Tunable daytime passive radiative cooling based on a broadband angle selective low-pass filter

Passive daytime cooling could contribute to the reduction of our global energy consumption. It is capable of cooling materials down to below ambient temperatures without the necessity of any additional input energy. Yet, current devices and concepts all lack the possibility to switch the cooling properties on and off. Here, we introduce dynamic control for passive radiative cooling during daytime. Using an angle-selective solar filter on top of a nocturnal passive radiator allows tuning the surface temperature of the latter in a wide range by just tilting the filter from normal incidence up to around 23°. This angle-selective filter is based on optically engineered, one-dimensional photonic crystal structures. We use numerical simulations to investigate the feasibility of a switchable low-pass filter/emitter device.

S1, which can be used as guidelines for the construction of such a multilayered filter.
The area covered by the filter (A f ) should be slightly larger than that of the radiator (A c ). This ensures that the later is fully covered when the filter is tilted. For a tilting angle of 20 • the ratio of areas is A c /A f ≈ 0.94.

COMPLEMENTARY POWER CALCULATIONS
Energy balance for the radiator and filter Figure S3 shows diagrams of the power inputs and outputs considered in the energy balance of the (a) radiator and the (b) filter. Yellow arrows indicate inputs (positive terms) and blue arrows indicate outputs (negative terms). This represents schematically Equations (1) and (2) of the main text. P dev contributes in both cases, because is the power radiated by the combined radiatorfilter system, i.e., it depends on the optical properties of both the filter and the radiator. P exc accounts only for the radiative transfer between the bottom surface of the filter and the radiator (in steady-state, this term is always zero, as shown in Fig. 3c of the main text).
radiator radiator (a) (b) a n g le -s e le c ti v e fi lt e r a n g le -s e le c ti v e fi lt e r Power expressions for the filter P sun,f il is the input power per unit area that the filter absorbs from the sun. Accordingly: where I AM 1.5 (λ) is the spectral irradiance of the Sun. [2] f il (λ) is the spectral emissivity of the angle-selective filter. It is computed using Kirchhoff's law ). The emissivity of the (non-absorbing) filter is almost zero. Consequently, P sun,f il ≈ 0 for all incidence angles.
The input power radiated from the atmosphere to the filter is where I BB (T, λ) is the black-body spectral radiance at temperature T . In equation (S3), T = T amb . The emissivity of the atmosphere is computed as atm (λ, θ) = 1 − [1 − t atm (λ, 0 o )] 1/ cos θ and t atm (λ, 0 o ) is the transmittance spectrum of the atmosphere at zenit. [3] Because the emissivity of the filter is almost zero, it is expected a small contribution from the atmosphere to the heating of the filter.
The convective loss at both surfaces of the filter is where h conv is the heat transfer coefficient due to convection to the surrounding air. The air gap temperature is considered as the mean value between the temperature of the radiator T and the temperature of the filter T f il . The exchanged power by radiation between the radiator surface and the bottom surface of the filter can be computed as: where rad (λ) and f il (λ) are the spectral emissivities of the radiator and the filter, respectively. Under steadystate conditions, the exchange power between the radiator and filter goes to zero.
The cooling power of the device, i.e., the radiator in presence of the filter, is given by: The power radiated by the upper surface of the filter can be computed as: This power is practically zero, because the emissivity of the filter is almost zero. The filter does not present radiative cooling characteristics by itself. Figure S4a shows exemplary spectra of the emissivity of the device dev (λ) at three different incidence angles. For normal incidence (θ i = 0 • ), the emissivity of the device coincides with the one of the radiator surface. In this case, a solar absorber covered by a visibly transparent nocturnal radiator is considered. [4] The dark blue line corresponds to its emission spectrum. Furthermore, another two extreme cases of radiators are considered: an ideal solar absorber, whose emissivity is one over the entire solar spectrum and zero at any other wavelength (including the sky-window), as shown by the dark-green spectrum in Fig. S4b. Likewise, an ideal total absorber, whose emissivity is one over the entire spectrum (also within the sky-window), as shown in Fig. S4c in darkorange color. In all cases, the emissivity within the solar spectrum becomes almost zero for θ i = 23 • . The spectral irradiance of the sun I AM 1.5 (λ) is shown in Fig. S4d and Fig. S4e shows the transmittance spectrum t atm (λ) of the atmosphere.
Ambient temperature performance Table S2 shows numerical values of the temperature of a nocturnal radiator (T ) and the temperature of a solar filter (T f il ) as the incidence angle is changed, the filter  is tilted. This radiator-filter device is the one studied in the main text. The surrounding atmosphere is at temperature T amb = 298.3 K. All power contributions per unit area considered in equations (1) and (2) of the main text are also listed.
The heating power from the sun P sun to the radiator drops two orders of magnitude when the incidence angle with respect to the filter is equal or larger than 23 • . Consequently, the nocturnal radiator can be heated up by solar radiation (θ i < 23 • ) or not heated up (θ i ≥ 23 • ).
The negative sign of the convective power P conv from the radiator surface to the air gap for θ i < 23 • is because for those incidence angles, the steady-state temperature of the radiator is larger than that of the filter (T > T f il ), i.e., the radiator surface is losing heat by convection to the air gap. This behavior is expected, due to the fact that the radiator used is a nocturnal radiative cooler surface and solar absorber. Hence, its emissivity is high in the solar spectrum. [4] Consequently, it is heated up when the solar radiation is not properly blocked by the filter. On the other hand, for θ ≥ 23 • , the radiator surface is always at lower temperature than the one of the filter (T < T f il ). In this circumstances, the convective power from the radiator to the filter is positive, i.e., the air gap is losing heat by convection to the radiator surface.
The total convective power P conv,f il on the filter is always positive because, the difference between the ambient temperature and the filter temperature is always larger than the difference between the air gap mean temperature and the filter temperature.
In the case of replacing the radiator by an ideal solar absorber, its surface can be maintained at ambient temperature (∆T ≈ 0) only for optimum operation conditions of the angle-selective solar filter (θ i ≥ 23 • ), as shown in Fig. S5a by green diamond markers. For lower incidence angles, part of the solar radiation reaches the ideal solar absorber and its surface temperature increases accordingly. For normal incidence, all solar radiation is absorbed by the ideal solar absorber and its temperature rises around 306 K above the ambient. All calculations were performed assuming steady-state conditions and T amb = 298.3 K.

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The incident solar radiation on the ideal solar absorber can be as high as around 1000 Wm −2 for normal incidence and drops down to around zero for θ ≥ 23 • (see Fig. S5b, green star markers). The power radiated by the device is zero for θ ≥ 23 • , because the emissvity of the device within the sky-window is zero. Consequently, this ideal solar absorber does not present passive radiative cooling properties.
Finally, when replacing the radiator by an ideal total absorber, its surface can be cooled down to ∼ 28 K below the ambient, for optimum operation conditions of the angle-selective solar filter (θ i ≥ 23 • ), as shown in Fig. S5a by orange squared markers. For lower incidence angles, part of the solar radiation reaches the ideal total absorber and its surface temperature increases accordingly. For normal incidence, all solar radiation is absorbed by the ideal total absorber and its temperature rises around 68 K above the ambient. However, this temperature increase is 4.5 times lower than the corresponding temperature rise for the ideal solar absorber. This is because, the ideal total absorber also emits radiation through the sky-window as a cooling mechanism. All calculations were performed assuming steady-state conditions and T amb = 298.3 K.
The incident solar radiation on the ideal total absorber can be as high as around 1000 Wm −2 for normal inci-dence and drops two orders of magnitude for θ ≥ 23 • (see Fig. S5b, orange star markers). The net cooling power radiated by the device is ∼ 147 Wm −2 for θ ≥ 23 • , it is non zero because the emissvity of the device within the sky-window is one. Consequently, this ideal total absorber presents passive radiative cooling properties.
The sum of terms on the right hand side of Equation (1) in the main text is represented by the grey dashed line. P total,rad = 0 for any incidence angle, as expected in the steady-state regime.