulses having a
pulse duration .tau..sub.p=10 ns, according to an embodiment of the
invention.
[0045] FIG. 11 is a graph showing the ratio C of the power P.sub.SR
removed from the sample via superradiance to the power P.sub.SP
removed from the sample via incoherent anti-Stokes fluorescence as
a function of the pump power of a pump laser beam with laser pulses
is having a pulse duration .tau..sub.p=10 ns, according to an
embodiment of the invention.
[0046] FIG. 12 is a graph showing the number of laser pulses of the
pump laser beam as a function of sample temperature, according to
an embodiment of the invention.
[0047] FIG. 13 illustrates a laser pulse of pump laser beam having
a pulse duration .tau..sub.p that is shorter than the formation
delay time .tau..sub.D of a superradiant pulse.
[0048] FIG. 14 is a flow chart of another method for laser cooling
of a fluorescent material according to an embodiment of the
invention.
[0049] FIG. 15 illustrates the energy levels of the rare-earth ion
Er.sup.3+ in a KPb.sub.2Cl.sub.5 host crystal.
[0050] FIG. 16 is a graph showing the net cooling power P.sub.cool
of a sample of Er.sup.3+:KPb.sub.2Cl.sub.5 as a function of the
pump power P.sub.p.sup.(1) of the first pump laser beam, at a
wavelength .lamda..sub.p.sup.(1)=1567 nm, for different values of
the second pump power P.sub.p.sup.(2) of the second pump laser
beam, at a wavelength .lamda..sub.p.sup.(2)=860 nm, according to an
embodiment of the invention.
[0051] FIG. 17 is a graph showing the net cooling power P.sub.cool
of a sample of Er.sup.3+:KPb.sub.2Cl.sub.5 as a function of the
pump power P.sub.p.sup.(2) of the second pump laser beam, at a
wavelength .lamda..sub.p.sup.(2)=860 nm, for different values of
the first pump power P.sub.p.sup.(1) of the first pump laser beam,
at a wavelength .lamda..sub.p.sup.(1)=1567 nm, according to an
embodiment of the invention.
DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION
[0052] The present invention generally relates to methods for
cooling a fluorescent material with laser radiation. As known in
the art, laser cooling of materials, also referred to as optical
refrigeration, optical cooling or anti-Stokes fluorescence, may
occur in a fluorescent material that absorbs pumping laser
radiation at one wavelength and subsequently emits fluorescent
radiation that has an average wavelength shorter than that of the
pumping laser radiation.
[0053] It is known in the art that an electron may be excited by a
photon having an energy corresponding to a difference in energy
between two atomic levels. Moreover, it is also known that
phonons--quanta of vibrational energy that generates heat--may also
be part of the excitation process of an electron by being absorbed
thereby, along with a pump photon, in order to provide the
appropriate energy for promoting the electron to an upper atomic
level. Accordingly, when the excited electron relaxes in a
radiative way, the emitted photon has an energy that is higher than
that of the pump photon.
[0054] In laser cooling of fluorescent materials, the excess energy
involved in emitting anti-Stokes photons may be provided by
extracting phonons from the material. This phonon extraction via
anti-Stokes emission of radiation leads to a decrease of the
thermal energy stored inside the material, which may lead to
optical cooling thereof if the phonon extraction rate is higher
than the phonon absorption rate so that the material exhibits net
anti-Stokes fluorescence. FIG. 2 (PRIOR ART) shows a schematic
energy diagram illustrating a process of laser cooling according to
which the absorption of a pump photon by the material is followed
by rapid thermalization within the excited state with the
absorption of phonons and subsequent emission of anti-Stokes
fluorescence.
[0055] In this regard, it should be understood that expressions
such as "traditional anti-Stokes cooling cycle" or "incoherent
anti-Stokes fluorescence" are used herein to refer to methods that
are known in the art and that are based on the cooling process
illustrated in FIG. 2 (PRIOR ART). In particular, the two methods
described below provide improved and more efficient laser cooling
methods when compared to what is known in the art.
[0056] In the present description, the term "thermalization" is
understood to refer to the absorption of phonons by electrons found
on an electronic level in order to increase the energy thereof. For
typical host materials involved in optical cooling applications,
the thermalization process usually takes on a time scale of the
order of picoseconds or less. Moreover, as used herein, the term
"phonon" refers to a quasiparticle characterized by the
quantization of the collective modes of vibrational energy of
elastic structures of interacting particles in condensed matter. It
should be noted that while phonons are typically studied in
periodic materials (e.g. crystals), they may also exist in
non-periodic or amorphous materials (e.g. glasses).
[0057] It will thus be understood by one skilled in the art that
laser cooling requires that the wavelength of the pump photons be
larger than the mean fluorescence wavelength of the anti-Stokes
photons. In this context, an ideal cooling cycle of a material may
be characterized by a cooling efficiency .eta..sub.cool given
by
.eta..sub.cool,ideal=(h.nu..sub.F-h.nu..sub.p)/h.nu..sub.p=(.lamda..sub.-
p-.lamda..sub.F)/.lamda..sub.F, (1)
which represents the fractional cooling energy provided by each
absorbed pump photon. In Equation (1),
h.apprxeq.6.63.times.10.sup.-34 Js, is the Planck constant,
.nu..sub.p and .lamda..sub.p are the frequency and wavelength of
the pump photon, respectively, and .nu..sub.F and .lamda..sub.F are
the mean fluorescence frequency and wavelength of the anti-Stokes
photons. However, is the excited electron may alternatively decay
non-radiatively, for example via multiphonon emission, and thus
introduce undesired heating of the material.
[0058] As known in the art, the competition between radiative and
non-radiative decays may be characterized by the internal quantum
efficiency
.eta. = W r W r + W nr , ( 2 ) ##EQU00001##
where W.sub.r and W.sub.nr are the radiative and non-radiative
multiphonon relaxation rates, respectively. It will be understood
that a non-zero value for W.sub.nr reduces the cooling efficiency
from that of the ideal cooling cycle to
.eta..sub.cool=(.eta..lamda..sub.p-.lamda..sub.F)/.lamda..sub.F
(3)
so that the non-radiative relaxation rate of the laser-pumped
excited levels should be as small as possible in comparison to the
radiative relaxation rate.
[0059] The multiphonon relaxation rate may be expressed as [see H.
W. Moos, J. Luminesc. vol. 1-2, p. 106 (1970)]:
W.sub.nr=B[n(T)+1].sup.pexp(-.alpha..DELTA.E.sub.g), (4)
where n(T)=[exp( h.omega..sub.eff/k.sub.BT)-1].sup.-1 is the
Bose-Einstein occupation number at temperature T of the effective
phonon of energy h.omega..sub.eff involved in the transition,
h=h/2.pi. is the reduced Planck constant, and
k.sub.B=1.38.times.10.sup.-23 J/K is the Boltzmann constant.
Moreover, B and .alpha. are material-dependent parameters that
should be determined empirically. Finally, .DELTA.E.sub.g is the
energy gap between two phonon manifolds is that is bridged by p
phonons in the multiphonon relaxation process.
[0060] It should be noted that, in most cases, the effective
phonons involved in non-radiative relaxation processes are the
highest-energy phonons available in the material, since this
minimizes the number of phonons required to bridge a given energy
gap and results in the lowest possible order for the decay process.
Alternatively, in some other cases, this may not be true if the
coupling strengths or density of states of lower-energy phonons are
greater than those of high-energy phonons.
[0061] Furthermore, it is known in the art that in order to provide
efficient optical refrigeration, via traditional anti-Stokes
cooling the maximum phonon energy h.omega..sub.max of the material
and the energy E.sub.p=h.nu..sub.p of the pump photons should
fulfill the condition [see M. P. Hehlen, Proc. SPIE vol. 7228, p.
72280E (2009)]
E.sub.P>8 h.omega..sub.max, (5)
which indicates that more than eight phonons should be involved to
bridge the energy gap corresponding to the pump photon energy
E.sub.p.
[0062] It should be mentioned that the laser cooling methods
according to embodiments of the invention may generally be applied
to any fluorescent material. The term "fluorescent material" as
used herein is intended to refer to any substance which, in
response to irradiation by electromagnetic radiation, is capable of
exhibiting fluorescence, that is, of itself emitting
electromagnetic radiation. It should be understood herein that
suitable fluorescent materials may include solid, liquid or gaseous
materials, without departing from the scope of the invention.
[0063] For example, in some embodiments of the laser cooling
methods described herein, the fluorescent material may be a solid
material including a host material doped with ions of a rare-earth
element. Indeed, the benefits of using rare-earth doped in
transparent host materials for laser cooling of solids have been
known for several decades due, in part, to their high quantum
efficiencies and narrow spectral lines. Another advantage of
rare-earth ions lies in the fact that their optically active 4f
electrons are shielded by the filled 5s and 5p outer shells,
thereby limiting their interaction with the lattice of the host
material surrounding the rare-earth ions and significantly reducing
non-radiative multiphonon decay.
[0064] In the present description, the term "rare-earth element" is
understood herein to encompass the lanthanides elements having
atomic numbers from 57 through 71, preferably erbium (Er), thulium
(Tm) and ytterbium (Yb). Likewise, the term "rare-earth ion" is
understood to refer to an ion (i.e. a particle having a net
electric charge) of a rare-earth element. In some embodiments, the
rare-earth ions may be trivalent rare-earth ions, preferably
Er.sup.3+, Tm.sup.3+ and Yb.sup.3+.
[0065] It will be understood that any suitable host material may
generally be employed in embodiments of the laser cooling method
100. The host material should be optically transparent, that is,
capable of transmitting photons with relatively little absorption
and reflection at the wavelength of operation of a pump laser and
emission radiation employed in the laser cooling method 100. For
example, in some embodiments, the host material may be a
transparent glass or crystal, for example fluoride or chloride
glasses and crystals having low phonon energy, so as to further
reduce non-radiative decay and hence increase internal quantum
efficiency [see Equation (2)].
[0066] It will also be understood that characteristics of host
material such as refractive index, chemical durability, mechanical
and thermal properties should be considered when selecting an
ion-host combination for the solid material to be cooled in
embodiments of the laser cooling method 100. For example, an
appropriate host material should not, in some embodiments, be
hygroscopic in order to avoid deterioration in the presence of
water molecules, which would reduce internal quantum efficiency.
Likewise, the host material should preferably have good hardness so
as to provide easy processing thereof.
[0067] In what follows, two laser cooling methods will be described
which may be used in the context of the present invention. In a
first aspect of the invention, a pulsed laser beam is used to
induce an anti-Stokes cooling of a fluorescent material in a regime
of superradiance. In a second aspect of the invention, two laser
beams are directed simultaneously on a sample of fluorescent
material to produce both an anti-Stokes and an upconversion cooling
cycle for inducing a cooling of the sample.
Method for Cooling a Fluorescent Material with Superradiance
Fluorescence
[0068] According to one aspect of the invention, there is provided
a first method 100 for cooling a fluorescent material. Referring to
FIG. 3, there is shown a flow chart of an embodiment of the method
100.
[0069] The method 100 according to this aspect of the invention
generally relates to the laser cooling of fluorescent materials
employing the optical phenomenon of superradiance to improve the
efficiency of laser cooling in the anti-Stokes regime. More
particularly and contrary to prior art methods of laser cooling
with superradiance, the method 100 makes possible the use of a
single pulsed pump laser beam at a pump wavelength longer than a
mean fluorescence wavelength of the fluorescent material to be
cooled, so as generate superradiant pulses without CW
co-pumping.
[0070] As will be described in further detail below, embodiments of
the method 100 involve is using a pulse of a pump laser beam to
excite electrons of fluorescent material from the top of the
ground-state manifold to the bottom of an excited manifold where
phonons are absorbed, as shown in FIG. 4. The excited ions then
correlate with each other and relax to the ground state as a
coherent ensemble at an accelerated relaxation rate caused by
radiation of a superradiant pulse. Hence, in the method 100
according to an aspect of the invention, a single pulsed pump laser
source causes absorption of phonons, resulting in cooling, and,
simultaneously, constitutes a source of accelerated relaxation
rate, caused by radiation of a superradiant pulse. It will be
understood that in the laser cooling method 100 described herein,
no additional laser source that would generate phonons and result
in heating of the system is necessary.
[0071] Still referring to FIG. 3, the laser cooling method 100
first involves a step 102 of providing a sample of the fluorescent
material, the sample having an elongated light propagation
direction.
[0072] FIG. 5 provides a schematic representation of an embodiment
of the sample 20 of the fluorescent material to which the laser
cooling method 100 may be applied. In this embodiment, the
fluorescent material is a fluorozirconate
ZrF.sub.4--BaF.sub.2--LaF.sub.3--AlF.sub.3--NaF (ZBLAN) glass doped
with trivalent ytterbium ions (Yb.sup.3+). In other embodiments,
the fluorescent material may be another fluoride glass doped with
Yb.sup.3+ (e.g. Yb.sup.3+:ZBLANP, Yb.sup.3+:BIG, Yb.sup.3+:ABCYS),
a fluoro-chloride glass doped with Yb.sup.3+ (e.g.
Yb.sup.3+:CBNZn), an oxide crystal doped with Yb.sup.3+[e.g.
Yb.sup.3+:KGd(WO.sub.4).sub.2, Yb.sup.3+:KY(WO.sub.4).sub.2,
Yb.sup.3+:YAG, Yb.sup.3+:Y.sub.2SiO.sub.5], a fluoride crystal
doped with Yb.sup.3+ (e.g. Yb.sup.3+:BaY.sub.2F.sub.8,
Yb.sup.3+:YLF), a chloride crystal doped with Yb.sup.3+ (e.g.
Yb.sup.3+: KPb.sub.2Cl.sub.5), a fluoride glass doped with
Tm.sup.3+ (e.g. Tm.sup.3+:ZBLAN), a fluoride crystal doped
Tm.sup.3+ (e.g. Tm.sup.3+:BaY.sub.2F.sub.8), a fluoro-chloride
glass doped Er.sup.3+ (e.g. Er.sup.3+:CNBZn) or a chloride crystal
doped with Er.sup.3+ (e.g. Er.sup.3+:KPb.sub.2Cl.sub.5) [see, e.g.,
Table 1 in G. Nemova and R. Kashyap, Rep. Prog. Phys. vol. 73, p.
086501 (2010)]. In further embodiments, the fluorescent material
may be ceramic glasses, crystals, polymers, semiconductors, is
chalcogenide glasses, with nanoparticles or quantum dots. In still
further embodiments, the fluorescent material may be a liquid or a
gaseous material.
[0073] As used herein, the expression "elongated light propagation
direction" may refer to the fact that the sample of the fluorescent
material is geometrically elongated along one direction thereof.
However, the expression "elongated light propagation direction" may
also be used to encompass cases wherein the sample of the
fluorescent material allows electromagnetic radiation to undergo
multiple passes through the sample, thereby creating an effectively
elongated sample along one direction thereof. This may be achieved,
for example, by placing the sample in a resonant cavity or by
exciting specific electromagnetic modes in the sample.
[0074] In the embodiment shown in FIG. 5, by way of example, the
sample 20 is shaped as a cylinder of radius r=0.5 mm, length L=5 mm
and aspect ratio L/r=10, so that the sample 20 may considered
elongated along a direction 22 coinciding with the axis of the
cylinder. The cylindrical sample 20 thus has an elongated light
propagation along the axis thereof. In other embodiments, the
sample may be shaped as a rectangular parallelepiped.
[0075] One skilled in the art will understand that the sample may
have another shape than described herein without departing from the
scope of the laser cooling method 100, as long as it is elongated
along one direction thereof or has an elongated light propagation
direction as defined above. In this context, the expression
"elongated sample" is understood to refer to a sample of a shape
having a length significantly greater along one axis of an
appropriate three-dimensional coordinate system.
[0076] In further embodiments, the sample of the fluorescent
material may also be a sphere or a substantially spherical sample
supporting whispering gallery modes, which are used to extend the
sample in one dimension. As used herein, the expression is
"whispering gallery modes" should be understood to refer to closed
circular waves trapped by total internal reflection inside an
axially symmetric dielectric body. Hence, due to the trapping and
multiple reflections associated therewith, the excitation of
whispering gallery modes in a spherical sample of fluorescent
material may effectively produce an elongated light propagation
direction in the sample.
[0077] Referring back to FIG. 3, in the providing step 102, the
fluorescent material making up the sample exhibits fluorescence at
a mean fluorescence wavelength and is capable of entering a
superradiance regime wherein superradiant pulses are emitted with a
formation delay time.
[0078] In the present description, the term "fluorescence" is
understood to refer to the emission of electromagnetic radiation by
a substance that has absorbed electromagnetic radiation. A
fluorescent material usually absorbs electromagnetic radiation in
particular regions of the electromagnetic spectrum, thereby
defining an absorption spectrum which is characteristic of this
particular material. The fluorescent material may then re-emit
electromagnetic radiation at different fluorescence wavelengths so
as to define a corresponding fluorescence spectrum. It will be
understood that fluorescence spectrum may, but need not, be similar
to the absorption spectrum, and may comprise one or a plurality of
emission bands of various strengths. By way of example, the spectra
of absorption and emission cross-sections of Yb.sup.3+ ions in a
ZBLAN host material have been presented by J. Parker et al., J.
Appl. Phys. vol. 105, p. 013116 (2009), and is illustrated in FIG.
6 (PRIOR ART).
[0079] Furthermore, the term "mean fluorescence wavelength" is
understood herein to refer to an appropriately averaged wavelength
that accounts for the fluorescence spectrum of the fluorescent
material. In particular, as described above, pumping the
fluorescent material at a pump wavelength .lamda..sub.p longer than
the mean fluorescence wavelength .lamda..sub.F is will yield
anti-Stokes fluorescence emission and possibly optical
refrigeration.
[0080] In embodiments of the laser cooling method 100 described
herein and exemplified by the embodiment corresponding to the flow
chart of FIG. 3, the optical cooling of the sample of the
fluorescent material results from a process of superradiance. In
the present description, the term "superradiance" refers to a
process of spontaneous collective emission of coherent photons by
an ensemble of excited particles coupled by electromagnetic
radiation and noise field.
[0081] As a result of this collective effect, the relaxation time
to the ground state of the ensemble of excited particles is shorter
than the spontaneous relaxation time of a corresponding single
excited particle. This spontaneous coherent emission of radiation
constitutes a superradiant pulse, characterized in that all the
energy stored in the sample is released in the form of coherent
emitted light. A system exhibiting such a cooperative effect is
referred to as being "superradiant" or to have entered a
"superradiance regime". The source of this coherence is the excited
ions correlated over the electromagnetic field. It will also be
understood by one skilled in the art that the superradiance regime
does not involve stimulated emission, which is another source of
coherent radiation.
[0082] The time needed for the superradiant pulse to form is
referred to as the "formation delay time" of the superradiant
pulse, which is denoted by the symbol .tau..sub.D. The formation
delay time may equivalently be interpreted as the time in which the
ensemble of excited particles is capable of entering a
superradiance regime. It will be understood by one skilled in the
art that no stimulated emission is involved in the superradiance
process.
[0083] As mentioned above, it is known in the art that incoherent
fluorescence in a is fluorescent material made of rare-earth doped
crystal or glass is a result of spontaneous relaxation of
independent ions in a transparent host. It will thus be understood
that, in embodiments of the laser cooling method 100 wherein the
fluorescent material is a solid material doped with ions of a
rare-earth element, the intensity I of this incoherent fluorescence
is proportional to the number N of excited rare-earth ions in a
sample of the solid material, that is, I.about.N. On the other
hand, in his theoretical work on superradiance, Dicke considered
the entire collection of two-level atoms of sample of the solid
material as a single quantum-mechanical system [see R. H. Dicke,
Phys. Rev. vol. 93, p. 99 (1954)]. Moreover, Dicke found that under
certain conditions to be discussed below, the atoms cooperate and
relax to the ground state in a time .tau..sub.sR much shorter than
the spontaneous relaxation time .tau..sub.s. associated with
incoherent fluorescence, namely that
.tau..sub.SR.apprxeq..tau..sub.S/N. As a result, the intensity of
radiation in the superradiance regime is shown to be proportional
to the square of the number of excited atoms, that is,
I.about.N.sup.2.
[0084] It must be noted that some conditions should be fulfilled by
the size, shape and physical properties of the sample of the
fluorescent material for superradiance to be achieved according to
the laser cooling method 100. For example, as in the embodiment of
FIG. 5, the sample 20 should preferably be greatly extended along
one direction 22 thereof to allow the formation of a superradiant
pulse 28. Indeed, since the superradiant pulse is correlated and
has a narrow angle of emission, an elongated sample should
preferably be used to allow emission in that direction, principally
by exciting all the available ions.
[0085] Furthermore, as described in further detail below, the time
of flight .tau. of a photon through the sample 20 should preferably
remain short in comparison with the other characteristic times
involved in the formation of the superradiant pulses 28. As known
in the art, the time of flight .tau. of a photon along the
elongated direction 22 (i.e. length is L) of the sample 20 shown in
FIG. 5 is given by .tau.=Ln/c, where n is the refractive index of
the fluorescent material, which is equal to n=1.5 in this
particular embodiment, and c.apprxeq.3.times.10.sup.8 m/s is the
speed of light in vacuum. Hence, as described below, the size of
and refractive index of the fluorescent material should be selected
appropriately in the laser cooling method 100 described herein.
[0086] Additionally, since superradiance is a cooperative process,
the total concentration N.sub.T of rare-earth ions in the host
material (i.e. both ground-state and excited-state ions) should be
high. Preferably, the total concentration N.sub.T of rare-earth
ions in the host material is selected to be about 10.sup.9
ions/.mu.m.sup.3. For example, in the embodiment of FIG. 5, the
sample 20 is a doped with Yb.sup.3+ ions at a concentration N.sub.T
equal to 1.45.times.10.sup.9 ions/.mu.m.sup.3.
[0087] Referring to FIG. 3, the laser cooling method 100 next
involves a step 104 of generating a pump laser beam 24 including
laser pulses 26, as illustrated in FIG. 5. Indeed, it is known in
the art that optical cooling should involve laser radiation, so as
to provide an excitation source with a sufficiently narrow spectral
power distribution.
[0088] In the present description, the term "laser beam" is
understood to refer to a high-intensity, spatially-coherent and
nearly monochromatic beam of electromagnetic radiation. The
electromagnetic radiation may be photons of energy encompassing the
visible, infrared and ultraviolet portions of the electromagnetic
spectrum. As discussed below, the laser beam may characterized by
several optical characteristics, including a pump wavelength
.lamda..sub.p and a pump power P.sub.p. The term "pump" is
understood herein to refer to the fact that, as described below,
the laser cooling method 100 employs the laser beam as an
excitation source for inducing atomic electron transitions in a
sample of rare-earth-doped host material.
[0089] As known in the art, the pump laser beam according to the
laser cooling method 100 may be produced by a laser source, which
may be embodied, for example, by an electrically-pumped
semiconductor lasers, an optically-pumped solid-state laser, an
optical fiber laser, a solid state amplification system, an optical
parametric amplification system, a fiber amplification system, a
chirped pulse amplification system, a combination of these lasers
and amplification systems, or the like.
[0090] The expression "laser pulses" is understood herein to refer
to the discrete onset of laser radiation separated by an
inter-pulse period where light is absent or negligible. Any given
laser pulse has optical characteristics which define it with
respect to time, space and wavelength, for example a pulse duration
.tau..sub.p and a pulse shape.
[0091] In the present description, the expression "pulse duration"
generally refers to the period of time between the beginning and
the end of an individual pulse. Several conventions may be used to
determine the moment at which a laser pulse begins and ends, as
will be readily understood by one skilled in the art. For example,
it may be determined accordingly to a given fraction, such as 50%
or 1/e.sup.2 or any other fraction, of the maximum intensity of a
simple pulse temporal profile. It will be understood herein that
both the laser pulses composing the pump laser beam and the
superradiant pulses composing the superradiance regime may be
assigned a pulse duration.
[0092] The expression "pulse shape" is used to refer herein to the
shape of the temporal profile of the laser pulses, that is, the
form obtained when the pulse amplitude or intensity is plotted as a
function of time. For example, in the embodiment of the method 100
shown in FIG. 5, the laser pulses 26 of the pump laser beam 24 are
is rectangular in shape.
[0093] It will be understood that, in addition to the conditions
mentioned above regarding the size, shape and physical properties
of the sample of the fluorescent material, achieving superradiance
also involves conditions on the pulse duration .tau..sub.p of the
laser pulses composing the pump laser beam. All these conditions
have been presented and discussed by Dicke and may be summarized by
the following inequalities:
.tau.<.tau..sub.c<.tau..sub.s,.tau..sub.2, (6)
.tau..sub.p<.tau..sub.D. (7)
[0094] Here, .tau., .tau..sub.p and .tau..sub.D have been
introduced above and denote the time of flight of a photon through
the sample of the fluorescent material, the pulse duration of the
pump laser pulses and the formation delay time of a superradiant
pulse, respectively, while .tau..sub.c is the correlation
self-formation time in the fluorescent material characterizing the
full width at mid-height of the intensity of the superradiant
pulse, .tau..sub.s is the spontaneous relaxation time
characterizing incoherent fluorescence in the fluorescent material,
.tau..sub.2 is the time of phase irreversible relaxation.
[0095] On the one hand, the left inequality in Equation (6)
indicates that the propagation time .tau. of photons in the sample
of the fluorescent material should be shorter than the
characteristic times thereof, that is, .tau..sub.c, .tau..sub.s,
and .tau..sub.2. On the other hand, the right inequality in
Equation (6) indicates that the formation of a superradiant pulse
in the sample should to be a faster process than the process of
spontaneous relaxation resulting in incoherent anti-Stokes
fluorescence emission. It will be understood herein that as soon as
the left inequality in Equation (6) is satisfied, the sample
becomes essentially free from re-absorption since all generated
photons leave the sample.
[0096] Meanwhile, the inequality of Equation (7), which is
illustrated in FIG. 13, indicates that a laser pulse of the pump
laser beam should have a pulse duration .tau..sub.p that is shorter
than the formation delay time .tau..sub.D of a superradiant pulse
or, in other words, that the pump laser pulses and the superradiant
pulses should not or minimally overlap in time.
[0097] It is of interest to note that the process of formation of a
superradiant pulse is entirely different from the process of
formation of the amplified signal in a laser system, which is based
on stimulated emission, although both cases result in coherent
radiation emission.
[0098] Referring to FIG. 3, the generating 104 first involves a
substep 106 of selecting a pump wavelength of the pump laser beam
that is longer than the mean fluorescence wavelength of the
fluorescent material.
[0099] As one skilled in the art will understand, this substep 106
ensures that anti-Stokes fluorescence emission is generated within
the sample of the fluorescent material. For example, in the case of
the embodiment shown in FIG. 5, the wavelength .lamda..sub.p of the
pump laser beam 24 is equal to 1015 nm, which is longer than the
mean fluorescence wavelength .lamda..sub.F=999 nm of the Yb.sup.3+
ions in the ZBLAN host material. Of course, depending on the
fluorescence emission spectrum of the fluorescent material to be
laser cooled by the method 100 described herein, different values
for the wavelength of the pump laser beam may be selected.
[0100] Referring back to FIG. 3, the generating 104 then involves a
substep 108 of selecting a pump power of the pump laser beam so as
to reach the superradiance regime of the fluorescent material.
[0101] In general, the pump power of the pump laser beam needs to
be within a certain range of values for the fluorescent material to
emit superradiant pulses. More particularly, the pump power should
be high enough to trigger the onset of superradiance, but not so
high as to generate non-linear optical effects in the fluorescent
material to be cooled. Preferably, the pump power of the pump laser
beam is selected to be of the order of several hundred watts. For
example, in the embodiment of FIG. 5, the pump power P.sub.p of the
pump laser beam 24 is equal to 433.5 W.
[0102] It should also be mentioned that varying the pump power
value of the pump laser beam may have an impact on the value of
some of the characteristic times of the fluorescent material
involved in the inequalities of Equations (6) and (7). In
particular, the formation delay time .tau..sub.D and the
correlation self-correlation time .tau..sub.c of the superradiant
pulses change according to the value of the pump power P.sub.p
since the number of excited rare-earth ions in the sample of the
fluorescent material participating in the formation of a
superradiant pulse depends itself on P.sub.p. In this regard, FIGS.
9 and 10 show that both .tau..sub.D and .tau..sub.c decreases with
increasing value of P.sub.p. Hence, it will be understood that the
value of the pump power of the pump laser beam should preferably be
selected so that the corresponding values of .tau..sub.D and
.tau..sub.c fulfill Equations (6) and (7), which should be
satisfied in order for the fluorescent material to enter the
superradiance regime.
[0103] The generating 104 next involves a substep 110 of selecting
a pulse duration of the laser pulses that is shorter than the
formation delay time of the superradiant pulses. It will be
understood that this substep corresponds to the fulfillment of the
condition .tau..sub.p<.tau..sub.D given in Equation (7).
[0104] For example, in rare-earth-doped solid materials, the
formation delay time .tau..sub.D of is superradiant pulses is
typically of the order of tens of nanoseconds so that, in such
embodiments, the pulse duration .tau..sub.p of the laser pulses
should be shorter than that. However, it will understood that in
order for the pump power PP of the pump laser beam to be
sufficiently high for superradiance to be achieved, the pulse
duration .tau..sub.p may preferably be of the order of tens of
nanoseconds, rather than in the picosecond and femtosecond range.
In the embodiment of FIG. 5, the pulse duration .tau..sub.p of the
laser pulses 26 is equal to 10 ns.
[0105] The method 100 further then a step 112 of directing the
laser pulses of the pump laser beam onto the sample of the
fluorescent material along the elongated light propagation
direction thereof so as to produce the superradiant pulses in
anti-Stokes process inducing a cooling of the sample. In the
embodiment of FIG. 5, the directing step 112 includes directing the
laser pulses 26 of the pump laser beam 24 along the extended
direction 22 of the sample 20 of the fluorescent material due to
the low emission angle of the superradiant pulses. Preferably, and
in order to provide a more efficient cooling, the laser cooling
method 100 includes a step of mounting the sample of the
fluorescent material in a vacuum chamber prior to directing the
laser pulses thereonto
[0106] In general, it will be understood that in the directing step
112, the pulses of the pump laser beam having parameters selected
in the generating step 104, illuminates the sample of the
fluorescent material in order to achieve coherent anti-Stokes
fluorescence via emission of superradiant pulses, thereby cooling
the sample. In the following, the formation of superradiant pulses
upon directing the laser pulses of the pump laser beam onto the
sample according to embodiments of the laser cooling method 100
will be described in detail. In particular, the improved efficiency
of the cooling cycle provided by embodiments of the method 100 over
a traditional anti-Stokes cooling cycle will be discussed.
[0107] It will be understood that this description is meant to
provide assistance in comprehending the physical phenomena
underlying the method 100 as understood by the inventors, and is in
no way meant to be limitative to the scope of the present
invention.
[0108] As described above, the process of forming a superradiant
pulse begins as incoherent fluorescence, wherein rare-earth ions in
the host material do not interact with each other. Gradually,
interactions between the ions through electromagnetic radiation and
noise field increase and lead to a correlation of their dipole
moments, which reaches a maximum at a time .tau..sub.D
corresponding to the formation delay time of the superradiant
pulse. It is known in the art that in the superradiance regime, a
major proportion of the power emitted by superradiance is radiated
as highly directional emission of superradiance pulses along or
close to the direction along which the sample is most extended.
This is illustrated in the embodiment of FIG. 5, wherein the
superradiance pulses 28 exhibit a sharp directionality in space
along the extended direction 22 of the sample 20 of the fluorescent
materials and are observed simultaneously both along and against
the direction of propagation of the pump laser beam 24.
[0109] The instantaneous power of the superradiant signal is given
by the following equation [see V. V. Samartsev and A. A. Kalachev,
Hyp. Interact. vol. 135, p. 257 (2001)]:
P ( t ) = hc .tau. s .lamda. F .mu. N 2 4 sech 2 ( t - .tau. D 2
.tau. c ) , ( 8 ) ##EQU00002##
where t is the time, .lamda..sub.F is the mean fluorescence
wavelength, N is the number of excited rare-earth ions in the
sample of the fluorescent material, and .mu. is a
geometry-dependent parameter of the sample which has been
investigated in the art [see is T. R. Gosnell, Opt. Lett. vol. 24,
p. 1041 (1999)]. In particular, for a cylindrically-shaped sample
20, such as in the embodiment shown in FIG. 5, the
geometry-dependent parameter is given by
.mu. = .lamda. F 2 2 A eff ( 1 + 1 + F - 2 ) , ( 9 )
##EQU00003##
where A.sub.eff is an effective mode area and
F=A.sub.eff/(.lamda..sub.FL) with L being the length of the
sample.
[0110] It will be understood that Equation (8) described the
evolution of the power P(t) of the superradiant pulse as a function
of time. In particular, FIG. 8 shows a graph of P(t) normalized to
the maximum value thereof, corresponding to the sample 20 of ZBLAN
doped with Yb.sup.3+ in the embodiment of FIG. 5. It may be seen
that P(t) is maximum at a time corresponding to the formation delay
time of the superradiant pulse, which is equal to
.tau..sub.D.apprxeq.14 ns in FIG. 8 and satisfies Equation (7)
since the pulse duration .tau..sub.p of the laser pulses 26 is
equal to 10 ns in this embodiment. Furthermore, the correlation
self-formation time in the fluorescent material corresponds to the
full width at mid-height of P(t), which is equal to
.tau..sub.c.apprxeq.1 ns in FIG. 8. This value for .tau..sub.c
satisfies Equation (6) since the time of spontaneous relaxation
.tau..sub.s.apprxeq.1.9 ms while the time of flight of a photon
through the sample 20 .tau.=Ln/c.apprxeq.25 ps.
[0111] Then, the total energy radiated from the sample of the
fluorescent material via the emission of a superradiant pulse may
be obtained by integrating Equation (8) over time, which yields
E SR = hc .lamda. F .tau. c .tau. s .mu. N 2 2 [ 1 + tanh ( .tau. D
2 .tau. c ) ] . ( 10 ) ##EQU00004##
[0112] In order to apply the model used by Dicke to the embodiment
of FIG. 5 to which the laser cooling method 100 illustrated in FIG.
3 is applied, the trivalent ytterbium ions Yb.sup.3+ of the
Yb.sup.3+:ZBLAN sample 20 may be described with two-level model for
absorption and emission processes between the ground-state
.sup.2F.sub.7/2 and the excited-state .sup.2F.sub.5/2 manifolds. In
this case, it has been shown by Dicke that the correlation
self-formation time .tau..sub.c and the formation delay time
.tau..sub.D may be calculated using the following relations
.tau. c = .tau. s N .mu. , ( 11 ) .tau. D = .tau. c ln ( N .mu. ) .
( 12 ) ##EQU00005##
[0113] Moreover, the population density N.sub.2 in the excited
state manifold changes with time and should satisfy the
relation:
N 2 t = P p ( t ) A eff .lamda. p hc [ .sigma. abs ( .lamda. p ) N
1 ( t ) - .sigma. es ( .lamda. p ) N 2 ( t ) ] - N 2 ( t ) .tau. s
( 13 ) ##EQU00006##
where P.sub.p(t) is the instantaneous pump power at the pump
wavelength .lamda..sub.p at time t, .sigma..sub.abs(.lamda..sub.p)
and .sigma..sub.se(.lamda..sub.p) respectively the absorption and
emission cross-sections at the pump wavelength .lamda..sub.p,
respectively, and N.sub.1(t) is the population density of the
ground-state manifold at time t. It will be understood that the
total density N.sub.T of Yb.sup.3+ ions is constant in time and is
given by N.sub.1(t)+N.sub.2(t)=N.sub.T.
[0114] Referring back to the embodiment of FIG. 5, the pump laser
beam 24 has a pump power P.sub.p and includes laser pulses 26
having a pulse duration .tau..sub.p and a rectangular pulse shape.
In this particular case, the number of excited Yb.sup.3+ ions in
the sample 20 of length L is given by
N = L .sigma. abs N T .tau. p P p .lamda. p hc . ( 14 )
##EQU00007##
[0115] For this particular embodiment, with a pump power
P.sub.p=433.5 W and a pulse duration .tau..sub.p=10 ns, the number
of the trivalent ytterbium ions Yb.sup.3+ in the sample 20 of
Yb.sup.3+:ZBLAN participating in the cooling process with
superradiance is approximately equal to N=6.times.10.sup.12
ions.
[0116] Then, due to the process of thermalization mentioned above,
some of the excited electrons may be promoted from the bottom to
the top of the excited-state manifold (e.g. .sup.2F.sub.5/2 for the
exemplary embodiment of FIG. 5) by absorbing the energy of phonons,
which, as known in the art, are responsible for heat generation in
the sample, as illustrated schematically in the inset of the graph
shown in FIG. 6 (PRIOR ART). As a result, anti-Stokes fluorescence
emission of photons may follow with mean photon energy
E.sub.F=h.nu..sub.F, where .nu..sub.F=c/.lamda..sub.F is the mean
frequency of anti-Stokes photons, which is higher than the energy
E.sub.p of the laser pulses of the pump laser beam. As will be
understood by one skilled in the art, this anti-Stokes emission may
remove energy from the sample and realize an optical cooling
thereof.
[0117] As known in the art, the time in which energy is removed
from the sample via incoherent anti-Stokes fluorescence cooling is
of the order of .tau..sub.s, which corresponds to the time of
spontaneous relaxation. Hence, the emission power of incoherent
anti-Stokes fluorescence is equal to
P SP = Nhc .tau. s .lamda. F . ( 15 ) ##EQU00008##
[0118] On the other hand, considering Equation (10), the power
P.sub.SR removed from the sample of the fluorescent material by the
superradiant pulse, which corresponds to the energy E.sub.SR
removed from the sample per cooling cycle, is given by
P SR = hc .lamda. F .tau. c .tau. s 1 .tau. cool SR .mu. N 2 2 [ 1
+ tanh ( .tau. D 2 .tau. c ) ] , ( 16 ) ##EQU00009##
where .tau..sub.cool.sup.SR is the time duration of the
superradiant cooling cycle, which is equal to the sum of the pump
pulse duration .tau..sub.p and the formation delay time .tau..sub.D
of the superradiant pulses.
[0119] Comparing Equations (15) and (16), one may calculate the
ratio C of the power P.sub.SR removed from the sample via
superradiance to the power P.sub.SP removed from the sample via
incoherent anti-Stokes fluorescence, which is given by
C = .tau. c .tau. cool SR .mu. N 2 [ 1 + tanh ( .tau. D 2 .tau. c )
] . ( 17 ) ##EQU00010##
[0120] The parameter C thus characterizes the increase in the
radiative relaxation rate with superradiance with respect to the
radiative relaxation rate with incoherent anti-Stokes fluorescence.
Moreover, one may also define an effective radiative relaxation
time as {tilde over (.tau.)}.sub.s=.tau..sub.s/C, so as to
characterize the rate of electron relaxation in the superradiance
regime compared to the rate of spontaneous relaxation
.tau..sub.s.
[0121] Hence, if C>1, then {tilde over
(.tau.)}.sub.s<.tau..sub.s and the energy leaves the sample
faster with the laser cooling method 100 with superradiance
according to embodiments of the invention than traditional cooling
experiments based on the emission of incoherent anti-Stokes
fluorescence. For example, in the embodiment of FIG. 5, the sample
20 of ZBLAN doped with Yb.sup.3+ with the material and geometrical
properties given above has a value of C=1.4.times.10.sup.5 when the
pump power P.sub.p=433.5 W. The behavior of C as a function of
P.sub.p is illustrated in FIG. 11. As a result, the energy removed
from the sample 20 of Yb.sup.3+:ZBLAN by the superradiant pulses 28
is, at each second of the cooling cycle, larger by a factor of
about 10.sup.5 than the energy that would be removed with
incoherent anti-Stokes fluorescence. The laser cooling method 100
may thus yield a significant increase (i.e. by a factor of about
10.sup.5 in some embodiments) of the radiative relaxation rate
compared to other laser cooling methods known in the art.
[0122] The cooling efficiency per cooling cycle of superradiant
cooling may be determined from the ratio of the energy E.sub.SR
removed from the sample 20 by a superradiant pulse 28 to the energy
of a pulse 26 of the pump laser beam 24, during one cooling cycle.
Using Equation (10) and the fact that the energy absorbed by the
sample from the laser pulse 26 is equal to Nh.nu..sub.p, the
superradiant cooling efficiency per cooling cycle is given by
.eta. cool SR = v F v p .tau. cool SR .tau. s C - 1 ( 18 )
##EQU00011##
[0123] Referring to FIG. 7, there are shown computer simulations
made from Equation (18). The superradiant cooling efficiency per
cooling cycle provided by the laser cooling is method 100 according
to embodiments of the invention is compared with the anti-Stokes
cooling efficiency per cooling cycle, which may be expressed as
.rho..sub.cool.sup.SP=.nu..sub.F/.nu..sub.p-1 and has been
calculated by Luo et al. and by Allain et al. [see X. Luo et al.
Opt. Lett. vol. 23, p. 639 (1998) and J. Y Allain et al., Electron.
Lett. vol. 28, p. 988 (1992)]. It is to be noted that in both
cases, non-radiative relaxations in the host have not been taken
into account.
[0124] Upon examining FIG. 7, one skilled in the art will recognize
that, in this embodiment, heat removal with the laser cooling
method 100 with superradiance described herein is about twice as
effective as incoherent anti-Stokes cooling. However, it should be
emphasized that since the time duration .tau..sub.cool.sup.SR of
the superradiant cooling cycle is shorter by a factor
.tau..sub.cool.sup.SR/.tau..sub.s than the time of the traditional
anti-Stokes cooling cycle, which in some embodiments may be as
large as 10.sup.5. Hence, the cooling efficiency per unit with
superradiance may increase considerably compared to that provided
by incoherent anti-Stokes fluorescence.
[0125] It should also be noted that in order to generate
superradiant pulses, the number of N excited ions in the sample of
the fluorescent material should be in excess of a threshold value
N.sub.th, which may be calculated by using the right in inequality
of Equation (6) and by taking into account that
.tau..sub.c=.tau..sub.s/(.mu.N), such that:
N th > .tau. s .tau. 2 .mu. . ( 19 ) ##EQU00012##
[0126] According to the laser cooling method 100 of the present
invention, this threshold value may preferably be reduced by
increasing the pump power P.sub.p of the pump laser beam or the
total density N.sub.T of the rare-earth ions in the host material.
Furthermore, N.sub.th also decreases when the temperature of the
sample decreases since .tau..sub.2 increases is as the temperature
of the sample drops.
[0127] In summary the coherence introduced in the cooling process
with a superradiant pulse permits a noticeable increase of the
cooling rate, thus increasing the efficiency of the laser cooling
method 100 in comparison with traditional cooling with anti-Stokes
fluorescence of low phonon hosts.
[0128] Following the traditional experiments devoted to laser
cooling with incoherent anti-Stokes fluorescence, one may consider
that in the embodiment shown in FIG. 5, the sample 20 of
Yb.sup.3+:ZBLAN that is cooled with superradiance is mounted in a
vacuum chamber (not shown) and only the radiative heat load is
present. In this case, the temperature of the sample of the
fluorescent material may be calculated from the equation:
2.pi.rL.di-elect
cons..sigma..sub.B(T.sub.amb.sup.4-T.sub.s.sup.4)=P.sub.cool.sup.SR,
(20)
where .di-elect cons. is the hemispherical emissivity of the
sample, .sigma..sub.B=5.67.times.10.sup.-8 Wm.sup.-2K.sup.-4 is the
Stefan-Boltzmann constant, .tau..sub.amb is the ambient temperature
in the vacuum chamber, T.sub.s is the sample temperature to be
determined and P.sub.cool.sup.SR is the cooling power with SR.
[0129] The cooling power per single pump pulse is the difference
between the energy Nhc/.lamda..sub.p absorbed by the sample of the
fluorescent material from the laser pulse of the pump laser beam
and the energy E.sub.SR of the superradiant pulse radiated by the
sample [see Equation (10)], divided by the time duration
.tau..sub.cool.sup.SR=.tau..sub.p+.tau..sub.D of the cooling cycle,
which is equal to the sum of the laser pulse duration .tau..sub.p
and the formation delay time of the superradiant pulse .tau..sub.D.
The evolution of the number of pump pulses as a function of is
sample temperature T.sub.s is illustrated in FIG. 12, again for a
peak power of the pump laser P.sub.p=433.5 W and a pulse duration
.tau..sub.p=10 ns.
[0130] The cooling rate per cycle in the superradiance regime may
be described by the expression
P.sub.cool.sup.SR/.tau..sub.cool.sup.SR, which represents the ratio
of the cooling power P.sub.cool.sup.SR leaving the sample of the
fluorescent material during a cooling cycle in the superradiance
regime to the duration .tau..sub.cool.sup.SR of the cooling cycle.
Similarly, when a sample is pumped with a CW laser so as to
generate optical via incoherent anti-Stokes fluorescence, the
duration of the cooling cycle corresponds to the lifetime
.tau..sub.s of the excited level and the cooling rate per cycle is
given by P.sub.cool.sup.SR/.tau..sub.s. The cooling power of
incoherent anti-Stokes fluorescence may then be calculated with the
following expression [see X. Luo et al., Opt. Lett. vol. 23, p. 639
(1998)]:
P cool SP = VN ( .lamda. p .lamda. F - 1 ) I s .sigma. abs (
.lamda. p ) [ 1 + .sigma. se ( .lamda. p ) .sigma. abs ( .lamda. p
) ] + I s A eff P p ( 21 ) ##EQU00013##
where
I.sub.s=hc/[.tau..sub.s.lamda..sub.p.sigma..sub.abs(.lamda..sub.p)]-
, and V is the volume of the sample of the fluorescent
material.
[0131] From Equation (21), it will be understood by one skilled in
the art that the cooling rate P.sub.cool.sup.SR/.tau..sub.s with
incoherent anti-Stokes fluorescence depends on the value of the
pump power P.sub.p of the pump laser beam, that is,
P.sub.cool.sup.SR/.tau..sub.s increases as P.sub.p increases. FIG.
7 illustrates the variation of the cooling rate
P.sub.cool.sup.SR/.tau..sub.cool.sup.SR and
P.sub.cool.sup.SR/.tau..sub.s as a function of the pump power
P.sub.p for cooling with superradiance and incoherent anti-Stokes
fluorescence, respectively. As can be understood by one skilled in
the art upon examining FIG. 7, the cooling rate
P.sub.cool.sup.SR/.tau..sub.cool.sup.SR with superradiance exceeds
considerably the cooling rate P.sub.cool.sup.SR/.tau..sub.s with
the anti-Stokes fluorescence. In particular, although both cooling
rates increase with increasing pump power, the slope is greater
with is superradiance cooling. In particular, in the superradiance
regime, the formation delay time .tau..sub.D of the superradiant
pulse, and, thus duration
.tau..sub.cool.sup.SR=.tau..sub.p+.tau..sub.D of the cooling cycle,
decreases with increasing pump power, as shown in FIG. 9, thereby
providing a steeper slope for
P.sub.cool.sup.SR/.tau..sub.cool.sup.SR as a function of
P.sub.p.
[0132] As mentioned above, an ion (e.g. a rare-earth ion) that has
been promoted to an excited state may decay non-radiatively via
interactions with optical phonons of the host material. In the
context of laser cooling of materials, non-radiative decay caused
undesired heating of the sample. The competition between radiative
and non-radiative decays may be characterized by the internal
quantum efficiency .eta. of Equation (2), wherein the non-radiative
rate W.sub.nr due to multiphonon transition given above in Equation
(4) can be rewritten as
W nr = W 0 [ 1 - exp ( - E ph / k B T ) ] n p , ( 22 )
##EQU00014##
where W.sub.0=B exp(-.alpha..DELTA.E.sub.8) is the spontaneous
transition rate T=0 K due to the zero-point fluctuations of the
phonon field, E.sub.ph is the dominant phonon energy and .DELTA.E
is the energy gap that is bridged by the emission of n.sub.p
phonons. As mentioned above, the internal quantum efficiency .eta.
reduces the cooling efficiency provided by the sample of the sold
material to .eta..sub.cool=.eta..lamda..sub.p/.lamda..sub.F-1 [see
Equation (3)].
[0133] In the superradiance regime, since the radiative relaxation
time {tilde over (.tau.)}.sub.s=.tau..sub.s/C decreases
significantly compared to the spontaneous relaxation time
.tau..sub.s, the radiative relaxation is rate W.sub.r increases
accordingly. As previously mentioned, in the case of the sample 20
of Yb.sup.3+:ZBLAN considered in the embodiment of FIG. 5, the
radiative relaxation rate IN, increases approximately by a factor
of 10.sup.5 in the superradiance regime.
[0134] As consequence, the laser cooling method 100 with
superradiance according to embodiments of the invention may
increase the internal quantum efficiency .eta. given in Equation
(3) significantly compared to the case of traditional cooling with
anti-Stokes fluorescence and this, independently of the nature of
the host material.
[0135] It should also be noted that, in general, the radiative
relaxation rate IN, only slightly depends of the nature of host
material in comparison with the non-radiative relaxation rate
W.sub.nr. As a result, the laser cooling method 100 with
superradiance of the present invention may allow using host
materials characterized by a considerably higher value for the
non-radiative rate W.sub.nr, and thus maximum phonon energy
h.omega..sub.max, than traditional hosts used for anti-Stokes
fluorescence cooling, while still maintaining a suitably high value
for the internal quantum efficiency .eta., as may be understood
from Equation (2). Indeed, in the superradiance regime, the
condition given in Equation (5) is relaxed as higher phonon energy
host materials may be used, and bridging the gap with fewer phonons
may be allowed. It will be understood that even though the
probability for the transitions increase exponentially, the
probability of multiphonon absorption decreases as an exponential
function of the number of phonons n.sub.p [see, e.g., Equation
(22)].
[0136] For example, the laser cooling method 100 with superradiance
according to embodiments of the invention may allow cooling down a
sample composed of a silica host doped with rare-earth ions and
having a maximum phonon energy h.omega..sub.max.apprxeq.1100
cm.sup.-1 (or other rare-earth-doped hosts with similar maximum
phonon energies) with an internal quantum efficiency .eta. that is
similar to that observed in cooling of rare-earth-doped
low-energy-phonon host with incoherent anti-Stokes
fluorescence.
[0137] Furthermore, as known in the art, laser cooling of
rare-earth-doped solids with incoherent anti-Stokes fluorescence
ceases at about 77 K since, as known in the art, the phonon number
decreases exponentially with decreasing temperature. On the
contrary, due to the considerably high rate of radiation
de-excitation of superradiant pulses, the embodiments of the laser
cooling method 100 may break this limitation so that
rare-earth-doped solid materials may be laser cooled below 77 K. It
should also be emphasized that an important feature of the laser
cooling method 100 is the recognition that the increased relaxation
rate achievable in the superradiance regime plays a role in
accelerating the cooling process in comparison to traditional laser
cooling methods known in the art and based on incoherent
anti-Stokes fluorescence.
[0138] Additionally, the laser cooling method 100 described herein
opens up new possibilities for designing entirely solid-state
optical coolers since, as shown in FIG. 5, the superradiance regime
facilitates removal from the sample 20 of the heat extracted
thereto due to the high directionality of the emitted superradiant
pulses 28 along the elongated direction 22. In particular, the
laser cooling method 100 allows for a significant reduction of the
risks of re-absorbing energy, and thus of re-heating the sample 20,
in comparison to traditional anti-Stokes fluorescence cooling,
wherein fluorescence is emitted uniformly in all directions over a
solid angle of 4.pi..
[0139] Finally, in embodiments where the fluorescent material is a
rare-earth-doped host material, the laser cooling method 100
described herein broadens the range of host materials that can be
used for laser cooling to host materials having a higher maximum
phonon energy (e.g. silica, polymers, semiconductors, borosilicate
glasses and other crystals with high phonon energies), which have
been so far considered unsuitable as rare-earth-doped hosts for
laser cooling applications.
Method for Cooling a Fluorescent Material Using Two Simultaneous
Cooling Cycles
[0140] According to another aspect of the invention, there is
provided a second method 200 for cooling a fluorescent material.
Referring to FIG. 14, there is shown a flow chart of an embodiment
of the method 200.
[0141] The method 200 according to this aspect of the invention
generally relates to the laser cooling of fluorescent materials
combining simultaneously a traditional anti-Stokes cooling cycle
and an upconversion cooling cycle, in such a way as to help to
overcome the self-termination effects that may present in either of
these two cooling cycles when used on its own.
[0142] As mentioned before, the traditional cooling cycle is based
on the emission of incoherent anti-Stokes florescence involving the
emission of photons having higher energy than the photons absorbed
from an excitation pump source. Hence, net anti-Stokes fluorescence
may cause removal of energy from an illuminated material and, as a
consequence, its refrigeration.
[0143] As also previously mentioned, the upconversion cooling cycle
may rely on the infrared-to-visible upconversion process which is
often found in rare-earth-doped low-phonon-energy host material due
to the reduced multiphonon transition thereof. As understood
herein, the term "upconversion" broadly refers to a process by
which a material emits light with photon energies higher than those
of the light generating the excitations. For example, in the
infrared-to-visible upconversion process, at least two low-energy
infrared photons are required to generate one high-energy visible
photon. In upconversion fluorescence, at least two photons are
absorbed during the excitation process of an electron, such that
the emitted photon resulting from the de-excitation of the electron
has a shorter wavelength than the absorbed photons. Hence, these
excited-states levels constitute reservoirs of electrons that may
be further excited by absorbing other photons.
[0144] As one skilled will understand, upconversion may be
accomplished by several multiphoton mechanisms. As used herein, the
expression "multiphoton absorption" is understood to refer to a
process by which an electron in a material is excited by more than
one photon (i.e. two or more) from a single pump source. For
example, one mechanism known as excited state absorption (ESA)
involves sequential absorption of pump photons. A first absorption
typically leads to some metastable excited level with a relatively
long lifetime. Then, an ion that has been excited to that
metastable level is promoted into a higher excited level by at
least one other photon from where it later decays spontaneously. As
known in the art, ESA typically involves high pump power values,
but not necessarily high doping concentrations.
[0145] Another mechanism, referred to as energy-transfer
upconversion (ETU), involves energy transfer between two different
ions in the material. In this case, two electrons of two different
ions interact with each other and, as a result, one of them decays
to a lower lying state while the other is promoted to a higher
energy state. As opposed to ESA, ETU generally involves high doping
concentrations.
[0146] In a further mechanism, multiphoton absorption may consist
in the excitation of an electron by the absorption of two or more
photons that allow this electron to acquire the energy
corresponding to the energy difference between two electronic
levels by going through intermediate virtual levels.
[0147] Referring to FIG. 14, the laser cooling method 200 first
involves a step 202 of providing a sample of the fluorescent
material, the fluorescent material having an absorption spectrum
comprising at least one absorption band, each of the at least one
absorption band having a corresponding maximum absorption
wavelength.
[0148] As discussed above, the laser cooling method 200 may be
employed for cooling a fluorescent material that may be a solid
material composed of a rare-earth-doped host material. The
rare-earth ions may be trivalent rare-earth ions, preferably
Er.sup.3+, Tm.sup.3+ and Yb.sup.3+. Likewise, the host material may
be a transparent glass or crystal, for example fluoride or chloride
glasses and crystals having low phonon energy.
[0149] In an embodiment of the method 200, the fluorescent material
is a potassium-lead chloride host crystal KPb.sub.2Cl.sub.5 doped
with trivalent erbium ions (Er.sup.3+), which is known as an
particularly low-phonon-energy crystal (e.g. the maximum phonon
energy is about 203 cm.sup.-1. In other embodiments, the
fluorescent material may be selected from other rare-earth-doped
host materials in which net laser cooling has been observed.
[0150] In other embodiments, the fluorescent material may be a
fluoride glass doped with Yb.sup.3+ (e.g. Yb.sup.3+:ZBLAN,
Yb.sup.3+:ZBLANP, Yb.sup.3+:BIG, Yb.sup.3+:ABCYS), a
fluoro-chloride glass doped with Yb.sup.3+ (e.g. Yb.sup.3+:CBNZn),
an oxide crystal doped with Yb.sup.3+[e.g.
Yb.sup.3+:KGd(WO.sub.4).sub.2, Yb.sup.3+:KY(WO.sub.4).sub.2,
Yb.sup.3+:YAG, Yb.sup.3+:Y.sub.2SiO.sub.5], a fluoride crystal
doped with Yb.sup.3+ (e.g. Yb.sup.3+:BaY.sub.2F.sub.8,
Yb.sup.3+:YLF), a chloride crystal doped with Yb.sup.3+ (e.g.
Yb.sup.3+: KPb.sub.2Cl.sub.5), a fluoride glass doped with
Tm.sup.3+ (e.g. Tm.sup.3+:ZBLAN), a fluoride crystal ici doped
Tm.sup.3+ (e.g. Tm.sup.3+:BaY.sub.2F.sub.8), or a fluoro-chloride
glass doped Er.sup.3+ (e.g. Er.sup.3+:CNBZn) [see, e.g., Table 1 in
G. Nemova and R. Kashyap, Rep. Prog. Phys. vol. 73, p. 086501
(2010)].
[0151] In further embodiments, the fluorescent material may be
ceramic glasses, crystals, is polymers, semiconductors,
chalcogenide glasses, with nanoparticles or quantum dots. In still
further embodiments, the fluorescent material may be a liquid or a
gaseous material.
[0152] In the present description, the term "absorption spectrum"
is understood to refer to a spectrum of radiant energy over a range
of wavelengths whose intensity at each wavelength corresponds to a
measure of the fraction of incident radiation that is absorbed by a
material. As known in the art, the absorption spectrum depends
mostly on the composition of the material since absorption is more
likely to take place at photon energies corresponding to the energy
difference between two energy levels in the material. Likewise, the
expression "absorption band" is understood herein to refer a range
of energies or wavelengths in the absorption spectrum which are
capable of exciting a particular transition in material. Moreover,
the "maximum absorption wavelength" of a particular absorption band
refers to the wavelength beyond which an excitation photon cannot
excite the transition associated with that absorption band.
[0153] Referring to FIG. 15, there is shown the energy levels of
the rare-earth ion Er.sup.3+ in a KPb.sub.2Cl.sub.5 host crystal,
to which the laser cooling method 200 may be applied. As can be
seen from this diagram, the absorption spectrum of
Er.sup.3+:KPb.sub.2Cl.sub.5 includes two absorption bands
corresponding to the .sup.4I.sub.15/2.fwdarw..sup.4I.sub.13/2 and
.sup.4I.sub.15/2.fwdarw..sup.4I.sub.9/2 transitions. The
wavelengths corresponding to these transitions are 1530 nm and 810
nm, respectively.
[0154] Referring back to FIG. 14, the laser cooling method 200 next
involves a step 204 of illuminating the sample of the fluorescent
material with a first pump laser beam having a first pump
wavelength that is longer than the corresponding maximum absorption
wavelength of one of the at least one absorption band, so as to
generate an anti-Stokes cooling cycle. As one skilled in the art
will understand, the step 204 of illuminating the sample with the
first pump laser consists in producing optical cooling is via a
traditional anti-Stokes cooling cycle, the characteristics of which
have been described above and shown, for example, in FIG. 2 (PRIOR
ART).
[0155] In the embodiment shown in FIG. 15, the absorption band
excited by the first pump laser beam corresponds to the
.sup.4I.sub.15/2.fwdarw..sup.4I.sub.13/2 transition of
Er.sup.3+:KPb.sub.2Cl.sub.5, which has maximum absorption
wavelength equal to 1530 nm. Hence, according to the current method
200, a suitable wavelength .lamda..sub.p.sup.(1) for the first pump
laser beam may be .lamda..sub.p.sup.(1)=1567 nm, but may also have
a different value, as long as .lamda..sub.p.sup.(1)=1530 nm.
[0156] Referring again to FIG. 14, the laser cooling method 200
involves, simultaneously to the previous step 202, a step 204 of
illuminating the sample of the fluorescent material with a second
pump laser beam having a second pump wavelength, the second pump
wavelength being selected for exciting electrons of the fluorescent
material so as to generate an upconversion cooling cycle. As a
result, the anti-Stokes and the upconversion cooling cycles act
cooperatively to induce a cooling of the sample of the fluorescent
material.
[0157] As known in the art, the first and second pump laser beams
according to the laser cooling method 200 may be produced by a
laser source, which may be embodied, for example, by an
electrically-pumped semiconductor lasers, an optically-pumped
solid-state laser, an optical fiber laser, a solid state
amplification system, an optical parametric amplification system, a
fiber amplification system, a chirped pulse amplification system, a
combination of these lasers and amplification systems, or the
like.
[0158] As mentioned above, the upconversion cooling cycle according
to this laser cooling method 200 may involve different mechanisms,
including ESA, ETU, multiphoton absorption through virtual levels,
or a combination thereof. Hence, it will be understood herein that
the wavelength .lamda..sub.p.sup.(2) of the second pump laser beam
may, but need not, correspond to any absorption band of the
fluorescent material and need not be able to excite an electron
other than by a multiphoton absorption process.
[0159] In an embodiment of the invention, the laser cooling method
200 is performed on a sample of Er.sup.3+:KPb.sub.2Cl.sub.5, that
is, by applying simultaneously thereto a traditional anti-Stokes
cooling cycle and an upconversion cooling cycle. The
Er.sup.3+:KPb.sub.2Cl.sub.5 sample is considered to be pumped
simultaneously at a first and a second pump wavelengths equal to
.lamda..sub.p.sup.(1)=1567 nm and .lamda..sub.p.sup.(1)=860 nm, as
illustrated in FIG. 15. The first pump laser beam at a pump power
value P.sub.p.sup.(1) provides cooling via a traditional
anti-Stokes cooling cycle, while the second pump laser beam at a
pump power value P.sub.p.sup.(2) provides cooling via an
upconversion cooling cycle. Contrary to the case wherein
Er.sup.3+:KPb.sub.2Cl.sub.5 is cooled with the traditional cooling
cycle alone, in the embodiment of FIG. 15, the .sup.4I.sub.13/2 is
additionally populated with electrons which relax from higher lying
levels (e.g. .sup.4I.sub.9/2, .sup.4S.sub.3/2,
.sup.2H.sub.9/2).
[0160] Upconversion processes in Er.sup.3+-doped KPb.sub.2Cl.sub.5
have been investigated in details by Galba et al. [see R. Balda et
al., Phys. Rev. B vol. 69, p. 205203 (2004)]. As shown therein, the
energy gap between the .sup.4I.sub.9/2 and .sup.4I.sub.11/2 levels
in chloride systems is too large to be effectively bridged by
multiphonon relaxation so that, in this case, the .sup.4I.sub.9/2
level acts as an intermediate level for upconversion processes,
contrary to oxide and fluoride systems wherein excitation into the
.sup.4I.sub.9/2 level is followed by fast non-radiative decay to
the .sup.4I.sub.11/2 level due to the relatively high phonon
energies.
[0161] Furthermore, it will be understood that the population
dynamics of the electronic levels taking part in the simultaneous
traditional and upconversion cooling cycles may be taken into
account by the following set of rate equations:
N 1 t = I p ( 1 ) .lamda. p ( 1 ) hc [ .sigma. a ( 1 ) N 0 -
.sigma. e ( 1 ) N i ] - N 1 .tau. 1 + .beta. 21 N 2 .tau. 2 +
.beta. 31 N 3 .tau. 3 + .beta. 41 N 4 .tau. 4 + .gamma. 2 N 2 2 - 2
.gamma. 1 N 1 2 , ( 23 ) N 2 t = I p ( 2 ) .lamda. p ( 2 ) hc [
.sigma. a ( 2 ) N 0 - .sigma. e ( 2 ) N 2 ] - .beta. 20 N 2 .tau. 2
- .beta. 21 N 2 .tau. 2 - 2 .gamma. 2 N 2 2 - .sigma. ESA ( 24 ) I
p ( 2 ) .lamda. p ( 2 ) hc N 2 + .gamma. 1 N 1 2 + .sigma. e ( 2 )
I p ( 2 ) .lamda. p ( 2 ) hc N 4 - .sigma. ESA ( 23 ) I p ( 1 )
.lamda. p ( 1 ) hc N 2 , N 3 t = - .beta. 30 N 3 .tau. 3 - .beta.
31 N 3 .tau. 3 + .gamma. 2 N 2 2 + .sigma. ESA ( 23 ) I p ( 1 )
.lamda. p ( 1 ) hc N 2 , N 4 t = I p ( 2 ) .lamda. p ( 2 ) hc [
.sigma. ESA ( 24 ) N 2 - .sigma. e ( 2 ) N 4 ] - .beta. 40 N 4
.tau. 4 - .beta. 41 N 4 .tau. 4 , with N T = N 0 + N 1 + N 2 + N 3
+ N 4 , ( 24 ) ##EQU00015##
where N.sub.i (i=0, . . . , 4) and .tau..sub.i are respectively the
population and radiative lifetime of the i.sup.th level, N.sub.T is
the total density of active ions in the sample, while .beta..sub.i0
and .beta..sub.i1 are respectively the branching ratios for the i
to 0 and i to 1 transition. Moreover, .gamma..sub.1 is the strength
of the ETU process, by which one electron in level .sup.4I.sub.13/2
decays to the .sup.4I.sub.15/2 and, at the same time, another
electron in a different ion is promoted from the .sup.4I.sub.13/2
level to the .sup.4I.sub.9/2 energy level. Likewise, .gamma..sub.2
is the strength of the ETU process in which one electron in level
.sup.4I.sub.9/2 decays to the .sup.4I.sub.13/2 and, at the same
time, another electron in a different ion is promoted from the
.sup.4I.sub.9/2 level to the .sup.4S.sub.3/2 energy level. Finally,
.sigma..sub.ESA.sup.(23) is the ESA cross-section at the pump
wavelength .lamda..sub.p.sup.(1), .sigma..sub.ESA.sup.(23) is the
ESA cross-section at the pump wavelength .lamda..sub.p.sup.(2), and
I.sub.p.sup.(1) and I.sub.p.sup.(2) are the pump intensities at the
wavelengths .lamda..sub.p.sup.(1) and .lamda..sub.p.sup.(2),
respectively.
[0162] In the general case, the system of Equation (24) cannot be
solved analytically. However, analytical approximations may be used
to find a solution to the system is under the reasonable
approximations that the radiative components are much larger than
the other terms that depopulate the level. This condition may be
expressed mathematically by the following inequalities:
N 1 .tau. 1 , N 2 .tau. 2 , N 3 .tau. 3 >> .gamma. 1 N 1 2 ,
.gamma. 2 N 2 2 ( 25 ) ##EQU00016##
[0163] At steady-state, the populations of the levels satisfies the
relation dN.sub.i/dt=0, with i=0, . . . , 4. As a result, the net
cooling power deposited into the sample may be expressed as
P cool = - A eff L { I p ( 1 ) [ .sigma. a ( 1 ) N 0 - .sigma. e (
1 ) N 1 ] + I p ( 2 ) [ .sigma. a ( 2 ) N 0 - .sigma. e ( 2 ) N 2 +
.sigma. ESA ( 24 ) N 2 - .sigma. e ( 2 ) N 4 ] } + A eff Lhc ( N 1
.tau. 1 .lamda. ~ 1 + .beta. 20 N 2 .tau. 2 .lamda. ~ 20 + .beta.
21 N 2 .tau. 2 .lamda. ~ 21 + .beta. 30 N 3 .tau. 3 .lamda. ~ 30 +
.beta. 31 N 3 .tau. 3 .lamda. ~ 31 + .beta. 40 N 4 .tau. 4 .lamda.
~ 40 + .beta. 41 N 4 .tau. 4 .lamda. ~ 41 ) + .alpha. b I ( 26 )
##EQU00017##
where .alpha..sub.b is the background absorption coefficient and
A{tilde over (.lamda.)}.sub.ij is the mean fluorescence wavelength
for the i.fwdarw.j transition. Using Equation (26), it may be
possible to calculate the net cooling power deposited into the
sample as function of the pump power of the first and second pump
laser beams at wavelengths .lamda..sub.p.sup.(1) and
.lamda..sub.p.sup.(2), respectively.
[0164] In an embodiment of the laser cooling method 200 according
to an aspect of the invention, a cylindrical sample of a
KPb.sub.2Cl.sub.5 host material doped with Er.sup.3+ is pumped
simultaneously with a first and a second pump laser beams at
wavelengths .lamda..sub.p.sup.(1)=1567 nm and
.lamda..sub.p.sup.(2)=860 nm. The first pump laser beam provides
cooling with a traditional anti-Stokes cooling cycle that involves
the .sup.4I.sub.15/2 and .sup.4I.sub.13/2 levels. One skilled in
the art will recognize that this is the same transition used in
optical communications is in the 1500 nm window, so that lasers at
this frequency are well developed. The second pump source provides
cooling based on an upconversion cycle, which includes the
.sup.4I.sub.15/2, .sup.4I.sub.9/2 and .sup.2H.sub.9/2 levels.
[0165] Referring to Equation (5), in some embodiments of the laser
cooling method 200, the values of the first and second pump
wavelengths .lamda..sub.p.sup.(1) and .lamda..sub.p.sup.(2) are
preferably selected so as to yield pump photon energies
E.sub.p.sup.(1)=hc/4.sup.1) and
E.sub.p.sup.(2)=hc/.lamda..sub.p.sup.(2) equal to at least eight
times a maximum phonon energy h.omega..sub.max of the host
material.
[0166] To perform the simulations presented below in FIGS. 16 and
17, the spectroscopic properties of Er.sup.3+:KPb.sub.2Cl.sub.5
crystals were used based on investigations performed by other
workers in the field [see, R. Balda et al., Phys. Rev. B vol. 69,
p. 205203 (2004), Z. Hasan et al., Proc. SPIE vol. 7228, p. 72280H
(2009) and A. Ferrier et al., J. Opt. Soc. Am. B vol. 24, p. 2526
(2007)]. The absorption spectra for the
.sup.4I.sub.15/2.fwdarw..sup.4I.sub.13/2 and
.sup.4I.sub.15/2.fwdarw..sup.4I.sub.9/2 transitions are illustrated
in K. Nitsch et al., J. Cryst. Growth vol. 131, p. 612 (1993) (see,
respectively, FIGS. 6 and 3 therein), while the excited-state
absorption cross section for the
.sup.4I.sub.9/2.fwdarw..sup.2H.sub.912 transition is illustrated in
A. Ferrier et al., J. Opt. Soc. Am. B vol. 24, p. 2526 (2007) (see
FIG. 7 therein).
[0167] In particular, Ferrier et al. that the ESA cross section for
the .sup.4I.sub.9/2.fwdarw..sup.2H.sub.9/2 transition is comparable
to the ground-state absorption cross section of the
.sup.4I.sub.15/2.fwdarw..sup.4I.sub.9/2 transition. As a result,
one skilled in the art will understand that this means that
upconversion plays a significant role in this optical cooling
process. Moreover, it was shown by is Z. Hasan et al. that the
absorption strength of the .sup.4I.sub.15/2.fwdarw..sup.4I.sub.9/2
transition is much weaker than that of the
.sup.4I.sub.15/2.fwdarw..sup.4I.sub.13/2 transition. Hence, by
taking into account the extremely weak absorption for the
.sup.4I.sub.15/2.fwdarw..sup.4I.sub.9/2 transition, one skilled in
the art may understand why the temperature of the sample dropped by
0.7.+-.0.1 K, thus resulting in an upconversion-based cooling cycle
with a very low cooling efficiency.
[0168] On the contrary, in the laser cooling method 200 described
herein, the Er.sup.3+:KPb.sub.2Cl.sub.5 sample is pumped
simultaneously with two pump laser beams so as produce a
traditional anti-Stokes cooling cycle and an upconversion cooling
that act cooperatively to induce a cooling of the sample. Using
Equation (26), it is possible to calculate the net cooling power
P.sub.cool deposited in the sample as a function of the pump powers
P.sub.p.sup.(1) and P.sub.p.sup.(2) of the first and second pump
laser beams, respectively. In the simulations presented in FIGS. 16
and 17, the diameter and length of the cylindrical sample of
Er.sup.3+:KPb.sub.2Cl.sub.5 are D=3 mm and L=3 mm.
[0169] In general, the process of fluorescence re-absorption and
trapping in solid-state optical materials may influence the
efficiency of optical cooling. However, it was shown that the
effect of radiation trapping may be neglected in this range of
diameters [see N.J. Condon et al., Opt. Express vol. 17, p. 5466
(2009)]. Moreover, it was estimated that the depletion of the pump
power over the length of the sample is insignificant so that it was
not taken into account in the simulations.
[0170] Referring now to FIG. 16, there is shown a graph of the net
cooling power P.sub.cool of a sample of Er.sup.3+:KPb.sub.2Cl.sub.5
as a function of the pump power P.sub.p.sup.(1) of the first pump
laser beam, at a wavelength .lamda..sub.p.sup.(1)=1567 nm, for
different values of the second pump power P.sub.p.sup.(2) of the
second pump laser beam, at a wavelength .lamda..sub.p.sup.(2)=860
nm, according to an embodiment of the laser cooling method 200.
Upon examination of FIG. 16, it may be concluded that adding the
second pump laser beam with pump power P.sub.p.sup.(2) may is
increase the net cooling power P.sub.cool deposited into the
sample, even though the cooling efficiency provided by
P.sub.p.sup.(2) at .lamda..sub.p.sup.(2)=860 nm is relatively weak.
Indeed, a pump power P.sub.p.sup.(2)=2 kW should be provided in
order to increases the net cooling power P.sub.cool deposited into
the sample by about 0.45 .mu.W.
[0171] In some embodiments of the laser cooling method 200, the
sample may be mounted in a vacuum chamber, so that only radiative
heat load takes place. In these embodiments, supplementing a pump
power P.sub.p.sup.(2).apprxeq.2 kW via the second pump laser beam
at .lamda..sub.p.sup.(2)=860 nm may provide an additional 100 K
drop in the temperature of the sample.
[0172] Referring now to FIG. 17, there is shown a graph
illustrating the net cooling power P.sub.cool of a sample of
Er.sup.3+:KPb.sub.2Cl.sub.5 as a function of the pump power
P.sub.p.sup.(2) of the second pump laser beam, at a wavelength
.lamda..sub.p.sup.(2)=860 nm, for different values of the first
pump power P.sub.p.sup.(1) of the first pump laser beam, at a
wavelength .lamda..sub.p.sup.(1)=1567 nm, according to an
embodiment of the invention. Upon examining FIG. 17, it can be seen
that when the value of the pump power P.sub.p.sup.(1) at
.lamda..sub.p.sup.(1)=1567 nm is zero, the net cooling power
P.sub.cool deposited in the sample is only 0.45 .mu.W, even with a
very high pump power of p.sub.p.sup.(2)=2 kW.
[0173] However, as can be seen from FIG. 17, even a small amount of
supplementary pump power P.sub.p.sup.(1) at
.lamda..sub.p.sup.(1)=1567 nm applied to the sample significantly
affects the value of cooling power P.sub.cool deposited into the
sample and proves that the laser cooling method 200 according to an
aspect of the invention and based on a combination of a traditional
anti-Stokes cooling cycle and an upconversion cooling cycle may be
more is than a cooling cycle based only upconversion. Indeed, the
supplementary pump power P.sub.p.sup.(1)=25 W at
.lamda..sub.p.sup.(1)=1567 nm increases the net cooling power
deposited in the sample by 1.9 .mu.W. Furthermore, in embodiments
of the method 200 wherein the sample of Er.sup.3+:KPb.sub.2Cl.sub.5
is mounted in a vacuum chamber, the supplementary pump power
P.sub.p.sup.(1) may provide an additional 180 K drop in the
temperature of the sample.
[0174] As one skilled in the art will readily understand, broadened
spectral absorption lines at or near room temperature become
significantly narrower and more intense as temperature is lowered.
As the sample cools, the thermal population of those lines
decreases, such that cooling slows and eventually stops. Moreover,
laser cooling is generally sensitive to impurities, for example
hydroxyl ions OH.sup.- or microscopic defects in glasses. Indeed,
impurities open up various pathways for the excitation to decay by
non-radiative relaxation, which thereby cause what can be referred
to as "parasitic heating".
[0175] In summary, the laser cooling process of a sample of
Er.sup.3+:KPb.sub.2Cl.sub.5 pumped simultaneously with two pump
laser beams at wavelengths of 860 nm and 1567 nm has been presented
as an exemplary embodiment of the laser cooling method 200
according to an aspect of the invention. It was shown that
simultaneous pumping of the Er.sup.3+:KPb.sub.2Cl.sub.5 sample at
two wavelengths leads to an increase in the net cooling power
deposited into the sample due to a combination of a traditional
anti-Stokes cooling cycle and an upconversion cooling cycle,
wherein the two cooling cycles act cooperatively to help to
overcome the self-termination effects that may present in either of
the two cooling cycles when used on its own.
[0176] Of course, numerous modifications could be made to the
embodiments described is above without departing from the scope of
the present invention.
* * * * *