ABSTRACT
Expectedly there are challenging issues to be tackled. For example, the purity level of the (undoped) fiber needs to be high to avoid excessive parasitic absorption of photons by impurities. When the fiber cooler and the object to be cooled are macroscopic (centimeter scale or larger), managing the (conductive and convective) heat and photon flows is also a pertinent issue. These and related issues will be discussed below. In Section 3.2, we describe our theoretical developments in this investigation. We discuss the calculation of the cooling powers
of the Tm atoms and of a model isolated fiber and the simulation of heat flow in the cooling of the heat load. In Section 3.3, we discuss experimental progress in fabricating high-purity fiber and temperature measurements under optical pumping conditions. 3.2 Theoretical Developments
3.2.1 Modeling the Cooling of Thulium AtomsThe basic cooling agents in our setup are the thulium (Tm) atoms doping the fiber. We describe in this subsection a photoexcitation model of a Tm atom in a glass host, which we use to estimate its laser cooling efficiency. More detail can be found in [7]. The model, given in Ref. [8], is shown in Fig. 3.2. It consists of four energy levels, each with a degree of degeneracy gi, as designated in the figure. The lower two levels represent the manifold of states created by the splitting of the 13-fold degenerate ground state (3H6) of Tm by interactions with the glass host, and the upper two levels represent the split ninefold excited-state (3F4) manifold. The pump laser energy hn is tuned to the energy between |1> and |2>, which is the lowest excitation energy between the two manifolds. The pumped Tm atoms de-excite (incoherently) to a level in the ground-state manifold via luminescence, at rate Wrad, and nonradiative transitions, at a rate Wnr. If the de-excitation happens sufficiently slowly, the excited atoms have time to thermalize in the excited-state manifold. The luminescent photons are thus at higher energies than that of the pump photons. In each cycle of operation in which a Tm atom absorbs a pump photon and emits a luminescent photon, which then escapes, heat is removed from the system. The population dynamics of the four-level model obeys the following rate equations [8]:
( ) g B/inc1 1 112 1 2 2 3 1 1 02 02 E k TIdN g gRN N N N w N N edt g h g ds n -Ê ˆÊ ˆ= - - + + - -Á ˜Á ˜Ë ¯ Ë ¯ (3.1) u B/inc 32 1
dN dt
RN w N g
2 2= - - -
Ê ËÁ
ˆ ¯˜
-d u B/ (3.3) N N N N Ntotal = + + +0 1 32 (3.4)where Ni and gi are the population density and degree of degeneracy, respectively, of level |i>, and Ntotal is the total density of Tm atoms. The pump laser has intensity Iinc and frequency n. R = 2Wrad + 2Wnr, and s12 denotes the photoabsorption cross section of the Tm atoms. dEg and w1 are the energy difference between the two levels and the intramanifold relaxation rate in the ground-state manifold, and dEu and w2 are the corresponding quantities for the excited-state manifold. T is the sample temperature, and kB is the Boltzmann constant. In Eq. 3.1, the first term on the right side represents stimulated absorption from and emission into the pump laser mode. The second term models the decay of the excited manifold population and the third term the thermalization within a manifold. The terms in Eqs. 3.2 and 3.3 have the same interpretation.
