Letter

pubs.acs.org/NanoLett

Ultrabroadband Photonic Structures To Achieve High-Performance Daytime Radiative Cooling Eden Rephaeli,*,†,§ Aaswath Raman,*,†,§ and Shanhui Fan*,‡

† ‡ Department of Applied Physics and Department of Electrical Engineering, Stanford University, Stanford, California 94305, United States

ABSTRACT: If properly designed, terrestrial structures can passively cool themselves through radiative emission of heat to outer space. For the first time, we present a metal-dielectric photonic structure capable of radiative cooling in daytime outdoor conditions. The structure behaves as a broadband mirror for solar light, while simultaneously emitting strongly in the mid-IR within the atmospheric transparency window, achieving a net cooling power in excess of 100 W/m2 at ambient temperature. This cooling persists in the presence of significant convective/conductive heat exchange and nonideal atmospheric conditions. KEYWORDS: Radiative cooling, thermal radiation, broadband solar mirror, phonon-polariton, selective emission

he ’s atmosphere has a transparency window for Building upon these developments, in this Letter we present T electromagnetic waves between 8−13 μm that coincides for the first time a single compact planar device capable of with peak thermal radiation wavelengths at typical ambient achieving substantial radiative cooling in the daytime. We also temperatures. By exploiting this window one can cool a body present a theoretical and numerical analysis identifying the ’ on the Earth s surface by radiating its heat away into cold outer critical performance metric targets needed to accomplish space. This radiative cooling mechanism is attractive to energy ffi ff daytime radiative cooling. Our design for a daytime radiative e ciency improvement e orts because it provides a purely cooler, shown in Figure 1a, represents a strong departure from passive cooling strategy for terrestrial structures without the previously published systems. Rather than designing a cover foil need for any energy inputs. that is spatially separated from a black emitter we introduce an While nighttime radiative cooling has been extensively 1−7 integrated thermally selective emitter atop a broadband mirror. studied, the peak demand for cooling occurs during the fi daytime. Thus, it is of great importance to explore the Doing so enables us to exploit near- eld coupling between possibility of daytime radiative cooling. To achieve daytime material layers, leading to stronger control over emission, fl cooling one needs to design a structure that is simultaneously a absorption, and re ection. Using nanophotonic concepts, our broadband mirror for solar light and a strong thermal emitter in photonic structure is able to strongly suppress solar absorption the atmospheric transparency window. Previous work in while enhancing thermal emission in the atmospheric trans- daytime radiative cooling has sought to accomplish this by parency window: an ultrabroadband performance, shown in − covering a near-black emitter with a cover foil.1,8 10 The foil, Figure 1b, capable of achieving a net cooling power exceeding made of ZnS or ZnSe9 or polymers and pigments,10 transmits 100 W/m2 at ambient temperature. thermal radiation while reflecting sunlight. However, no actual Radiative cooling devices operate at near-ambient temper- cooling was demonstrated because the reported solar radiation atures and therefore do not suffer from many of the difficulties fl 9 re ection achieved by these cover foils was no larger than 85%. associated with other thermal applications of photonic fl The limited re ection achieved is partly due to the constraint of structures that have typically involved high-temperature simultaneous broadband solar reflection and transparency in ffi λ − μ operation. These di culties include numerical uncertainty the =813 m range on a single material, forcing a associated with the temperature-dependence of optical proper- compromise between the two.8 fi ties, material cohesion, small-feature evaporation, and durability In recent years, signi cant progress has been made in the ff 30 control of thermal emission of light from nanostructured that a ect other thermal applications. Our approach and − materials.11 13 Enhancement and suppression of thermal design is thus a departure from previous work in using nano- emission of light using photonic structures has been and microphotonic structures for thermal applications. − theoretically and experimentally demonstrated in 1D,14 16 − − 2D,17 20 and 3D11,21 25 photonic crystals, with application to Received: November 29, 2012 ,21,26,27 solar thermophotovoltaics,16,28 and Revised: February 21, 2013 waste heat recovery.29 Published: March 5, 2013

© 2013 American Chemical Society 1457 dx.doi.org/10.1021/nl4004283 | Nano Lett. 2013, 13, 1457−1461 Nano Letters Letter

to a clear sky subject to , and also atmospheric irradiance corresponding to an ambient temperature Tamb. The net cooling power Pnet(T) of a structure with area A is given by

Pnet()TPTPT=− rad () atm ( amb ) − P (1) where ∞ Prad()TA=Ω∫∫ d cosθλλελθ d ITBB (,)(,) 0 (2) is the power radiated by the structure

Patm(T amb) = ∞ Ad∫∫Ω cosθλ dITBB ( amb , λελθελθ ) ( , ) atm ( , ) 0 (3) is the absorbed power stemming from atmospheric radiation, and Figure 1. (a) Optimized daytime radiative cooler design that consists ∞ of two thermally emitting photonic crystal layers comprised of SiC and Psun = Ad∫ λε(,0) λ IAM1.5 () λ quartz, below which lies a broadband solar reflector. The reflector 0 (4) fi consists of three sets of ve bilayers made of MgF2 and TiO2 with ε λ is the incident absorbed by the structure. Here varying periods on a silver substrate. (b) Emissivity ( ,0) of the ∫ dΩ =2π∫ π/2dθ sin θ is the angular integral over a optimized daytime radiative cooler shown in (a) at normal incidence 0 λ λ 2 λ5 hc/( kBT) − hemisphere. IBB(T, ) = [(2hc )/( )](1/(e 1)) is (black) with the scaled AM1.5 solar spectrum (yellow) and 31 λ the spectral radiance of a blackbody at temperature T.In atmospheric transmittance t( ) (blue) plotted for reference. The ff’ structure has minimal absorption throughout the solar spectrum and obtaining eq 3 and eq 4 we used Kircho s law to replace the has very strongly selective emission in the atmospheric transparency structure’s absorptivity with its emissivity ε(λ,θ). The angle- 3 ε λ θ window, as is desirable and necessary for a high-performance daytime dependent emissivity of the atmosphere is given by atm( , )= radiative cooler. 1 − t(λ)1/cos θ, where t(λ) is the atmospheric transmittance in the zenith direction.32 In eq 4, the solar illumination is λ To begin our analysis, we consider a photonic structure at represented by IAM1.5( ), the AM1.5 Global Tilt spectrum with temperature T whose radiative properties are described by a an irradiance of 964 W/m2, which represents the average solar spectral and angular emissivity ε(λ,θ). The structure is exposed conditions of the continental U.S. We assume the structure is

Figure 2. (a) Emissivity (Absorptivity) spectrum ε(λ,0) of selective emitters with 3,5, or 10% absorption of AM 1.5 solar spectrum (shaded yellow). λ The atmospheric transmittance t( ) is plotted in shaded blue. (b) Net cooling power Pnet versus radiative cooler temperature for selective emitters shown in (a). The equilibrium temperatures Teq for these emitters, noted by the dots along the Pnet = 0 dashed line, are 195 K, 245 K, 265 K, and 300 K, for 0 (ideal) 3, 5, and 10% absorption, respectively. The net cooling power for the optimized design shown in Figure 1a is plotted (in black), achieving an equilibrium temperature of 260 K, and greater cooling power than all but the ideal selective emitter with 0% solar absorption at T = Tamb. (c) Net cooling power Pnet of the optimized design versus radiative cooler temperature for the total nonradiative (conductive + convective) heat constant of 0, 6, or 12 W/m2/K, for the case of either high (solid curves) or low (dashed curves) atmospheric transmittance.

1458 dx.doi.org/10.1021/nl4004283 | Nano Lett. 2013, 13, 1457−1461 Nano Letters Letter facing the sun. Hence the term Psun is devoid of an angular radiative cooler to achieve well below 10% solar absorption. integral, and the structure’s emissivity is represented by its value Finally, we note that Figure 2b demonstrates the great potential in the zenith direction, θ =0. of daytime radiative cooling with cooling powers in excess of For a cooling structure, there are two important metrics 150 W/m2 theoretically possible when solar radiation is fl which are indicative of its capacity to cool. Pnet, the cooling maximally re ected. fi power, is the rst metric. To achieve Pnet > 0 at a given T and At a system level, the radiative cooler would receive heat ε λ θ Tamb, in eq 1 the emissivity ( , ) must be high within the conducted from the building or device it is cooling at a rate ≪ atmospheric transparency window and absorptivity must be low Pconducted.IfPconducted Pnet(Tbldg), where Tbldg is the at wavelengths in which the atmosphere is emissive. Thus in temperature of the building, then the building provides a general, for both daytime and nighttime cooling, the structure negligible amount of heat and the radiative cooler will reach a must emit selectively only where the atmospheric transmittance temperature close to Teq. However, as Pconducted increases, so λ fi t( ) is signi cant, that is, the transparency window from 8 to 13 does the relative importance of the metric Pnet(T). Thus, μm. Emission of light from the structure at wavelengths of low depending on the specific application and location, the relative atmospheric transmittance entails absorption of atmospheric importance of either one of the two performance metrics will radiation, thereby increasing Patm. This need for selective change. For example, Pnet is thought to be a more important thermal emission motivates our interest in using phonon- metric in warm tropical climates.33 The key point here is that polariton materials in the structure shown in Figure 1a. For once solar absorption is brought to a low enough level, as we daytime cooling, in addition, the structure must minimize Psun. accomplish with our design, one can further customize the The other cooling metric is Teq, the temperature at which Pnet design to either give preference to, or balance the requirements = 0 in eq 1. A radiative cooler with Teq below the ambient for achieving, a low Teq or a high Pnet. temperature would thus cool an attached structure, via heat On the basis of the theoretical discussion above, we now conduction, to a temperature below ambient over time and present a compact planar photonic structure that minimizes perform the system-wide cooling desired. Thus, in evaluating absorbed solar radiation, Psun, and atmospheric radiation, Patm, our radiative cooler design one of our key goals will be to while maximizing its emitted radiative power Prad.The numerically demonstrate an integrated cooling structure which structure, shown in Figure 1a, consists of two components: a − has an equilibrium temperature Teq below the ambient Tamb two-layer 2D photonic crystal employing phonon polariton under peak daylight conditions. This has never been done modes to maximize emissivity in the atmospheric transparency before in a compact planar structure. window and a chirped 1D photonic crystal reflector designed to Using the theory described above, we first evaluate the ideal minimize absorbed solar radiation and lying beneath the situation. In the absence of sunlight, for a radiative cooler at thermally emitting photonic crystal layers. temperature T approximately equal or larger than Tamb, the As discussed above, maximizing Prad while minimizing Patm greatest cooling power Pnet is achieved by a blackbody emitter. involves emitting selectively within the atmospheric trans- μ However, Pnet of a blackbody emitter drops sharply as T falls parency window that exists from 8 to 13 m while minimizing below Tamb. It follows that the lowest possible Teq is attained by emission above and below these wavelengths. To achieve this an ideal selective emitter with ‘tophat’ emissivity ε(λ,θ) = 1 for level of granular spectral selectivity in thermal emission the 2D 8 μm<λ <13μm, and ε(λ,θ) = 0 elsewhere.3 The emissivity of periodic photonic design we describe here uses two materials such an ideal selective emitter is shown in Figure 2a. The with phonon−polariton resonances in the 8−13 μm range, requirement for the emissivity to go to zero everywhere outside quartz and SiC. The dielectric function of quartz has a sharp the 8−13 μm wavelength range is a formal one, and at night resonance at 9.3 μm whereas that of SiC has a resonance at 12.5 need only be satisfied in the vicinity of the atmospheric μm, thus providing complementary resonances that cover, and transparency window. maximize emission selectively in, the atmospheric transparency During the day, however, the requirement of zero emissivity window. The use of surface phonon−polariton modes to outside the atmospheric window is quite formidable and enhance the structure’s emissivity further enables broad-angle minimizing the absorption of solar light becomes an overriding emission due to their flat energy bands and also keeps the layer imperative in order to achieve radiative cooling. To thicknesses small. Quartz and SiC are in addition desirable for demonstrate this we plot Pnet(T) in Figure 2b, where Tamb = daylight operation since they are very weak absorbers in the 300 K, for an ideal radiative cooler with the selective emissivity visible and IR, ensuring that a minimal amount of solar power is described above. The performance of the cooler degrades as it absorbed in the thermally emitting layers. All optical properties absorbs increasing fractions of the incident solar light, as shown of materials considered are obtained via ellipsometry34 or in Figure 2a. The ideal daytime radiative cooler (0% solar through tabulated values.35 − absorption) can reach a very low Teq = 195 K, but with just 10% To take advantage of the phonon polariton resonances of solar absorption Teq shoots up to nearly the ambient each material we place quartz and SiC as the top two layers of temperature, such that no meaningful cooling is achieved. our cooler and introduce a two-dimensional periodic array of As can also be seen from comparing the curves in Figure 2b, square air holes in both layers to form photonic crystal absorbing even a small fraction of solar radiation has direct and structures. Extensive optimization for selective thermal significant implications on the achievable cooling powers of emission in the transparency window yields a Quartz layer these radiative coolers. The 10% solar spectrum absorption thickness of 2.5 μm, a SiC layer thickness of 8 μm, a periodicity 2 μ yields a meager cooling power of 3 W/m at T = Tamb,as for both layers of 6 m, and square air rectangles etched in the opposed to 3% solar absorption that leads to a practically quartz and SiC layers of 5.4 μm width. 2 meaningful cooling power of 100 W/m . These results indicate To minimize the absorbed solar radiation, Psun, we introduce the importance of suppressing solar absorption maximally. This areflector made of chirped 1D photonic crystals below the two- in turn points to a key aspect of our design that is novel: we use layer photonic crystal. The 1D photonic crystals consist of fl dielectric, instead of metallic, re ective substrates in the alternating layers of TiO2 (high-index) and MgF2 (low-index)

1459 dx.doi.org/10.1021/nl4004283 | Nano Lett. 2013, 13, 1457−1461 Nano Letters Letter lying on a silver substrate. To cover the entire solar spectrum observe the contribution of each material’s resonances to the we combine three 1D photonic crystal sets, each having five overall emissivity of the photonic crystal. ff bilayers with di erent thicknesses, resulting in three over- In Figure 2b, we plot Pnet(T) given Tamb = 300 K for our lapping photonic bandgaps.36 The first set of five bilayers have structure, calculated via hemispheric integration of the ’ thicknesses of 25 nm of TiO2 and 35 nm of MgF2, the second structure s emissivity, shown along with the previously plotted set 50 nm of TiO2 and 70 nm MgF2, and the third set 75 nm of Pnet(T) for a selective emitter with added 3, 5, and 10% solar TiO2 and 105 nm of MgF2. absorption. Our designed structure is seen to have a remarkably We simulate this optimized structure using the rigorous low daytime equilibrium temperature of 260 K. It furthermore 37 2 coupled-wave analysis (RCWA) method. To evaluate the has a cooling power of 105 W/m at Tamb. We note that structure’seffectiveness as a daytime radiative cooler we Pnet(Tamb) surpasses the highest achievable cooling rate of the calculate its absorptivity/emissivity at 2 nm resolution across ideal selective emitter with 3% solar absorption owing to our an ultrabroadband wavelength range from 300 nm (UV) to 30 structure’s broader emission spectrum. Thus, the design strikes μm (mid-IR). The resulting absorptivity/emissivity spectrum is a good balance between obtaining a large Pnet at ambient shown in Figure 1b, along with overplots of the AM1.5 solar temperature, and achieving a low Teq. spectrum and the atmospheric transmittance t(λ). For wave- The key technical issues that can hamper radiative cooling lengths within the solar spectrum, the structure absorbs are nonradiative heat transport and nonideal atmospheric minimally with only 3.5% of solar radiation at normal incidence conditions leading to diminished transmittance. The effects of absorbed by the overall structure. The thermally emitting top conductive and/or convective heat exchange is accounted for − layers are transparent to solar light, and the chirped 1D by adding a term Pcond+conv = hc(Tamb T) in eq 1 for T < Tamb. photonic crystal reflector is indeed effective at maximizing Placing the structure on polystyrene results in a conductive heat ffi 2 reflection over the entire solar spectrum. The choice of only coe cient value of hcond = 0.3 W/m /K. The presence of 1 m/s five bilayers for each period in the chirped reflector represents a and 3 m/s wind speed would result in a combined nonradiative ffi ≈ ≈ 2 compromise between achieving high reflectance and practicality heat coe cient of hc = hcond + hconv of 6 and 12 W/m /K, 9 given the need for less than 5% solar absorption identified in respectively. The primary phenomenon causing diminished the previous section. atmospheric transmission is continuum absorption. This Within the atmospheric transparency window the structure absorption is dependent on the amount of water vapor in the acts as a very strong and selective emitter. Many sharp peaks atmosphere, the air temperature, and the dewpoint temper- 39 can be observed in the spectrum in addition to some notable ature but can be captured by an effective atmospheric dips due to the material properties of SiC and quartz. The transmittance, t(λ) in eq 3. In ref 4, an effective transmittance structure’s emissivity is strongly suppressed outside the plateau of t(λ) ≈ 0.6 between 8−13 μm is given as an accurate transparency window. We also note here many emissivity representation of three locations in the U.S. In Figure 2c, we − μ plot Pnet(T) of our structure given Tamb = 300 K for various peaks in the 20 30 m range. These peaks are actually 32 4 beneficial due to the presence of a secondary atmospheric values of hc and both high and low (an average of 0.6) fi transparency window between 20 and 25 μm that is also atmospheric transmittance. In both cases, signi cant cooling 2 highlighted in Figure 1b. can still be achieved even for a value of hc = 12 W/m /K in To elucidate the source of the emissivity in the transparency which case the structure reaches an equilibrium temperature of window across all angles we calculate the folded-band structure T = 293 K and T = 296 K with cooling powers of 105 and 70 2 for bulk SiC and quartz assuming a period of 6 μm in Figure 3a. W/m at ambient, respectively. Thus, even in the presence of We then use emissivity data for the structure at various polar realistic conductive heat exchange and moderate wind-induced fi angles of incidence to plot the emissivity versus parallel wave convection, signi cant cooling remains possible. Moreover, vector k∥ in Figure 3b. Many of the bands calculated in Figure encapsulating our structure with a cover can completely 3a, in particular the flat phonon-polariton bands38 for both eliminate wind convection. Because our structure already fl quartz and SiC, are clearly visible in Figure 3b. Moreover, we strongly re ects solar light, the demands on the cover material are significantly reduced, in contrast to previously proposed radiative coolers. These previously proposed coolers relied on the cover foil to both transmit in the 8−13 μm wavelength range and reflect solar light, whereas for our design it need merely be transparent in the window. From this discussion, it is evident that using photonic structures in a radiative cooler setup not only allows daytime cooling to occur, but also leads to a more robust cooling performance, relative to previously published systems, in the face of nonidealities. In considering the systemwide impact of the daytime radiative coolers we have designed, we first place the cooling powers achieved in context. Consider for example that solar panels at 10% efficiency will generate roughly 100 W/m2 at Figure 3. (a) Folded band structure of semi-infinite slabs of SiC and α− μ peak. The passive daytime radiative coolers proposed here can Quartz above the lightline with a 6 m period. Light-line in dashed thus be thought of as substitutes by reducing the red. Flat bands corresponding to the surface modes of SiC and quartz are clearly visible near their surface phonon−polariton frequencies. (b) demand on a rooftop solar system from air conditioning Absorptivity/emissivity versus parallel wavenumber k∥. We observe systems. A recent study from NREL found a peak cooling load strong emission to large angles (large k∥) corresponding to the surface of approximately 6 kW in Chicago and Orlando for canonical 40 modes of SiC and quartz, a highly desirable feature since the power 2233 ft2 one-story homes in the summer. Assuming the radiated Pcooling and Teq are hemispherically integrated quantities. radiative cooler is operating at its peak cooling rate, then for

1460 dx.doi.org/10.1021/nl4004283 | Nano Lett. 2013, 13, 1457−1461 Nano Letters Letter just 20 m2 of daytime radiative cooler on the rooftop (10% of a (7) Gentle, A. R.; Smith, G. B. Nano Lett. 2010, 10, 373−379. total of 200 m2 available rooftop space), one can offset 35% of (8) Nilsson, T. M.; Niklasson, G. A.; Granqvist, C. G. Sol. Energy − the house’s air conditioning needs during the hottest hours of Mater. Sol. Cells 1992, 28, 175 193. (9) Nilsson, T. M.; Niklasson, G. A. Sol. Energy Mater. Sol. Cells 1995, the day. − Finally, we note that the techniques needed to fabricate the 37,93 118. (10) Covering Element screening off the solar radiation for the structures discussed here are well validated and understood, applications in the refrigeration by radiation. U.S. Patent 4,323,619, and within the scope of current technology. Recent work on 1982. roll-to-roll nanoimprint lithography has already successfully (11) Lin, S.-Y.; Fleming, J. G.; Chow, E.; Bur, J.; Choi, K. K.; 41 produced nanoscale patterns on large areas and may be of Goldberg, A. Phys. Rev. B 2000, 62, R2243−R2246. particular relevance to producing large area samples of such (12) Schuller, J.; Taubner, T.; Brongersma, M. Nat. Photonics 2009, 3, photonic structures. Furthermore, the feature sizes of our 658−661. design are amenable to conventional wafer-scale photo- (13) Greffet, J. Nature 2011, 478, 191−192. lithography and processing steps, making large scale production (14) Narayanaswamy, A.; Chen, G. Phys. Rev. B 2004, 70, 125101. possible with existing facilities. (15) Celanovic, I.; Perreault, D.; Kassakian, J. Phys. Rev. B 2005, 72, In conclusion, we have numerically demonstrated for the first 075127. (16) Rephaeli, E.; Fan, S. Opt. Express 2009, 17, 15145−15159. time a macroscopically planar structure capable of achieving (17) Le Gall, J.; Olivier, M.; Greffet, J. Phys. Rev. B 1997, 55, 10105. radiative cooling in the daytime, even in the presence of (18) Greffet, J.-J.; Carminati, R.; Joulain, K.; Mulet, J.-P.; Mainguy, S.; realistic nonradiative heat transfer. In contrast to previous Chen, Y. Nature 2002, 416,61−64. approaches to radiative cooling, we have used concepts from (19) Luo, C.; Narayanaswamy, A.; Chen, G.; Joannopoulos, J. D. nanophotonics to design a dielectric reflector, which minimizes Phys. Rev. Lett. 2004, 93, 213905. solar absorption, and a two-layer 2D photonic crystal of SiC (20) Chan, D. L. C.; Soljacíc,̌ M.; Joannopoulos, J. D. Opt. Express and quartz, which selectively emits thermal radiation in the 2006, 14, 8785−8796. (21) Fleming, J. G.; Lin, S. Y.; El-Kady, I.; Biswas, R.; Ho, K. M. atmospheric transparency window. These two functionalities − are combined into a single device that achieves the ultra- Nature 2002, 417,52 55. broadband performance needed to radiatively cool in the (22) Rephaeli, E.; Fan, S. Appl. Phys. Lett. 2008, 92, 211107. (23) Arpin, K. A.; Losego, M. D.; Braun, P. V. Chem. Mater. 2011, 23, daytime. Currently, applications of thermal light sources are − fi 4783 4788. being explored mainly in the eld of power (24) Wang, M.; Hu, C.; Pu, M.; Huang, C.; Zhao, Z.; Feng, Q.; Luo, conversion but the demands of high-operating temperatures X. Opt. Express 2011, 19, 20642−20649. inevitably leads to nano- and microscopic material degradation, (25) Zhang, S.; Li, Y.; Feng, G.; Zhu, B.; Xiao, S.; Zhou, L.; Zhao, L. presenting a formidable challenge. In our work, we have Opt. Express 2011, 19, 20462−20467. presented another application of thermal light emission from (26) Bermel, P.; Ghebrebrhan, M.; Chan, W.; Yeng, Y. X.; microstructured materials, radiative cooling. In contrast to Araghchini, M.; Hamam, R.; Marton, C. H.; Jensen, K. F.; Soljacič,́ M.; Joannopoulos, J. D.; Johnson, S. G.; Celanovic, I. Opt. Express previous applications, using thermal light emission to cool − structures does not require high temperature operation. We 2010, 18, A314 A334. thus anticipate that radiative cooling will motivate continued (27) Zhai, X.; Lai, J.; Liang, H.; Chen, S. J. Appl. Phys. 2010, 108, 074507. interest and research in thermal nanophotonics and meta- (28) Wu, C.; Neuner, B., III; John, J.; Milder, A.; Zollars, B.; Savoy, materials. S.; Shvets, G. J. Optics 2012, 14, 024005. (29) De Zoysa, M.; Asano, T.; Mochizuki, K.; Oskooi, A.; Inoue, T.; ■ AUTHOR INFORMATION Noda, S. Nat. Photonics 2012, 6, 535−539. Corresponding Author (30) Yeng, Y.; Ghebrebrhan, M.; Bermel, P.; Chan, W.; ̌́ *E-mail: (E.R.) [email protected]; (A.R.) aaswath@stanford. Joannopoulos, J.; Soljacic, M.; Celanovic, I. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 2280−2285. edu; (S.F.) [email protected]. ’ (31) where c is the speed of light, h is Planck s constant, kB is the Author Contributions λ § Boltzmann constant, and is the wavelength. These authors contributed equally to this work. (32) IR Transmission Spectra, Gemini Observatory. http://www. Notes gemini.edu/?q=node/10789 (accessed Nov 15, 2012). ff The authors declare no competing financial interest. (33) Ja er, A. Radiative Cooling in Hot Humid Climates. http:// people.csail.mit.edu/jaffer/cool/cool.pdf (accessed Nov 15, 2012). ■ ACKNOWLEDGMENTS (34) Hafeli, A. K.; Rephaeli, E.; Fan, S.; Cahill, D. G.; Tiwald, T. E. J. Appl. Phys. 2011, 110, 043517. A.R. acknowledges the support of Alberta Scholarship (35) Palik, E. Handbook of Optical Constants of Solids, Vol.s I, II, and Programs’ Sir James Lougheed Award of Distinction. III: Subject Index and Contributor Index; Academic Press Handbook Series; Elsevier Science & Tech: New York, 1985. ■ REFERENCES (36)Fink,Y.;Winn,J.N.;Fan,S.;Chen,C.;Michel,J.; Joannopoulos, J. D.; Thomas, E. L. Science 1998, 282, 1679−1682. (1) Catalanotti, S.; Cuomo, V.; Piro, G.; Ruggi, D.; Silvestrini, V.; (37) Liu, V.; Fan, S. Comput. Phys. Commun. 2012, 183, 2233−2244. Troise, G. Sol. Energy 1975, 17,83−89. − (38) Raman, A.; Fan, S. Phys. Rev. Lett. 2010, 104, 087401. (2) Granqvist, C. G.; Hjortsberg, A. Appl. Phys. Lett. 1980, 36, 139 (39) Berdahl, P.; Fromberg, R. 1982, 29, 299−314. 141. − (40) Burdick, A. Strategy Guideline: Accurate Heating and Cooling (3) Granqvist, C. G.; Hjortsberg, A. J. Appl. Phys. 1981, 52, 4205 Load Calculations; DOE/GO-102011-3304; U.S. Dept. of Energy: 4220. Washington, D.C., 2011. (4) Berdahl, P.; Martin, M.; Sakkal, F. Int. J. Heat Mass Transfer 1983, (41) Ahn, S. H.; Guo, L. J. ACS Nano 2009, 3, 2304−2310. 26, 871−880. (5) Orel, B.; Gunde, M.; Krainer, A. Sol. Energy 1993, 50, 477−482. (6) Suryawanshi, C. N.; Lin, C.-T. ACS Appl. Mater. Interfaces 2009, 1, 1334−1338.

1461 dx.doi.org/10.1021/nl4004283 | Nano Lett. 2013, 13, 1457−1461