Recently, a new approach to cool optically pumped solid-state lasers by converting the lattice heat into radiation was presented [Laser Phys.18, 430 (2008)]. It relies on a stimulated radiative process occurring in the laser host material. The internal heat gets partially converted through a four-wave mixing process into a radiating optical field. By adopting a Lorentz oscillator model for the field-atom interaction in the laser host, we identified a shortcut to treat the heating and cooling mechanisms going together with the Stokes and anti-Stokes radiation involved in the four-wave mixing. An energy balance between these mechanisms is derived from the differential equation for the material excitation. This balance will ultimately determine the crystal steady-state temperature. This analysis is the first step towards practical engineering implementations of the optical cooling principle for important new laser systems such as the silicon Raman laser and the Cr-ZnSe laser for the mid-IR.
Recently, a new approach to cool optically pumped solid-state lasers by converting the lattice heat into radiation was presented [Laser Phys.18, 430 (2008)]. It relies on a stimulated radiative process occurring in the laser host material. The internal heat gets partially converted through a four-wave mixing process into a radiating optical field. By adopting a Lorentz oscillator model for the field-atom interaction in the laser host, we identified a shortcut to treat the heating and cooling mechanisms going together with the Stokes and anti-Stokes radiation involved in the four-wave mixing. An energy balance between these mechanisms is derived from the differential equation for the material excitation. This balance will ultimately determine the crystal steady-state temperature. This analysis is the first step towards practical engineering implementations of the optical cooling principle for important new laser systems such as the silicon Raman laser and the Cr-ZnSe laser for the mid-IR.
A vibronic model of laser cooling for crystals doped with Yb3+ ions is proposed. The model involves the stimulated Raman adiabatic passage pumping through dipole-allowed 4f–5d transitions, electron transitions between Stark-split sublevels due to vibronic interaction, and anti-Stokes fluorescence from the excited ion state. Dynamics of the cooling process are described by the density matrix formalism. It is shown that the cooling power in the case of vibronic interaction is higher at least by a factor of 3.4 compared to the case of electron–phonon interaction. In the proposed model, an increase in the cooling power yields deeper and faster refrigeration of a crystal doped with Yb3+ ions. Estimations show that, on cooling by the stimulated Raman adiabatic passage pumping, the temperature of a crystal with an irradiated volume of 2.12×10−4 cm3 can reach 64 K in a time of 2 s. In the proposed model, the cooling temperature is 30 K lower and the cooling process is 100 times faster compared to the traditional model of direct pumping. The estimates are applicable to present-day materials of technologically attainable purity.
The laser cooling of vibrational states of solids has been achieved through photoluminescence in rare-earth elements, optical forces in optomechanics, and the Brillouin scattering light-sound interaction. The net cooling of solids through spontaneous Raman scattering, and laser refrigeration of indirect band gap semiconductors, both remain unsolved challenges. Here, we analytically show that photonic density of states (DoS) engineering can address the two fundamental requirements for achieving spontaneous Raman cooling: suppressing the dominance of Stokes (heating) transitions, and the enhancement of anti-Stokes (cooling) efficiency beyond the natural optical absorption of the material. We develop a general model for the DoS modification to spontaneous Raman scattering probabilities, and elucidate the necessary and minimum condition required for achieving net Raman cooling. With a suitably engineered DoS, we establish the enticing possibility of refrigeration of intrinsic silicon by annihilating phonons from all its Raman-active modes simultaneously, through a single telecom wavelength pump. This result points to a highly flexible approach for laser cooling of any transparent semiconductor, including indirect band gap semiconductors, far away from significant optical absorption, band-edge states, excitons, or atomic resonances.
We have observed a new type of sub-Doppler laser cooling with neither polarization gradients nor magnetic fields. All known sub-Doppler laser cooling methods require one of these two to resdistribute the atomic population among the energy levels. This allows the irreversible processes of optical pumping vels. This allows the irreversible processes of optical pumping (OP) to manipulate the conservative force of light shifts (e.g. resonant exchange between the two beams comprising a standing wave) into a damping force. Our scheme employs stimulated Raman transitions between ground state hyperfine levels of Rb with a bichromatic standing wave, accompanied by a momentum change of {Delta}p = 2{h_bar}k. OP, with {Delta}p = 1{h_bar}k, creates a population imbalance allowing repetition of the Raman process. When the detuning of the light from Raman resonance {delta} is properly chosen, the net momentum exchange damps the atomic motion. Changing {delta} by only {gamma}/6(1 MHz) replaces cooling by heating. This process separates the velocity selective Raman resonance and OP processes differently from others, and helps clarify the role of these different mechanisms.
Publisher Summary This chapter focuses on the concept of laser cooling of a solid, which may occur when the average energy of the photons emitted by the solid is larger than the energy of the ones it absorbs. More formally, the anti-Stokes emission, which occurs at frequencies larger than that of the pump laser, must dominate the Stokes emission that occurs at smaller frequencies. A crucial additional requirement is that the nonradiative decay rates of the laser-pumped states be negligible in comparison to their radiative decay rates. For the sake of specificity, these states will be taken to be those of a set of isolated ions embedded within an insulating host, although in general they could equally well be those of gas-, liquid-, or solid-phase neutral atoms or molecules, or even those of the energy bands of intrinsic semiconductors. Outside the realm of impurity-doped insulators, recent experiments with semiconductors make net anti-Stokes fluorescence cooling of these materials appear achievable. A long-term idea for improving laser cooling of solids takes advantage of photonic band gap materials. The idea is to fabricate a refractive-index structure within the cooling element that would establish a three-dimensional photonic gap immediately below the pump frequency. In this way, emission at Stokes frequencies falling within the gap would be inhibited, thereby enhancing the cooling power derived from the anti-Stokes emission.
A new method is analyzed for 3-D cooling of solids based on near-resonant, stimulated Raman scattering on a narrowband transition together with optical pumping on a broadband transition. Estimates of achievable cooling rates indicate that Raman cooling offers significant improvement over anti-Stkes fluorescence cooling at cryogenic temperatures and should enable the attainment of sub-Kelvin termperatures, starting from ambient conditions in bulk samples. Also the method is not restricted to ions with small Stokes shifts, and should therefore lead to diversification of the material platforms used for optical refrigeration.
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.