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arXiv:1507.08936 · Optica

Raman cooling of solids through photonic density of states engineering

Yin-Chung Chen, Gaurav Bahl

Published Oct 8, 2015• 28 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/optica.2.000893

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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.
Optical refrigeration of solids holds tremendous promise for applications in thermal management. It can be achieved through multiple mechanisms including inelastic anti-Stokes Brillouin and Raman scattering. However, engineering of these mechanisms remains relatively unexplored. The major challenge lies in the natural unfavorable imbalance in transition rates for Stokes and anti-Stokes scattering. We consider the influence of anisotropic photonic density of states on Raman scattering and derive expressions for cooling in such photonically anisotropic systems. We demonstrate optimization of the Raman cooling figure of merit considering all possible orientations for the material crystal and two example photonic crystals. We find that the anisotropic description of the photonic density of states and the optimization process is necessary to obtain the best Raman cooling efficiency for systems having lower symmetry. This general result applies to a wide array of other laser cooling methods in the presence of anisotropy.
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.
This review discusses the progress and ongoing efforts in optical refrigeration. Optical refrigeration is a process in which phonons are removed from a solid by anti-Stokes fluorescence. The review first summarizes the history of optical refrigeration, noting the success in cooling rare-earth-doped solids to cryogenic temperatures. It then examines in detail a four-level model of rare-earth-based optical refrigeration. This model elucidates the essential roles that the various material parameters, such as the spacing of the energy levels and the radiative quantum efficiency, play in the process of optical refrigeration. The review then describes the experimental techniques for cryogenic optical refrigeration of rare-earth-doped solids employing non-resonant and resonant optical cavities. It then examines the work on laser cooling of semiconductors, emphasizing the differences between optical refrigeration of semiconductors and rare-earth-doped solids and the new challenges and advantages of semiconductors. It then describes the significant experimental results including the observed optical refrigeration of CdS nanostructures. The review concludes by discussing the engineering challenges to the development of practical optical refrigerators, and the potential advantages and uses of these refrigerators.
Laser cooling of solids, also known as optical refrigeration, is an area of optical science investigating the interaction of light with condensed matter to remove thermal energy of a solid through the interaction of the pump photons and phonons in a solid. Apart from being of fundamental scientific interest, this topic addresses a number of important practical issues such as the development of all solid state optical cryo-coolers, and biological applications. A short history of laser cooling as well as latest achievement of optical refrigeration in rare-earth (RE) doped macro-samples are presented and discussed in the paper. The main technique of laser cooling of RE doped solids based on anti-Stokes fluorescence is presented in this paper. The new approach to optical refrigeration based on the Raman cooling is also considered. It is shown that the future prospects of the research are connected with laser cooling of μm- and nm-sized samples, are in their applications in biophysics in the fundamental studies of low-temperature physics.
Described are the prospects for broadband optical refrigeration based on Raman scattering of incoherent light. Laser pumped rare earth fluorescence has been demonstrated and commercial applications are sure to follow. Broadband refrigeration requires strong Raman scattering and large Raman shift. Also required are spectral management and photonic patterning to offset the unfavorable anti-Stoke’s to Stoke’s shift ratio. Materials such as diamond, silicon, and a number of molecular systems are ideal and have low absorption. Optics splits the broadband spectrum into light and dark bands with width corresponding to the Raman shift. Broadband spectrums where photon flux decreases with increasing photon energy are ideal. By tailoring the incoming spectrum, by utilizing extremely transparent strong Raman shift materials and by photonic inhibition of Stoke’s shifted light the prospect become feasible. The Raman optical cross- section increases with decreasing particle size (until the particle become too small to support the Raman-phonons). Where conservation of phonon states in these truncated Brillioun-zone particles requires an increased density (number/cm3) of the allowed-states to compensate for states lost to particle size. Nonetheless, the anti-Stokes to Stokes ratio is approximately one-to-two at laboratory temperature. Thin film deposited diamond is an excellent candidate for refrigeration applications due to its high transparency small grain size and its large Raman magnitude and large shift. Simple one-dimensional photonic structures selectively inhibit the Stoke’s shifted light making refrigeration possible.
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.